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Journal articles on the topic 'Optimal wavelet basis (OWB)'

Author: Grafiati

Published: 2 June 2025

Last updated: 5 July 2025

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Anakha, Satheesh P* Dr. D. Loganathan. "DE-SPECKLING OF SAR IMAGES BASED ON OPTIMAL BASIS WAVELET VIA PATCH ORDERING." Global Journal of Engineering Science and Research Management 3, no. 6 (2016): 49–55. https://doi.org/10.5281/zenodo.55960.

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Synthetic Aperture Radar (SAR) technology has mainly used for capturing high quality images from higher altitudes. SAR imagery has become an important application over optical satellite imagery because of its ability to operate in any whether condition. The SAR image acquired via coherent imaging are associated with a noise called speckle noise, which is multiplicative in nature. The presence of speckle noise degrades the quality of SAR image then leads to loss of crucial information. So it has become very important to remove the speckle noise from SAR images using suitable techniques. Many different SAR image-despeckling techniques proposed over past few years. In this paper, proposed a new idea for de-speckling the SAR image to the maximum and the proposed method achieves state-of-the-art de-speckling performance.

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Gu, Xiangping, Mingxue Zhu, and Liyun Zhuang. "Highly Efficient Spatial–Temporal Correlation Basis for 5G IoT Networks." Sensors 21, no. 20 (2021): 6899. http://dx.doi.org/10.3390/s21206899.

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One of the major concerns in 5G IoT networks is that most of the sensor nodes are powered through limited lifetime, which seriously affects the performance of the networks. In this article, Compressive sensing (CS) technique is used to decrease transmission cost in 5G IoT networks. Sparse basis is one of the important steps in the CS. However, most of the existing sparse basis-based method such as DCT (Discrete cosine transform) and DFT (Discrete Fourier Transform) basis do not capture data structure characteristics in the networks. They also do not take into consideration multi-resolution representations. In addition, some of sparse basis-driven methods exploit either spatial or temporal features, resulting in performance degradation of CS-based strategies. To address these challenging problems, we propose a novel spatial–temporal correlation basis algorithm (SCBA). Subsequently, an optimal basis algorithm (OBA) is provided considering greedy scoring criteria. To evaluate the efficiency of OBA, orthogonal wavelet basis algorithm (OWBA) by employing NS (Numerical Sparsity) and GI (Gini Index) sparse metrics is also presented. In addition, we discuss the complexity of the above three algorithms, and prove that OBA has low numerical rank. After experimental evaluation, we found that OBA is capable of the sparsest representing original signal compared to spatial, DCT, haar-1, haar-2, and rbio5.5. Furthermore, OBA has the low recovery error and the highest efficiency.

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He, Can, Jian Chun Xing, and Qi Liang Yang. "Optimal Wavelet Basis Selection for Wavelet Denoising of Structural Vibration Signal." Applied Mechanics and Materials 578-579 (July 2014): 1059–63. http://dx.doi.org/10.4028/www.scientific.net/amm.578-579.1059.

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Wavelet basis selection is an important part in the wavelet denoising of structural vibration signal. However, some defects are present in the existing methods, such as large computation and a single optimal index. In order to solve these problems, a new selection method based on multiple index is proposed in this paper. Firstly, the wavelet basis category which suits for the vibration signal denoising is determined by analyzing the characteristics of wavelet basis and vibration signal. Then, a multiple index evaluation function is constructed by mean square error indicator (MSE), signal-to-noise ratio indicator (SNR) and correlation coefficient indicator (ρ), the weights of index are received by analytic hierarchy process (AHP), the wavelet basis with biggest evaluation function value is considered as optimal wavelet basis. At the end of the paper, a experiment is provided to verify the effectiveness of the new method, the results show that the new method is better than the other four methods in MSE, SNR and ρ index.

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Saini, Manish Kumar, Rajiv Kapoor, Ajai Kumar Singh, and Manisha. "Performance Comparison between Orthogonal, Bi-Orthogonal and Semi- Orthogonal Wavelets." Advanced Materials Research 433-440 (January 2012): 6521–26. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.6521.

