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Journal articles on the topic 'Gaussian filtering and smoothing'

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Published: 3 June 2025

Last updated: 13 July 2025

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Imanuddin, Imanuddin, Raza Oktafian, and Munawir Munawir. "Image Smoothing Menggunakan Metode Mean Filtering." JOINTECS (Journal of Information Technology and Computer Science) 4, no. 2 (2019): 57. http://dx.doi.org/10.31328/jointecs.v4i2.1007.

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Pelembutan Citra (Image smoothing) bertujuan untuk menekan gangguan (noise) pada citra.Gangguan tersebut biasanya muncul sebagai akibat dari hasil penerokan yang tidak bagus (sensor noise, photographic grain noise) atau akibat saluran transmisi (pada pengiriman data).Penelitian ini telah menghasilkan sebuah program aplikasi untuk image smoothing dengan beberapa metode yaitu mean filtering,grayscale dan gaussian filtering. Citra uji yang digunakan pada penelitian ini menggunakan satu sampel gambar. Citra tersebut di-load dan ditampilkan pada program. Kemudian dilakuan proses image smoothing dengan menggunakan metode grayscale,gaussian dan mean.

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Peng, Anjie, Gao Yu, Yadong Wu, Qiong Zhang, and Xiangui Kang. "A Universal Image Forensics of Smoothing Filtering." International Journal of Digital Crime and Forensics 11, no. 1 (2019): 18–28. http://dx.doi.org/10.4018/ijdcf.2019010102.

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Digital image smoothing filtering operations, including the average filtering, Gaussian filtering and median filtering are always used to beautify the forged images. The detection of these smoothing operations is important in the image forensics field. In this article, the authors propose a universal detection algorithm which can simultaneously detect the average filtering, Gaussian low-pass filtering and median filtering. Firstly, the high-frequency residuals are used as being the feature extraction domain, and then the feature extraction is established on the local binary pattern (LBP) and the autoregressive model (AR). For the LBP model, the authors exploit that both of the relationships between the central pixel and its neighboring pixels and the relationships among the neighboring pixels are differentiated for the original images and smoothing filtered images. A method is further developed to reduce the high dimensionality of LBP-based features. Experimental results show that the proposed detector is effective in the smoothing forensics, and achieves better performance than the previous works, especially on the JPEG images.

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Deisenroth, Marc Peter, Ryan Darby Turner, Marco F. Huber, Uwe D. Hanebeck, and Carl Edward Rasmussen. "Robust Filtering and Smoothing with Gaussian Processes." IEEE Transactions on Automatic Control 57, no. 7 (2012): 1865–71. http://dx.doi.org/10.1109/tac.2011.2179426.

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Šimandl, Miroslav, and Jakub Královec. "Filtering, Prediction and Smoothing with Gaussian Sum Representation." IFAC Proceedings Volumes 33, no. 15 (2000): 1157–62. http://dx.doi.org/10.1016/s1474-6670(17)39910-x.

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Jeng, Yih-Nen, P. G. Huang, and You-Chi Cheng. "Decomposition of one-dimensional waveform using iterative Gaussian diffusive filtering methods." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2095 (2008): 1673–95. http://dx.doi.org/10.1098/rspa.2007.0031.

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The Gaussian smoothing method is shown to have a wide transition zone around the cut-off frequency selected to filter a given dataset. We proposed two iterative Gaussian smoothing methods to tighten the transition zone: one being approximately diffusive and the other being strictly diffusive. The first version smoothes repeatedly the remaining high-frequency parts and the second version requires an additional step to further smooth the resulting smoothed response in each of the smoothing operation. Based on the choice of the criterion for accuracy, the smoothing factor and the number of iterations are derived for an infinite data length in both methods. By contrast, for a finite-length data string, results of the interior points (sufficiently away from the two endpoints) obtained by both methods can be shown to exhibit an approximate diffusive property. The upper bound of the distance affected by the error propagation inward due to the lack of data beyond the two ends is numerically estimated. Numerical experiments also show that results of employing the iterative Gaussian smoothing method are almost the same as those obtained by the strict diffusive version, except that the error propagation distance induced by the latter is slightly deeper than that of the former. The proposed method has been successfully applied to decompose the wave formation of a number of test cases including two sets of real experimental data.

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Zhang, Qing, Hao Jiang, Yongwei Nie, and Wei-Shi Zheng. "Pyramid Texture Filtering." ACM Transactions on Graphics 42, no. 4 (2023): 1–11. http://dx.doi.org/10.1145/3592120.

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We present a simple but effective technique to smooth out textures while preserving the prominent structures. Our method is built upon a key observation---the coarsest level in a Gaussian pyramid often naturally eliminates textures and summarizes the main image structures. This inspires our central idea for texture filtering, which is to progressively upsample the very low-resolution coarsest Gaussian pyramid level to a full-resolution texture smoothing result with well-preserved structures, under the guidance of each fine-scale Gaussian pyramid level and its associated Laplacian pyramid level. We show that our approach is effective to separate structure from texture of different scales, local contrasts, and forms, without degrading structures or introducing visual artifacts. We also demonstrate the applicability of our method on various applications including detail enhancement, image abstraction, HDR tone mapping, inverse halftoning, and LDR image enhancement. Code is available at https://rewindl.github.io/pyramid_texture_filtering/.

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Fujita, Shu, and Norishige Fukushima. "Hyperspectral Gaussian Filtering : Edge-Preserving Smoothing for Hyperspectral Image and Its Separable Acceleration." Abstracts of the international conference on advanced mechatronics : toward evolutionary fusion of IT and mechatronics : ICAM 2015.6 (2015): 5–6. http://dx.doi.org/10.1299/jsmeicam.2015.6.5.

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Särkkä, Simo, and Juha Sarmavuori. "Gaussian filtering and smoothing for continuous-discrete dynamic systems." Signal Processing 93, no. 2 (2013): 500–510. http://dx.doi.org/10.1016/j.sigpro.2012.09.002.

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Guoyan, Wang, A. V. Fomichev, and Dy Yiran. "Research on Improved Gaussian Smoothing Filters for SLAM Application." Mekhatronika, Avtomatizatsiya, Upravlenie 20, no. 12 (2019): 756–64. http://dx.doi.org/10.17587/mau.20.756-764.

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To address the navigation issues of the planetary rover and construct a map for the unknown environment as well as the surface of the planets in our solar system, the simultaneous localization and mapping can be seen as an alternative method. In terms of the navigation with the laser sensor, the Kalman filter and its improving algorithms, such as EKF and UKF are widely used in the the process of processing information. Nevertheless, these filter algorithms suffer from low accuracy and significant computation expensive. The EKF algorithm has a linearization process, the UKF algorithm is better matched in a nonlinear system than the EKF algorithm, but it has more computational complexity. The GP-RTSS filtering algorithm, based on a Gaussian filter, is significantly superior to the EKF and UKF algorithms regarding the sensor fusion accuracy. The Gaussian Process can be used in different non-linear system, does not need prediction model and linearization. However, the main barrier in the process of implementing the GP-RTSS algorithm is that the Gaussian core function requires a lot of computation. In this paper, an algorithm, so-called DIS RTSS filter under a distributed computation scheme, derived from the GP-RTSS Gaussia n smoothing and filter, is proposed. The distributed system can effectively reduce the cost of computation (computation expense and memory). Moreover, four fusion methods for the DIS RTSS filter, i.e., DIS RTP, DIS RTGP, DIS RTB, DIS RTrB are discussed in this paper. The experiments show that among the four algorithms described above, the DIS RTGP algorithm is the most effective solution for practical implementation. The DIS RTSS filtering algorithm can realize a high processing rate and can theoretically process an infinite number of data samples.

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Cedeño, Angel L., Ricardo Albornoz, Rodrigo Carvajal, Boris I. Godoy, and Juan C. Agüero. "A Two-Filter Approach for State Estimation Utilizing Quantized Output Data." Sensors 21, no. 22 (2021): 7675. http://dx.doi.org/10.3390/s21227675.

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Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems. These algorithms are used to obtain an estimation of the system state based on the sequentially available noisy measurements of the system output. In a real-world system, the noisy measurements can suffer a significant loss of information due to (among others): (i) a reduced resolution of cost-effective sensors typically used in practice or (ii) a digitalization process for storing or transmitting the measurements through a communication channel using a minimum amount of resources. Thus, obtaining suitable state estimates in this context is essential. In this paper, Gaussian sum filtering and smoothing algorithms are developed in order to deal with noisy measurements that are also subject to quantization. In this approach, the probability mass function of the quantized output given the state is characterized by an integral equation. This integral was approximated by using a Gauss–Legendre quadrature; hence, a model with a Gaussian mixture structure was obtained. This model was used to develop filtering and smoothing algorithms. The benefits of this proposal, in terms of accuracy of the estimation and computational cost, are illustrated via numerical simulations.

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Lazzaro, Dwiki, Febryanti Sthevanie, and Kurniawan Nur Ramadhani. "Enhancing Fire Detection in Images using Faster R-CNN with Gaussian Filtering and Contrast Adjustment." JURNAL MEDIA INFORMATIKA BUDIDARMA 7, no. 3 (2023): 1572. http://dx.doi.org/10.30865/mib.v7i3.6486.

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A system is designed with an accurate and efficient model to detect fires, aiming to assist in fire prevention. Designing such a system poses a challenging task, as numerous aspects need to be considered, including model accuracy, parameter count, computational complexity, and more. Therefore, the research will incorporate techniques such as Image Smoothing Filtering and Contrast Adjustment to enhance the fire detection process. The primary objective is to develop a robust system that can effectively identify and detect fire occurrences. Accuracy is crucial to ensure reliable results, while efficiency plays a significant role in real-time fire detection. By implementing Image Smoothing Filtering, the system can reduce noise and enhance image quality, improving detection performance. Contrast Adjustment techniques will further contribute to the system's efficiency by emphasizing fire patterns and enhancing their visibility. The system's design encompasses careful consideration of various factors to strike a balance between accuracy, efficiency, and computational complexity. By utilizing Image Smoothing Filtering and Contrast Adjustment, the research aims to develop a comprehensive fire detection system that can aid in preventing fire incidents. This study endeavors to contribute to the advancement of fire detection technologies and pave the way for future innovations in this field.

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Sreevani, M., Pravalika Boya , Naveen Gadala , and Mohan Sai Bora. "Power-Optimized Gaussian Filtering with Approximate Adders and logical optimization." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 09, no. 01 (2025): 1–9. https://doi.org/10.55041/ijsrem40509.

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Gaussian filters are crucial in numerous image and signal processing applications for tasks like noise reduction and smoothing. In resource-constrained environments, such as embedded and mobile devices, optimizing these filters for power efficiency is paramount. This paper focuses on designing a power-efficient Gaussian filter architecture through Design Space Exploration (DSE). The approach leverages logical optimizations and introduces approximate adders to minimize power consumption without significantly impacting performance. The trade-offs between power, area, and output quality are analyzed, with results demonstrating significant power savings while maintaining an acceptable level of image quality. Index Terms—Gaussian filter, power-efficient architectures, design space exploration, approximated adders, logical optimiza- tion.

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Yang, Yuan, Manyi Wang, Yunxia Qiao, Bo Zhang, and Haoran Yang. "Efficient Marginalized Particle Smoother for Indoor CSS–TOF Localization with Non-Gaussian Errors." Remote Sensing 12, no. 22 (2020): 3838. http://dx.doi.org/10.3390/rs12223838.

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The time-series state and parameter estimations of indoor localization continue to be a topic of growing importance. To deal with the nonlinear and positive skewed non-Gaussian dynamic of indoor CSS–TOF (Chirp-Spread-Spectrum Time-of-Flight) ranging measurements and position estimations, Monte Carlo Bayesian smoothers are promising as involving the past, present, and future observations. However, the main problems are how to derive trackable smoothing recursions and to avoid the degeneracy of particle-based smoothed distributions. To incorporate the backward smoothing density propagation with the forward probability recursion efficiently, we propose a lightweight Marginalized Particle Smoother (MPS) for nonlinear and non-Gaussian errors mitigation. The performance of the position prediction, filtering, and smoothing are investigated in real-world experiments carried out with vehicle on-board sensors. Results demonstrate the proposed smoother enables a great tool by reducing temporal and spatial errors of mobile trajectories, with the cost of a few sequence delay and a small number of particles. Therefore, MPS outperforms the filtering and smoothing methods under weak assumptions, low computation, and memory requirements. In the view that the sampled trajectories stay numerically stable, the MPS form is validated to be applicable for time-series position tracking.

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Tanaka, Go, Noriaki Suetake, and Eiji Uchino. "Image Enhancement Based on Nonlinear Smoothing and Sharpening for Noisy Images." Journal of Advanced Computational Intelligence and Intelligent Informatics 14, no. 2 (2010): 200–207. http://dx.doi.org/10.20965/jaciii.2010.p0200.