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The main work in the wavelet analysis is to find a good wavelet basis to perform an optimal decomposition. The goal of the proposed study is to obtain a basis function that can give optimal information from PQ signal. The study presents the wavelet basis to obtain the reconstruction and decomposition filter coefficients for orthogonal, bi-orthogonal and semi-orthogonal wavelet basis. In this study, the task is to choose better wavelet basis which has been used for PQ signal compression or decomposition among orthogonal, bi-orthogonal and semi-orthogonal wavelet basis. Certain criterion have been adopted to decide the best basis for the decomposition of the PQ signal which are as energy compaction ratio (ECR), absolute mean square error (AMSE), percent residual difference (PRD) and peak signal to noise ratio (PSNR). Numbers of experiments have been performed on real time PQ signal. The comparisons have been made in tabular form to choose the best wavelet basis.

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Wang, Yaming, Jianmin Cheng, Junbao Zheng, Yingli Xiong, and Huaxiong Zhang. "Analysis of wavelet basis selection in optimal trajectory space finding for 3D non-rigid structure from motion." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 03 (2014): 1450023. http://dx.doi.org/10.1142/s0219691314500234.

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Trajectory representation model has been proposed to describe non-rigid deformation. An optimal trajectory space finding algorithm for 3D non-rigid structure from motion (OTSF-NRSFM) based on this model also has been proposed. However, the influence of the wavelet basis selection on the OTSF-NRSFM algorithm has still not been studied. To help OTSF-NRSFM researchers select wavelet basis properly, we investigated the influences of wavelet basis selection. Two typical wavelet bases, DCT basis and WHT basis, are discussed in this paper. The spectrum properties of wavelet basis and feature point trajectory, trajectory representation results on synthetic shark data, OTSF-NRSFM reconstruction results on synthetic data and real data are analyzed. The results show that the wavelet selection has much influence on OTSF-NRSFM reconstruction results of some non-rigid feature points, which have complicated trajectory. This paper gives researchers some inspiration about wavelet basis selection in OTSF-NRSFM algorithm.

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Mahdavi, Seyed Hossein, and Hashim Abdul Razak. "A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/956793.

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Wavelet solution techniques have become the focus of interest among researchers in different disciplines of science and technology. In this paper, implementation of two different wavelet basis functions has been comparatively considered for dynamic analysis of structures. For this aim, computational technique is developed by using free scale of simple Haar wavelet, initially. Later, complex and continuous Chebyshev wavelet basis functions are presented to improve the time history analysis of structures. Free-scaled Chebyshev coefficient matrix and operation of integration are derived to directly approximate displacements of the corresponding system. In addition, stability of responses has been investigated for the proposed algorithm of discrete Haar wavelet compared against continuous Chebyshev wavelet. To demonstrate the validity of the wavelet-based algorithms, aforesaid schemes have been extended to the linear and nonlinear structural dynamics. The effectiveness of free-scaled Chebyshev wavelet has been compared with simple Haar wavelet and two common integration methods. It is deduced that either indirect method proposed for discrete Haar wavelet or direct approach for continuous Chebyshev wavelet is unconditionally stable. Finally, it is concluded that numerical solution is highly benefited by the least computation time involved and high accuracy of response, particularly using low scale of complex Chebyshev wavelet.

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Kai Hu, Aiguo Song, Dan Mao, Ling Tan, and Le Yang. "An Optimal wavelet basis for ECG Compressed Sensing." International Journal of Digital Content Technology and its Applications 7, no. 7 (2013): 594–602. http://dx.doi.org/10.4156/jdcta.vol7.issue7.70.

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Lu, Binjie, and Xiaobing Zhang. "Improved wavelet threshold denoising method for magnetic field signals of magnetic targets." Measurement Science and Technology 36, no. 3 (2025): 036105. https://doi.org/10.1088/1361-6501/adafcc.