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The novel image enhancement approach we propose is based on blending the ε-filtering and a conventional unsharp masking. The proposed selective unsharp masking is especially effective in enhancing noisy images corrupted by Gaussian noise, as confirmed in image enhancement experiments.

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Nikolov, Nikolay, Sergiy Makeyev, Olga Korostynska, Tetyana Novikova, and Yelizaveta Kriukova. "Gaussian Filter for Brain SPECT Imaging." Innovative Biosystems and Bioengineering 6, no. 1 (2022): 4–15. http://dx.doi.org/10.20535/ibb.2022.6.1.128475.

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Background. The presence of a noise component on 3D images of single-photon emission computed tomography (SPECT) of a brain significantly distorts the probability distribution function (PD) of the radioactive count rate in the images. The presence of noise and further filtering of the data, based on a subjective assessment of image quality, have a significant impact on the calculation of volumetric cerebral blood flow and the values of the uptake asymmetry of the radiopharmaceutical in a brain. Objective. We are aimed to develop a method for optimal SPECT filtering of brain images with lipophilic radiopharmaceuticals, based on a Gaussian filter (GF), for subsequent image segmentation by the threshold method. Methods. SPECT images of the water phantom and the brain of patients with 99mTc-HMPAO were used. We have developed a technique for artificial addition of speckle noise to conditionally flawless data in order to determine the optimal parameters for smoothing SPECT, based on a GF. The quantitative criterion for optimal smoothing was the standard deviation between the PD of radioactive count rate of the smoothed image and conditionally ideal one. Results. It was shown that the maximum radioactive count rate of the SPECT image has an extremum by changing the standard deviation of the GF in the range of 0.3–0.4 pixels. The greater the noise component in the SPECT image, the more quasi-linearly the corresponding rate changes. This dependence allows determining the optimal smoothing parameters. The application of the developed smoothing technique allows restoring the probability distribution function of the radioactive count rate (distribution histogram) with an accuracy up to 5–10%. This provides the possibility to standardize SPECT images of brain. Conclusions. The research results of work solve a specific applied problem: restoration of the histogram of a radiopharmaceuticals distribution in a brain for correct quantitative assessment of regional cerebral blood flow. In contrast to the well-known publications on the filtration of SPECT data, the work takes into account that the initial tomographic data are 3D, rather than 2D slices, and contain not only uniform random Gaussian noise, but also a pronounced speckle component.

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Tronarp, Filip, Hans Kersting, Simo Särkkä, and Philipp Hennig. "Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective." Statistics and Computing 29, no. 6 (2019): 1297–315. http://dx.doi.org/10.1007/s11222-019-09900-1.

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Abstract We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with nonlinear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP—which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a nonlinear Bayesian filtering problem and all widely used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers that are formulated in terms of generating synthetic measurements of the gradient field come out as specific approximations. Based on the nonlinear Bayesian filtering problem posed in this paper, we develop novel Gaussian solvers for which we establish favourable stability properties. Additionally, non-Gaussian approximations to the filtering problem are derived by the particle filter approach. The resulting solvers are compared with other probabilistic solvers in illustrative experiments.

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Baccarelli, E., R. Cusani, and G. di Blasio. "Recursive filtering and smoothing for reciprocal Gaussian processes-pinned boundary case." IEEE Transactions on Information Theory 41, no. 1 (1995): 334–37. http://dx.doi.org/10.1109/18.370087.

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CHEN, YANG, YIWEN SUN, and EMMA PICKWELL-MACPHERSON. "IMPROVING EXTRACTION OF IMPULSE RESPONSE FUNCTIONS USING STATIONARY WAVELET SHRINKAGE IN TERAHERTZ REFLECTION IMAGING." Fluctuation and Noise Letters 09, no. 04 (2010): 387–94. http://dx.doi.org/10.1142/s0219477510000319.

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In terahertz imaging, deconvolution is often performed to extract the impulse response function of the sample of interest. The inverse filtering process amplifies the noise and in this paper we investigate how we can suppress the noise without over-smoothing and losing useful information. We propose a robust deconvolution process utilizing stationary wavelet shrinkage theory which shows significant improvement over other popular methods such as double Gaussian filtering. We demonstrate the success of our approach on experimental data of water and isopropanol.

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Hu, Sile, Qiaosheng Zhang, Jing Wang, and Zhe Chen. "Real-time particle filtering and smoothing algorithms for detecting abrupt changes in neural ensemble spike activity." Journal of Neurophysiology 119, no. 4 (2018): 1394–410. http://dx.doi.org/10.1152/jn.00684.2017.

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Sequential change-point detection from time series data is a common problem in many neuroscience applications, such as seizure detection, anomaly detection, and pain detection. In our previous work (Chen Z, Zhang Q, Tong AP, Manders TR, Wang J. J Neural Eng 14: 036023, 2017), we developed a latent state-space model, known as the Poisson linear dynamical system, for detecting abrupt changes in neuronal ensemble spike activity. In online brain-machine interface (BMI) applications, a recursive filtering algorithm is used to track the changes in the latent variable. However, previous methods have been restricted to Gaussian dynamical noise and have used Gaussian approximation for the Poisson likelihood. To improve the detection speed, we introduce non-Gaussian dynamical noise for modeling a stochastic jump process in the latent state space. To efficiently estimate the state posterior that accommodates non-Gaussian noise and non-Gaussian likelihood, we propose particle filtering and smoothing algorithms for the change-point detection problem. To speed up the computation, we implement the proposed particle filtering algorithms using advanced graphics processing unit computing technology. We validate our algorithms, using both computer simulations and experimental data for acute pain detection. Finally, we discuss several important practical issues in the context of real-time closed-loop BMI applications. NEW & NOTEWORTHY Sequential change-point detection is an important problem in closed-loop neuroscience experiments. This study proposes novel sequential Monte Carlo methods to quickly detect the onset and offset of a stochastic jump process that drives the population spike activity. This new approach is robust with respect to spike sorting noise and varying levels of signal-to-noise ratio. The GPU implementation of the computational algorithm allows for parallel processing in real time.

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Grishin, Yu P., and D. Janczak. "A robust fixed-lag smoothing algorithm for dynamic systems with correlated sensor malfunctions." Bulletin of the Polish Academy of Sciences Technical Sciences 62, no. 3 (2014): 517–23. http://dx.doi.org/10.2478/bpasts-2014-0056.