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Abstract The presence of complex electromagnetic noise significantly impacts the accuracy of magnetic targets signal detection, necessitating the development of an effective denoising method to enhance detection precision. Nevertheless, traditional denoising methods faces problems such as difficulty in selecting wavelet basis, difficulty in specifying the decomposition level, and unreasonable selection of thresholds. This study introduces improved wavelet threshold denoising based on peak-to-sum ratio and composite evaluation index T, named as (PSR-T-IWTD). PSR-T-IWTD integrates the improved wavelet basis selection method, improved wavelet decomposition level selection method, improved threshold selection method, and improved threshold function design method. Calculate the composite evaluation index T and select the wavelet basis with the smallest T as the optimal wavelet basis. The optimal number of decomposition level is determined by the PSR of the wavelet detail coefficients. An improved threshold selection method and threshold function are introduced to further enhance the performance of wavelet threshold denoising (WTD). Finally, the magnetic field denoising test of the ship model was designed and compared with Butterworth low-pass filter (BLPF), optimal wavelet selection wavelet adaptive threshold denoising (OWSWATD) and improved WTD based on T (T-IWTD) to verify the effectiveness of PSR-T-IWTD. The test results show that PSR-T-IWTD has lower computational complexity. Meanwhile, PSR-T-IWTD improves the signal-to-noise ratio by 10.2%, 6.8% and 8.3% compared to BLPF, OWSWATD and T-IWTD, respectively.

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Zemtsov, A. N. "Multiscale Analysis of High Resolution Digital Elevation Models Using the Wavelet Transform." Scientific Visualization 16, no. 2 (2024): 1–10. http://dx.doi.org/10.26583/sv.16.2.01.

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A technique is proposed for choosing the optimal wavelet basis in terms of decorrelation of the spectral coefficients of the wavelet basis when solving the problem of representation of digital elevation models. In the course of the work, it was revealed that the selection of the spectral transform basis significantly affects the accuracy of the representation of the original model. The proposed method to the decomposition of digital elevation models based on the discrete wavelet transform does not require large computational costs. A technique is proposed for selection the optimal wavelet basis from the position of the minimum mean square error of the reconstructed signal, when quantizing the high-frequency expansion coefficients. Expressions are obtained for generating scaling and wavelet functions in space. The method developed to represent digital elevation models has good properties, which allows to significantly increase the resolution of digital elevation models in the implemented regional geoinformation system.

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Arkhipova, O. V., N. N. Dolgikh, S. Yu Dolinger, V. Z. Kovalev, and D. S. Osipov. "Wavelet transform algorithm of daily load graphs for choosing parameters of hybrid energy storage." Omsk Scientific Bulletin, no. 174 (2020): 57–62. http://dx.doi.org/10.25206/1813-8225-2020-174-57-62.

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The paper presents an algorithm for frequency decomposition of daily load graphs based on a discrete wavelet transform. This algorithm makes it possible to choose the optimal type of wavelet function, optimal level and wavelet decomposition tree. The inverse wavelet transform (recovery) along a single branch of the approximating coefficient allows obtaining the lowfrequency component of the power graph for selecting the optimal mode of the hybrid energy storage battery. The detailing branch of the wavelet coefficients determines the operating mode of the supercapacitor. A numerical experiment is built on the basis of data obtained using certified equipment

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Yang, Sheng Long, Jun Jie Ma, Cui Hua Wang, and Sheng Ma Zhang. "Prediction of Short-Term Transportation Flow Based on Optimizing Wavelet Neural Network by Genetic Algorithm." Advanced Materials Research 694-697 (May 2013): 2715–20. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.2715.

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The weights and the parameter of Wavelet basis of the Wavelet neural network function are always initialized randomly, so the evolution of network tends to be local optima and each forecast results will vary widely. Genetic algorithm is used to optimal the weights and the parameter of Wavelet basis function of the Wavelet neural network, to construct a Wavelet neural network which is on the basis of genetic algorithm. In this paper, we apply this method to forecast short-term time traffic flow, verify with instances, and compare with Wavelet Neural Network Method. The results indicates that this method is not only more stable, but more precise.

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Wang, Yi Cong. "A Discussion on Optimal Wavelet Basis for Data De-Noising of Insulator Leakage Current." Advanced Materials Research 960-961 (June 2014): 851–55. http://dx.doi.org/10.4028/www.scientific.net/amr.960-961.851.

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Insulator leakage current contains important information which can reflect the condition of insulators. However, it is always swallowed by many other noises which hinder us to get precise signals. Wavelet transform is a kind of new method which has been widely used in signal-de-noising because of its good frequency effect. However, suitable wavelet bases should be used to guarantee better effect. In this paper, we compared three groups of wavelet basis: db/coif/sym in hunt for the most relative suitable wavelet basis for insulator leakage current signal. Experiment results prove the conclusion later.

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Low, Yin Fen, and Rosli Besar. "Optimal Wavelet Filters for Medical Image Compression." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 02 (2003): 179–97. http://dx.doi.org/10.1142/s0219691303000128.

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Recently, the wavelet transform has emerged as a cutting edge technology, within the field of image compression research. The basis functions of the wavelet transform are known as wavelets. There are a variety of different wavelet functions to suit the needs of different applications. Among the most popular wavelets are Haar, Daubechies, Coiflet and Biorthogonal, etc. The best wavelets (functions) for medical image compression are widely unknown. The purpose of this paper is to examine and compare the difference in impact and quality of a set of wavelet functions (wavelets) to image quality for implementation in a digitized still medical image compression with different modalities. We used two approaches to the measurement of medical image quality: objectively, using peak signal to noise ratio (PSNR) and subjectively, using perceived image quality. Finally, we defined an optimal wavelet filter for each modality of medical image.

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Wang, Xingjian, Bo Zhang, Fangyu Li, Jie Qi, and Bo Bai. "Seismic time-frequency decomposition by using a hybrid basis-matching pursuit technique." Interpretation 4, no. 2 (2016): T239—T248. http://dx.doi.org/10.1190/int-2015-0208.1.

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Analyzing the time-frequency features of seismic traces plays an important role in seismic stratigraphy analysis and hydrocarbon detection. The current popular time-spectrum analysis methods include short-time Fourier transform, continuous wavelet transform, S-transform, and matching pursuit (MP), among which MP is the most tolerant of the window/scalar effect. However, current MP algorithms do not consider the interfering effects of seismic events on the estimation of optimal wavelets in each decomposition iteration. The interfered reflection seismic events may result in inaccurate estimation of optimal wavelets during the whole decomposition procedure. We have developed a hybrid basis MP workflow to minimize the effect of event interference on the estimation of optimal wavelets. Our algorithm assumes that the wavelet features remain constant in a user-defined small time window. The algorithm begins with identifying the strongest reflection waveform. Next, we estimate the optimal wavelet and the corresponding reflectivity model for the selected waveform by using a basis pursuit algorithm. Then, we subtract the seismic traces from the waveform computed from the optimal wavelet and estimated reflectivity model. We repeat this procedure until the total energy of seismic traces falls below a user-defined value. We have determined the effectiveness of our algorithm by first applying it to a synthetic model and then to a real seismic data set.

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Xu, Hui Qun, and Zhi Xian Gui. "Wavelet Basis Function Optimization and its Application in Carbonate Reservoir Fluid Detection." Applied Mechanics and Materials 318 (May 2013): 263–66. http://dx.doi.org/10.4028/www.scientific.net/amm.318.263.

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he purpose of this paper was to perform optimize the best wavelet basis function and TFA (Time frequency analysis) techniques on a target, in order to provide high-resolution instant spectrum data to help in the fluid detection. Wavelet transform is an effective tool to calculate the frequency. And spectral decomposition technique can depict the frequency characters of seismic reflection that are caused by fluid. In order to optimize the best wavelet basis function, different wavelet basis was tested on a sin model to determine the optimum parameters on the noised-sinusoidal model. Several wavelet bases were tested for the frequency recognition capability on the model, and then the optimum wavelet base function was used in the subset of the seismic data. The optimal wavelet basis was selected to test in the subset of the seismic data, strong amplitude anomaly showed. And so may be use the well-log interpretation result to guarantee that the strong amplitude anomaly have effects at the target.