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Abstract A new robust fixed-lag smoothing algorithm for fault-tolerant signal processing in stochastic dynamic systems in the presence of correlated sensor malfunctions has been developed. The algorithm is developed using a state vector augmentation method and the Gaussian approximation of the current estimate probability density function. The algorithm can be used in the real-time fault-tolerant control systems as well as in radar tracking systems working in the complex interference environment. The performance of the developed algorithm are evaluated by simulations and compared with smoothing and nonlinear filtering algorithms.

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Srisuk, Sanun, Wachirapong Kesjindatanawaj, and Surachai Ongkittikul. "Real-Time Bilateral Filtering Using GPGPU." Applied Mechanics and Materials 781 (August 2015): 568–71. http://dx.doi.org/10.4028/www.scientific.net/amm.781.568.

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In this paper, we present a technique for accelerating the bilateral filtering using GPGPU. Bilateral filtering is a tool for an image smoothing with edge preserving properties. It serves as a mixture of domain and range filters. Domain filter suppresses Gaussian noise while range filter maintains sharp edges. Bilateral filtering is a nonlinear filtering in which the filter kernel must be computed pixel by pixel. Therefore conventional fast Fourier transform technique cannot be used to accelerate the bilateral filtering. Instead, general purpose GPU is used as a parallel machine to reduce time consuming of the bilateral filtering. We will show the experimental results by comparing the computation time of CPU and GPU. It was cleared that, from the experimental results, GPU outperformed the CPU in terms of computation time.

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Wang, Chang Tao, Bin Ma, and Kuan Huang. "Research of Recognition Algorithms by a Distance Feature Information Method on Digital Image." Applied Mechanics and Materials 380-384 (August 2013): 3595–98. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.3595.

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t be analysed about the recognition methods for digital image in this paper. In the digital image preprocessing, the conservative smoothing, mean filtering, Gaussian sharpening and binarization are used to improve the effectiveness of the digital feather extraction. A distance feature information method for recognizing digital images be proposed in this paper.The method be evaluated and compared by experimental tests.

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Baccarelli, E., and R. Cusani. "Recursive filtering and smoothing for reciprocal Gaussian processes with Dirichlet boundary conditions." IEEE Transactions on Signal Processing 46, no. 3 (1998): 790–95. http://dx.doi.org/10.1109/78.661349.

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Kitagawa, Genshiro. "Monte Carlo Filtering and Smoothing for Nonlinear NON-Gaussian State Space Model." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 1998 (May 5, 1998): 1–6. http://dx.doi.org/10.5687/sss.1998.1.

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Yao, Gang, Nuno V. da Silva, Vladimir Kazei, Di Wu, and Chenhao Yang. "Extraction of the tomography mode with nonstationary smoothing for full-waveform inversion." GEOPHYSICS 84, no. 4 (2019): R527—R537. http://dx.doi.org/10.1190/geo2018-0586.1.

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Full-waveform inversion (FWI) includes migration and tomography modes. The tomographic component of the gradient from reflection data is usually much weaker than the migration component. To use the tomography mode to fix background velocity errors, it is necessary to extract the tomographic component from the gradient. Otherwise, the inversion will be dominated by the migration mode. We have developed a method based on nonstationary smoothing to extract the tomographic component from the raw gradient. By analyzing the characteristics of the scattering angle filtering, the wavenumber of the tomographic component at a given frequency is seen to be smaller than that of the migration component. Therefore, low-wavenumber-pass filtering can be applied to extract the tomographic component. The low-wavenumber-pass smoothing filters are designed with Gaussian filters that are determined by the frequency of inversion, the model velocity, and the minimum scattering angle. Thus, this filtering is nonstationary smoothing in the space domain. Because this filtering is carried out frequency by frequency, it works naturally and efficiently for FWI based on frequency-domain modeling. Furthermore, because the maximum opening angle of the reflections in a typical acquisition geometry is much smaller than the minimum scattering angle for the tomographic component, which is generally set at 160°, there is a relatively large gap between the wavenumbers of the tomographic and migration components. In other words, the nonstationary smoothing can be applied once to a group of frequencies for time-domain FWI without leaking the migration component into the tomographic component. Analyses and numerical tests indicate that two frequency groups are generally sufficient to extract the tomographic component for the typical frequency range of time-domain FWI. The numerical tests also demonstrate that the nonstationary smoothing method is effective and efficient at extracting the tomographic component for reflection waveform inversion.

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Ma, Ye. "Construction of Biologic Microscopic Image Segmentation Model Based on Smoothing of Fourth-Order Partial Differential Equation." Scanning 2022 (July 25, 2022): 1–8. http://dx.doi.org/10.1155/2022/1908644.

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In order to solve the problem of microscopic image noise, a biological microscopic image segmentation model based on the smoothing of the fourth-order partial differential equation was proposed. Based on the functional description of image smoothness by directional curvature mode value, a fourth-order PDE image denoising model is derived, which can effectively reduce noise while preserving edges. The result of this method is piecewise linear image, and the gradient at the edge of the target has a step. Using the feature of noise reduction, a new geodesic active contour model is proposed. The experiment result shows that when the variance of Gaussian white noise is 15, the enhancement and denoising effects of the proposed method are 80.35% and 69.84 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3075 seconds slower than the original vibration filtering method and 17.5754 seconds faster than the L. Alvarez method. When the variance of Gaussian white noise is 25, the enhancement and denoising effects of the proposed method are 97.79% and 81.16 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3246 seconds slower than the original vibration filtering method and 17.5796 seconds faster than the L. Alvarez method. Conclusion. The new model is not only stable but also has strong ability of contour extraction and fast convergence.

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Shah, Yogendra Prasad. "Linear Transformation and its Properties with Application in Time Series Filtering." Journal of Population and Development 4, no. 1 (2023): 181–87. http://dx.doi.org/10.3126/jpd.v4i1.64258.

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The primary objective of this article is to justify the concept of a linear transformation that derives its algebraic properties by means of variation matrices represented so far. The mathematical formulas will be used to elaborate and justify the argument of linear transformation. By displaying the significance of the t-transformation for estimation of latent variables in the time series decomposition, the paper obtains a general expression for smoothing matrices characterized by symmetric and asymmetric weighting system. The article further elaborates the concept of sub-matrix of the symmetric weights that is t-invariant, whereas the sub matrices of the asymmetric weights are the t-transformation of each other. By virtue of this relation, the properties of the t-transformation project useful imperative information on the smoothing of time series data, which may be required to clarify the concept of the topic raised so far. Eventually, the paper illustrates the role of the t-transformation on the weighting systems of several smoothers often applied for trend cycle estimation such as the locally weighted regression smoother, the cube smoothing spine, the Gaussian Kernel and 13-term trend cycle Henderson filter. By so doing, the article will pose the interrelated facts of linear transformation, from which the prospective researchers can benefit.

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Tronarp, Filip, Angel F. Garcia-Fernandez, and Simo Sarkka. "Iterative Filtering and Smoothing in Nonlinear and Non-Gaussian Systems Using Conditional Moments." IEEE Signal Processing Letters 25, no. 3 (2018): 408–12. http://dx.doi.org/10.1109/lsp.2018.2794767.

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Zheng, Fei, Stéphane Derrode, and Wojciech Pieczynski. "Semi-supervised optimal recursive filtering and smoothing in non-Gaussian Markov switching models." Signal Processing 171 (June 2020): 107511. http://dx.doi.org/10.1016/j.sigpro.2020.107511.

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Bibic, Adnan, Linda Knutsson, Freddy Ståhlberg, and Ronnie Wirestam. "Denoising of arterial spin labeling data: wavelet-domain filtering compared with Gaussian smoothing." Magnetic Resonance Materials in Physics, Biology and Medicine 23, no. 3 (2010): 125–37. http://dx.doi.org/10.1007/s10334-010-0209-8.

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Tang, Guiji, Xiaoli Yan, and Xiaolong Wang. "Chaotic Signal Denoising Based on Adaptive Smoothing Multiscale Morphological Filtering." Complexity 2020 (February 17, 2020): 1–14. http://dx.doi.org/10.1155/2020/7242943.

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Nonlinear time series denoising is the prerequisite for extracting effective information from observation sequence. An effective chaotic signal denoising method not only has a good signal-to-noise ratio (SNR) enhancement performance, but also can remain as a good unpredictable denoised signal. However, the inherent characteristics of chaos, such as extreme sensitivity to initial values and broadband spectrum, pose challenges for noise reduction of polluted chaotic signals. To address these issues, an adaptive smoothing multiscale morphological filtering (ASMMF) is proposed to reconstruct chaotic signals. In the process of noise reduction for contaminated chaotic signals, firstly, a multiscale morphological filter is constructed adaptively according to the multiscale permutation entropy (MPE) of morphological filter residuals, and the contaminated signals are filtered. Secondly, the weight coefficients of scale structural element are calculated by the residual sum of squares operation, and the chaotic signals are reconstructed. Finally, the resampled filter signals are smoothed by cubic B-spline interpolation operation. In the experiment, the Lorenz signal with white Gaussian noise, the measured sunspot, and the chaotic vibration signal are reconstructed by four comparison methods. The test results show that the proposed ASMMF method has obvious advantages in noise suppression and topological trajectory restoration.

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Dermawan, Andre, Tommy Tommy, and Divi Handoko. "Penerapan Bilateral Filtering untuk Peningkatan Kualitas Citra Digital Fokus pada Gaussian, Salt-and-Pepper, dan Speckle Noise." Algoritma: Jurnal Ilmu Komputer dan Informatika 8, no. 2 (2024): 98. https://doi.org/10.30829/algoritma.v8i2.22130.

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The main objective of this research is to improve the quality of digital images without losing important details, such as object edges, while also developing efficient and user- friendly software for image processing. Bilateral filtering is a non-linear filtering method used to reduce noise in images while preserving edge details. This filter works by combining smoothing based on spatial proximity and pixel intensity similarity. Thus, bilateral filtering is effective in reducing noise without blurring the important edges of the image. This research develops an application that can open, process, and save digital images, allowing users to practically reduce noise in images. The results show that bilateral filtering can significantly enhance digital image quality with substantial noise reduction, although certain types of noise may require further parameter adjustments for optimal results. Keywords: Bilateral Filtering, Digital Image, Noise, Visual Basic, Image Processing.

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Ivashko, Andrey, Andrey Zuev, Dmytro Karaman, and Miha Moškon. "FPGA-BASED IMPLEMENTATION OF A GAUSSIAN SMOOTHING FILTER WITH POWERS-OF-TWO COEFFICIENTS." Advanced Information Systems 8, no. 2 (2024): 39–47. http://dx.doi.org/10.20998/2522-9052.2024.2.05.

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The purpose of the study is to develop methods for synthesizing a Gaussian filter that ensures simplified hardware and software implementation, particularly filters with powers-of-two coefficients. Such filters can provide effective denoising of images, including landscape maps, both natural and synthetically generated. The study also involves analyzing of methods for FPGA implementation, comparing their hardware complexity, performance, and noise reduction with traditional Gaussian filters. Results. An algorithm for rounding filter coefficients to powers of two, providing optimal approximation of the constructed filter to the original, is presented, along with examples of developed filters. Topics covered include FPGA implementation, based on the Xilinx Artix-7 FPGA. Filter structures, testing methods, simulation results, and verification of the scheme are discussed. Examples of the technological placement of the implemented scheme on the FPGA chip are provided. Comparative evaluations of FPGA resources and performance for proposed and traditional Gaussian filters are carried out. Digital modeling of the filters and noise reduction estimates for noisy images of the terrain surface are presented. The developed algorithm provides approximation of Gaussian filter coefficients as powers of two for a given window size and maximum number of bits with a relative error of no more than 0.18. Implementing the proposed filters on FPGA results in a hardware costs reduction with comparable performance. Computer simulation show that Gaussian filters both traditional and proposed effectively suppress additive white noise in images. Proposed filters improve the signal-to-noise ratio within 5-10 dB and practically match the filtering quality of traditional Gaussian filters.

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Kotera, Hiroaki. "Inverse-Scaled Lanczos Filtering for Image Sharpening." Color and Imaging Conference 2020, no. 28 (2020): 215–20. http://dx.doi.org/10.2352/issn.2169-2629.2020.28.34.

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The edge response in retinal image is the first step for human vision recognizing the outside world. A variety of receptive field models for describing the impulse response have been proposed. Which satisfies the uncertain principle? occupied the interest from a point of minimizing the product (Δx)(Δ w) both in spatial and spectral. Among the typical edge response models, finally Gabor function and 2nd. Gaussian Derivative GD2 remained as strong candidates. While famous D. Marr and R. Young support GD2, many vision researchers prefer Gabor. The retinal edge response model is used for image sharpening. Different from the conventional image sharpening filters, this paper proposes a novel image sharpening filter by modifying the Lanczos resampling filter. The Lanczos filter is used for image scaling to resize digital images. Usually it works to interpolate the discrete sampled points like as a kind of smoothing filter not as sharpening. The Lanczos kernel is given by the product of sampling Sinc function and the scaled Sinc function. The scaled Sinc function expanded by the scale "s" plays a role of window function. The author noticed that the inverse scaling of Lanczos window can be used not for smoothing but for sharpening filter. This paper demonstrates how the proposed model works effectively in comparison with Gabor and GD2.