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HUANG, JEFFREY, and HARRY WECHSLER. "EYE DETECTION USING OPTIMAL WAVELET PACKETS AND RADIAL BASIS FUNCTIONS (RBFs)." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 07 (1999): 1009–25. http://dx.doi.org/10.1142/s0218001499000562.

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The eyes are important facial landmarks, both for image normalization due to their relatively constant interocular distance, and for post processing due to the anchoring on model-based schemes. This paper introduces a novel approach for the eye detection task using optimal wavelet packets for eye representation and Radial Basis Functions (RBFs) for subsequent classification ("labeling") of facial areas as eye versus non-eye regions. Entropy minimization is the driving force behind the derivation of optimal wavelet packets. It decreases the degree of data dispersion and it thus facilitates clustering ("prototyping") and capturing the most significant characteristics of the underlying (eye regions) data. Entropy minimization is thus functionally compatible with the first operational stage of the RBF classifier, that of clustering, and this explains the improved RBF performance on eye detection. Our experiments on the eye detection task prove the merit of this approach as they show that eye images compressed using optimal wavelet packets lead to improved and robust performance of the RBF classifier compared to the case where original raw images are used by the RBF classifier.

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Xie, Haoyu, and Riki Honda. "Arbitrarily Oriented Phase Randomization of Design Ground Motions by Continuous Wavelets." Infrastructures 6, no. 10 (2021): 144. http://dx.doi.org/10.3390/infrastructures6100144.

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For dynamic analysis in seismic design, selection of input ground motions is of huge importance. In the presented scheme, complex Continuous Wavelet Transform (CWT) is utilized to simulate stochastic ground motions from historical records of earthquakes with phase disturbance arbitrarily localized in time-frequency domain. The complex arguments of wavelet coefficients are determined as phase spectrum and an innovative formulation is constructed to improve computational efficiency of inverse wavelet transform with a pair of random complex arguments introduced and make more candidate wavelets available in the article. The proposed methodology is evaluated by numerical simulations on a two-degree-of-freedom system including spectral analysis and dynamic analysis with Shannon wavelet basis and Gabor wavelet basis. The result shows that the presented scheme enables time-frequency range of disturbance in time-frequency domain arbitrarily oriented and complex Shannon wavelet basis is verified as the optimal candidate mother wavelet for the procedure in case of frequency information maintenance with phase perturbation.

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Li, Shuangquan, Shangyi Ma, and Shaoqing Wang. "Optimal Complex Morlet Wavelet Parameters for Quantitative Time-Frequency Analysis of Molecular Vibration." Applied Sciences 13, no. 4 (2023): 2734. http://dx.doi.org/10.3390/app13042734.

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When the complex Morlet function (CMOR) is used as a wavelet basis, it is necessary to select optimal bandwidth and center frequency. However, the method to select the optimal CMOR wavelet parameters for one specific frequency is still unclear. In this paper, we deeply investigate the essence of CMOR wavelet transform and clearly illustrate the time-frequency resolution and edge effect. Then, the selection method of the optimal bandwidth and center frequency is proposed. We further perform the quantitative time-frequency (QTF) analysis of water molecule vibration based on our method. We find that the CMOR wavelet parameters obtained by our method can not only meet the requirement of frequency resolution but also meet the limit of edge effect. Moreover, there is an uphill energy relaxation in the vibration of the water molecule, which agrees well with the experimental results. These results demonstrate that our method can accurately find the optimal CMOR wavelet parameters for the target frequency.

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ČASTOVÁ, NINA, DAVID HORÁK, and ZDENĚK KALÁB. "DESCRIPTION OF SEISMIC EVENTS USING WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (2006): 405–14. http://dx.doi.org/10.1142/s0219691306001336.