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Sarkka, Simo, Arno Solin, and Jouni Hartikainen. "Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering." IEEE Signal Processing Magazine 30, no. 4 (2013): 51–61. http://dx.doi.org/10.1109/msp.2013.2246292.

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Cosme, Emmanuel, Jacques Verron, Pierre Brasseur, Jacques Blum, and Didier Auroux. "Smoothing Problems in a Bayesian Framework and Their Linear Gaussian Solutions." Monthly Weather Review 140, no. 2 (2012): 683–95. http://dx.doi.org/10.1175/mwr-d-10-05025.1.

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Smoothers are increasingly used in geophysics. Several linear Gaussian algorithms exist, and the general picture may appear somewhat confusing. This paper attempts to stand back a little, in order to clarify this picture by providing a concise overview of what the different smoothers really solve, and how. The authors begin addressing this issue from a Bayesian viewpoint. The filtering problem consists in finding the probability of a system state at a given time, conditioned to some past and present observations (if the present observations are not included, it is a forecast problem). This formulation is unique: any different formulation is a smoothing problem. The two main formulations of smoothing are tackled here: the joint estimation problem (fixed lag or fixed interval), where the probability of a series of system states conditioned to observations is to be found, and the marginal estimation problem, which deals with the probability of only one system state, conditioned to past, present, and future observations. The various strategies to solve these problems in the Bayesian framework are introduced, along with their deriving linear Gaussian, Kalman filter-based algorithms. Their ensemble formulations are also presented. This results in a classification and a possible comparison of the most common smoothers used in geophysics. It should provide a good basis to help the reader find the most appropriate algorithm for his/her own smoothing problem.

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Ren, Honglin, and Zhihua Lu. "Measurement Bias Estimation in the Problem of Target Tracking." Wireless Communications and Mobile Computing 2019 (May 16, 2019): 1–10. http://dx.doi.org/10.1155/2019/9576785.

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In the problem of target tracking, different types of biases can enter into the measurement collected by sensors due to various reasons. In order to accurately track the target, it is essential to estimate and correct the measurement bias. Considering practical backgrounds, the bias is assumed to be locally stationary Gaussian distributed and an iterative estimation algorithm is proposed. Firstly, a mechanism is established to detect whether the bias switches between different Gaussian distributions. Secondly, the expectation maximization algorithm with the assistance of extended Kalman filtering and smoothing is proposed to iteratively estimate the bias and target state in an offline manner. Simulations show the proposed algorithm can suppress the impact of the measurement bias on target tracking.

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Wu, Chien Ting, and Ming Cheng Chen. "Comparison of 6 Common Noise Filter Methods for Terrestrial Laser Scanner Target." Applied Mechanics and Materials 170-173 (May 2012): 2929–34. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.2929.

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The terrestrial laser scanner (TLS) is a line-of-sight instrument which can directly acquire dense 3D point clouds in a very short time. The registration method is used to act as a control point for a reflective target placed in overlapping areas in neighboring scanning stations. The main purpose for a reflective target is to be an obvious and precise positioning feature for laser scanning point cloud data. This study compares six common noise filtering methods which are used to eliminate measuring noise in the primitive point cloud of reflective target for better positioning accuracy, i.e. Scatter points removal method, Spikes removal method, Least squares plane method, Gaussian smoothing method, Median smoothing method, and the Average smoothing method. The test results found for 30, 60, and 90 meter distances in this study was that six noise filtering methods can actually increase the reflective target positioning accuracy, and the least squares plane method is the best one in either precision or accuracy. Beside the reflective target, the test is carried out with self-made targets for the comparison of positioning accuracy between the reflective target and self-made targets. Regarding accuracy, the reflective target is superior to the object in 30 and 60m, and self-made target is superior to the reflective target in 90m.

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Limbong, Hanspran, Lailan Sofinah Harahap, and Rafli Arya Gading. "Comparison of Median Filter and Gaussian Filter Performance in Removing Salt and Pepper Noise." Journal of Artificial Intelligence and Engineering Applications (JAIEA) 4, no. 3 (2025): 1849–54. https://doi.org/10.59934/jaiea.v4i3.1033.

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Image processing plays a critical role in various applications, from medical diagnostics to surveillance systems. However, one of the major challenges in digital image processing is the presence of noise, particularly salt and pepper noise, which significantly degrades image quality. This study aims to compare the effectiveness of two popular filtering techniques—Median Filter and Gaussian Filter—in removing salt and pepper noise from digital images. The evaluation is conducted both quantitatively, using Peak Signal-to-Noise Ratio (PSNR) and Mean Squared Error (MSE) metrics, and qualitatively, through visual analysis. The experimental results show that the Median Filter consistently outperforms the Gaussian Filter in terms of noise reduction performance. Median filtering yields higher PSNR and lower MSE values across various levels of noise intensity (5%, 10%, and 15%). Moreover, the visual assessment indicates that Median Filter preserves image edges and fine details more effectively, whereas Gaussian Filter tends to introduce blurring artifacts due to its smoothing nature. These findings suggest that for impulsive noise such as salt and pepper, Median Filter is a more appropriate and robust method, offering better restoration quality without compromising important image features.

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Ali, Wasiq, Yaan Li, Zhe Chen, Muhammad Asif Zahoor Raja, Nauman Ahmed, and Xiao Chen. "Application of Spherical-Radial Cubature Bayesian Filtering and Smoothing in Bearings Only Passive Target Tracking." Entropy 21, no. 11 (2019): 1088. http://dx.doi.org/10.3390/e21111088.

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In this paper, an application of spherical radial cubature Bayesian filtering and smoothing algorithms is presented to solve a typical underwater bearings only passive target tracking problem effectively. Generally, passive target tracking problems in the ocean environment are represented with the state-space model having linear system dynamics merged with nonlinear passive measurements, and the system is analyzed with nonlinear filtering algorithms. In the present scheme, an application of spherical radial cubature Bayesian filtering and smoothing is efficiently investigated for accurate state estimation of a far-field moving target in complex ocean environments. The nonlinear model of a Kalman filter based on a Spherical Radial Cubature Kalman Filter (SRCKF) and discrete-time Kalman smoother known as a Spherical Radial Cubature Rauch–Tung–Striebel (SRCRTS) smoother are applied for tracking the semi-curved and curved trajectory of a moving object. The worth of spherical radial cubature Bayesian filtering and smoothing algorithms is validated by comparing with a conventional Unscented Kalman Filter (UKF) and an Unscented Rauch–Tung–Striebel (URTS) smoother. Performance analysis of these techniques is performed for white Gaussian measured noise variations, which is a significant factor in passive target tracking, while the Bearings Only Tracking (BOT) technology is used for modeling of a passive target tracking framework. Simulations based experiments are executed for obtaining least Root Mean Square Error (RMSE) among a true and estimated position of a moving target at every time instant in Cartesian coordinates. Numerical results endorsed the validation of SRCKF and SRCRTS smoothers with better convergence and accuracy rates than that of UKF and URTS for each scenario of passive target tracking problem.

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Ala-Luhtala, Juha, Simo Särkkä, and Robert Piché. "Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems." Signal Processing 111 (June 2015): 124–36. http://dx.doi.org/10.1016/j.sigpro.2014.12.013.

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Deng, Ruiqi, Gang Chen, Bo Li, Jianping Wu, Liang Guo, and Junting Liu. "Research on flexible stabilization strategy for power fluctuation characteristics of Distributed Renewable Energy cluster." Journal of Physics: Conference Series 2465, no. 1 (2023): 012011. http://dx.doi.org/10.1088/1742-6596/2465/1/012011.

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Abstract To fully use the flexible regulation resources of the grid to solve the fluctuation smoothing problem of massive distributed renewable energy clusters(DREC) power generation in the grid, a flexible smoothing method is proposed for the fluctuation characteristics of DREC. Firstly, the method of adaptive gaussian filtering strips out the power for DREC that meets the grid entry criteria and obtains the power generation that needs to be smoothed out; secondly, according to the proposed fluctuation characteristic evaluation index, quantitative analysis and grade evaluation are performed on the stripped power generation that needs to be smoothed out, and the corresponding flexible smoothing strategies are adopted according to the fluctuation grade. Then, corresponding strategies adopt the flexible regulation resources to realize the flexible stabilization effect of DREC. Finally, a simulation analysis is conducted to verify the feasibility and effectiveness of the method by using the power generation data of photovoltaic power plants in a region on typical days.

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Nakamori, Seiichi. "Robust Recursive Least-Squares Fixed-Point Smoother and Filter using Covariance Information in Linear Continuous-Time Stochastic Systems with Uncertainties." WSEAS TRANSACTIONS ON SIGNAL PROCESSING 20 (May 13, 2024): 56–66. http://dx.doi.org/10.37394/232014.2024.20.2.

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This study develops robust recursive least-squares (RLS) fixed-point smoothing and filtering algorithms for signals in linear continuous-time stochastic systems with uncertainties. The algorithms use covariance information, such as the cross-covariance function of the signal with the observed value and the autocovariance function of the degraded signal. A finite Fourier cosine series expansion approximates these functions. Additive white Gaussian noise is present in the observation of the degraded signal. A numerical simulation compares the estimation accuracy of the proposed robust RLS filter with the robust RLS Wiener filter, showing similar mean square values (MSVs) of the filtering errors. The MSVs of the proposed robust RLS fixed-point smoother are also compared to those of the proposed robust RLS filter.

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Sun, Wenwen, Dongliang Wang, and Xianliang Yan. "CT Imaging in the Diagnosis of Lung Injury of Organophosphorus Poisoning and Analysis of Its Correlation with Procalcitonin and C-Reactive Protein Levels." Scientific Programming 2021 (November 1, 2021): 1–8. http://dx.doi.org/10.1155/2021/9011630.

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This study focused on the application value of CT images of patients with organophosphorus poisoning lung injury. Specifically, 50 patients diagnosed with organophosphorus pesticide poisoning lung injury in the hospital were selected as research subjects. They all had chest CT examinations. Patients were classified according to different degrees of poisoning, and different groups were compared for the levels of C-reactive protein (CRP) and procalcitonin (PCT) in the serum. The results showed that, of the 50 patients, 25 patients had mild organophosphorus poisoning, accounting for 50%, 14 patients had moderate poisoning, accounting for 28%, and 11 patients suffered from severe organophosphorus poisoning. It was found that, in AOPP patients, cascade effect was exerted by stimulating the secretion of inflammatory mediators such as CRP, causing systemic inflammatory response syndrome, and multiorgan failure appeared in the early stage of the disease. After the histogram equalization treatment, the image was clearer than that processed by the other three methods. In terms of CT image smoothing, the effect of the Gaussian filtering was better than the mean filtering effect, and the effect of the median filtering was better than that of the Gaussian filtering. Therefore, the structure of the lungs became clearer, and the lung texture was also clearly displayed, and CT images after histogram equalization have an important value in the diagnosis of lung injury caused by organophosphorus poisoning.

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D. Uppalapati, Nagasubhadra. "Exploring Conventional Approaches for Color Image Denoising: A Comparative Study." International Journal on Recent and Innovation Trends in Computing and Communication 10, no. 11 (2022): 226–37. https://doi.org/10.17762/ijritcc.v10i11.11211.

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Image denoising plays a critical role in enhancing the quality of digital images by removing unwanted noise while preserving important image details. Among various noise types, color image denoising presents unique challenges due to the complex correlation between color channels. This paper explores conventional denoising approaches specifically tailored for color images, focusing on well-established techniques such as median filtering, Gaussian smoothing, bilateral filtering, Non-Local Means (NLM), and wavelet-based denoising. Each method is analyzed for its effectiveness in suppressing noise while maintaining image integrity. We perform a comparative study to evaluate the performance of these techniques across different noise models, including Gaussian, salt-and-pepper, and speckle noise. Objective metrics such as Peak Signal-to-Noise Ratio (PSNR) and Root Mean Square Error (RMSE) are used to assess image quality post-denoising. Our results highlight the strengths and limitations of each method, offering insights into which conventional approaches are most suitable for specific noise types and image content. This comparative analysis serves as a foundation for further research and development of advanced denoising techniques.

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Sari, Ni Larasati Kartika, Maria Oktavianti, and Samsun Samsun. "Analisis Karakter Segmen Abnormal pada Citra Mamografi dengan Menggunakan Berbagai Metode Preprocessing Citra." Jurnal Ilmiah Giga 22, no. 1 (2020): 1. http://dx.doi.org/10.47313/jig.v22i1.737.