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This paper deals with engineering application of wavelet transform for processing of real seismological signals. Methodology for processing of these slight signals using wavelet transform is presented in this paper. Briefly, three basic aims are connected with this procedure:. 1. Selection of optimal wavelet and optimal wavelet basis B opt for selected data set based on minimal entropy: B opt = arg min B E(X,B). The best results were reached by symmetric complex wavelets with scaling coefficients SCD-6. 2. Wavelet packet decomposition and filtration of data using universal criterion of thresholding of the form [Formula: see text], where σ is minimal variance of the sum of packet decomposition of chosen level. 3. Cluster analysis of decomposed data. All programs were elaborated using program MATLAB 5.

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Ouyang, Kewei, Yi Hou, Shilin Zhou, and Ye Zhang. "Adaptive Multi-Scale Wavelet Neural Network for Time Series Classification." Information 12, no. 6 (2021): 252. http://dx.doi.org/10.3390/info12060252.

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Wavelet transform is a well-known multi-resolution tool to analyze the time series in the time-frequency domain. Wavelet basis is diverse but predefined by manual without taking the data into the consideration. Hence, it is a great challenge to select an appropriate wavelet basis to separate the low and high frequency components for the task on the hand. Inspired by the lifting scheme in the second-generation wavelet, the updater and predictor are learned directly from the time series to separate the low and high frequency components of the time series. An adaptive multi-scale wavelet neural network (AMSW-NN) is proposed for time series classification in this paper. First, candidate frequency decompositions are obtained by a multi-scale convolutional neural network in conjunction with a depthwise convolutional neural network. Then, a selector is used to choose the optimal frequency decomposition from the candidates. At last, the optimal frequency decomposition is fed to a classification network to predict the label. A comprehensive experiment is performed on the UCR archive. The results demonstrate that, compared with the classical wavelet transform, AMSW-NN could improve the performance based on different classification networks.

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Setiawan, Iwan, Rachmat Hidayat, Abdul Mahatir Najar, Agus Indra Jaya, and Didi Rosiyadi. "Low-dose computed tomography image denoising using graph wavelet transform with optimal base." International Journal of Electrical and Computer Engineering (IJECE) 15, no. 2 (2025): 1696. https://doi.org/10.11591/ijece.v15i2.pp1696-1708.

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Noise in electronic components of computed tomography (CT) detectors behaves like a virus that infects visual quality of CT scans and might distort clinical diagnosis. Modern CT detector technology incorporates high-quality electronic components in conjunction with signal and image processing to ensure optimal image quality while retaining benign doses of x-rays. In this study, a new strategy in signal and image processing directions is proposed by finding the most optimal wavelet base for denoising low-dose CT scan data. The process begins by selecting the appropriate wavelet bases for CT image denoising, followed by a wavelet decomposition, thresholding, and reconstruction. Other methods, such as graph wavelet and learning-based, are used to assess the consistency of the outcomes. The wavelet base of biorthogonal 5.5 achieves the highest optimum performance for CT image denoising. Meanwhile, the Daubechies wavelet base is inconsistent and performs poorly compared to the optimum base. This research highlights the importance of wavelet properties such as orthogonality, regularity, and the number of vanishing moments in selecting an appropriate wavelet basis for noise reduction in CT images.

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Setiawan, Iwan, Rachmat Hidayat, Abdul Mahatir Najar, Agus Indra Jaya, and Didi Rosiyadi. "Low-dose computed tomography image denoising using graph wavelet transform with optimal base." International Journal of Electrical and Computer Engineering (IJECE) 15, no. 2 (2025): 1696–708. https://doi.org/10.11591/ijece.v15i2.pp1696-1708.

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Jiang, Yuan Yuan, You Ren Wang, and Hui Luo. "Denoising Method for Unknown Image Noise Based on FWT Optimal Order Selection." Advanced Materials Research 765-767 (September 2013): 2776–80. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.2776.

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The optimal fractional order is got for image denoising by 2-D fractional wavelet transform (FWT). But, the actual application environment is complex, and the input image has already been polluted by unknown noise frequently in the process of capture and transmission. And it's impossible to get the optimal fractional order on the basis of the objective evaluation standard in existence. Therefore, in view of the unknown image noise, a method to get the estimated value of optimal fractional order is put forward. Firstly, new objective evaluation standards for image denoising in fractional wavelet domain are defined, and its optimal value is obtained based on noise estimation. Then the optimal estimated fractional order is got. The experiment results show that, the optimal order of 2-D FWT can be selected reasonably by the proposed method and the unknown image noise can be filtered effectively in the estimated optimal fractional wavelet domain.