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Penelitian ini menganalisis pengaruh penerapan beberapa jenis algoritma preprocessing untuk mencari karakteristik segmen abnormal yang tampak pada citra mamografi. Mamografi merupakan pemeriksaan radiografi khusus payudara. Penerapan algoritma preprocessing yang terdiri dari metode filtering, contrast enhancement, sharpening, dan smoothing diharapkan dapat mengurangi noise dan meningkatkan kontras citra mamografi serta membantu ahli radiologi untuk melakukan diagnosis pada citra. Pada penelitian ini akan digunakan dua algoritma filtering yaitu median filter dan gaussian filter. Selain itu digunakan dua algoritma contrast enhancement yaitu global histogram equalization dan CLAHE (Contrast Limited Adaptive Histogram Equalization). Nilai piksel rata-rata segmen abnormal berkisar antara 206.9-213.3 dan rasio sumbu minor/mayor segmen abnormal berkisar antara 0.5-0.7.Pemilihan jenis metode filter (median filter dan gaussian filter) tidak mempengaruhi hasil nilai piksel rata-rata maupun rasio sumbu minor/mayor dan ukuran segmen abnormal, namun pemilihan jenis metode peningkatan kontras (CLAHE dan global histogram equalization) menghasilkan segmen abnormal dengan ukuran yang berbeda. Metode global histogram equalization menghasilkan segmen abnormal yang tidak dapat dibedakan dengan sekitarnya sehingga hasil ekstrasi segmen terlalu besar.

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KHAN, SAJID, Uzma Sadiq, and Sayyad Khurshid. "Statistical Analysis of Image with Various Noises and Filters." Journal of Information Technology and Computing 1, no. 1 (2020): 41–51. http://dx.doi.org/10.48185/jitc.v1i1.36.

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Research displays an extensive investigation for different factual statistical estimates and their practical implementation in picture handling with various noises and filter channel procedures. Noise is very challenging to take out it from the digital images. The purpose of image filtering is to eliminate the noise from the image in such a way that the new image is detectible. We have clarified different calculations and systems for channel the pictures and which calculation is the best for sifting the picture. Signal and maximum Peak proportion parameters are utilized for execution for factual estimating, Wiener channel performs preferred in evacuating clamor over different channels. Wiener channel functions admirably for a wide range of clamors. The exhibition of Gaussian channel is superior to anything Mean channel, Mask Filter and Wiener channel as per MSE results. In picture setting up, a Gaussian fog generally called Gaussian smoothing is the result of darkening an image by a Gaussian limit. We reason that Gaussian separating approach is the best method that can be effectively actualized with the assistance of the MSE of picture. The Gaussian channel is certifiably superior to different calculations at expelling clamor. The outcomes have been looked at for channels utilizing SNR, PSNR and Mean Square Error esteem.

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Politsch, Collin A., Jessi Cisewski-Kehe, Rupert A. C. Croft, and Larry Wasserman. "Trend filtering – I. A modern statistical tool for time-domain astronomy and astronomical spectroscopy." Monthly Notices of the Royal Astronomical Society 492, no. 3 (2020): 4005–18. http://dx.doi.org/10.1093/mnras/staa106.

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ABSTRACT The problem of denoising a 1D signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly varying intensity that is occasionally interrupted by abrupt dips or spikes. Likewise, in the spectroscopic setting, a noiseless spectrum typically contains intervals of relative smoothness mixed with localized higher frequency components such as emission peaks and absorption lines. In this work, we present trend filtering, a modern non-parametric statistical tool that yields significant improvements in this broad problem space of denoising spatially heterogeneous signals. When the underlying signal is spatially heterogeneous, trend filtering is superior to any statistical estimator that is a linear combination of the observed data – including kernel smoothers, LOESS, smoothing splines, Gaussian process regression, and many other popular methods. Furthermore, the trend filtering estimate can be computed with practical and scalable efficiency via a specialized convex optimization algorithm, e.g. handling sample sizes of n ≳ 107 within a few minutes. In a companion paper, we explicitly demonstrate the broad utility of trend filtering to observational astronomy by carrying out a diverse set of spectroscopic and time-domain analyses.

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Hu, Feng Xu, and Yu Hong Chen. "Image Processing Techniques and Application of Bilateral Filter Keeping Margin Random Noise Suppression." Advanced Materials Research 926-930 (May 2014): 3434–37. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.3434.

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Aiming at image denoising problem, some researchers put forward bilateral filtering algorithm. The algorithm makes weighting for spatial distance and pixel intensity difference. It introduces pixel weighting kernel function on the Gaussian locality smoothing mode, which is more favorable to keep the image margin detail. This paper tries the new improvement on the foundation of bilateral filter technique. It adopts coherent values scanning to treat energy center corresponding apparent dip as smoothing discontinuous geologic body direction. The directivity dramatically reduces, and it is easy to be generalized to non-planar geometrical morphology lineup. And it adopts the method based on waveform self-adaption mode on coherent values estimation. The estimated depending on the time dip and coherent values property are more reliable and physical significance. When calculating pixel value similarity weight, it uses discontinuous geologic body direction sampling point mean or median to replace calculate point. It is much easier to suppress random noise and more effective to keep geologic feature.

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Wu, Xi, Hai-Min Qian, Juan Liao, Liu-Sheng He, and Cheng-Quan Wang. "Bridge Deflection Prediction Based on Cascaded Residual Smoothing and Multiscale Spatiotemporal Attention Network." Applied Sciences 15, no. 6 (2025): 3147. https://doi.org/10.3390/app15063147.

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Bridge deflection values are significant for their health and safety, but current methods for predicting bridge deflection suffer from problems such as anomalous data and low prediction accuracy. To solve the problems of anomalous bias and loss of short-term trend in traditional smoothing methods, this paper proposes a preprocessing method for cascade residual smoothing. The method firstly uses Gaussian filtering to initially remove the high-frequency noise in the signal and retain the overall trend. Then, the residuals of the initial filtering and the original data are smoothed by quadratic exponential smoothing to extract the short-term trend in the deflection data, which is favorable for the data to have the advantages of both stabilization and retention of small fluctuations. In addition, to simultaneously acquire the temporal dependence and spatial features between long- and short-term temporal signals, this paper proposes a multiscale spatial attention network based on Multiscale Convolutional Neural Networks (MSCNNs), Gated Recurrent Units (GRUs), and self-attention (SA). The method obtains multi-level sensory field spatial information within each period through the MSCNN, focuses on the connection between different time steps using a GRU, and employs SA to automatically focus on the deflection features that have a significant impact and ignore unimportant perturbation variations, thus improving the prediction ability of the model. In this paper, compared with CNN-Attention-LSTM, the MAE is reduced by 25.79%, the RMSE is reduced by 24.69%, and the R2 is increased by 2.36%, which proves the superiority and advancement of the method.

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