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Kostashchuk, D. I., and G. M. Mitrofanov. "Optimal wavelet selection under determining of the palaeochannel features." Russian Journal of Geophysical Technologies, no. 3 (December 12, 2024): 74–86. https://doi.org/10.18303/2619-1563-2024-3-74.

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We present the results of the study of attributes, which are values of amplitudes obtained by wavelet decomposition at three fixed frequencies. Such attributes are used for RGB visualization. Comparison of RGB maps constructed using four wavelets: Ricker, Morlet, Gauss, Shannon, allowed us to determine the optimal type of wavelet that provides the best allocation of the paleochannel. The attribute values were also used to quantitatively assess the effective thickness of sediments related to the paleochannel. The results of the predictive estimates constructed on the basis of a linear relationship were compared with the thickness values obtained from wells. When solving this problem, the optimal wavelet was different from the one that provided the best allocation of the paleochannel using RGB technology.

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Yang, Jing Hong, Chang You Wu, and Gui Mei Zhang. "Coal Demand Prediction in Shandong Province Based on Artificial Firefly Wavelet Neural Network." Advanced Materials Research 962-965 (June 2014): 1931–35. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.1931.

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On the basis of the existing research results, after a systematic research of the wavelet neural network model, we found that the slow convergence and easily get into local optimal solutions. To solve this problem, using artificial firefly optimization method to optimize the parameters in wavelet neural network, and Artificial Firefly Wavelet neural network model is established. Apply this model to the Shandong coal demand forecast achieve better results, proved that establishing artificial Firefly Wavelet neural network model is scientific and feasible.

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Nakonechnyi, Adrian, and Ihor Berezhnyi. "The optimal selection of mother wavelet function for analysis remote photoplethysmographic signals." InterConf, no. 50(221) (October 19, 2024): 211–24. http://dx.doi.org/10.51582/interconf.19-20.10.2024.024.

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Analysis of remote photoplethysmography signals is important for non-invasive real-time monitoring of the cardiovascular system. To prevent cardiovascular diseases, it is necessary to predict the disease, support remote medical care and integration with telemedicine. The aim of the work is to analyze the low-quality signal of a remote photoplethysmogram based on a wavelet transformation and selection of the corresponding mother wavelet function. The developed approach provides a wavelet analysis of the remote photoplethysmogram signal by means of the optimal choice of the mother wavelet function, which allows analyzing the cardiovascular system in the frequency-time domain. In accordance with the developed approaches, the approximation of the obtained data to the signals obtained by contact is more than 93% and thus confirms the possibility of using frequency-time signal analysis for remote photoplethysmography. On the basis of the wavelet transform, a principle has been formed that ensures obtaining a true plethysmogram without interference and noise for further study and analysis of the human cardiovascular system.

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Rackov, D. M., M. V. Popovic, and A. Mojsilovic. "On the selection of an optimal wavelet basis for texture characterization." IEEE Transactions on Image Processing 9, no. 12 (2000): 2043–50. http://dx.doi.org/10.1109/83.887972.

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Stutz, Thomas, and Andreas Uhl. "Efficient and Rate-Distortion Optimal Wavelet Packet Basis Selection in JPEG2000." IEEE Transactions on Multimedia 14, no. 2 (2012): 264–77. http://dx.doi.org/10.1109/tmm.2011.2177644.

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Singh, Brij N., and Arvind K. Tiwari. "Optimal selection of wavelet basis function applied to ECG signal denoising." Digital Signal Processing 16, no. 3 (2006): 275–87. http://dx.doi.org/10.1016/j.dsp.2005.12.003.

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Wei, Dong, and Alan C. Bovik. "Enhancement of Compressed Images by Optimal Shift-Invariant Wavelet Packet Basis." Journal of Visual Communication and Image Representation 9, no. 1 (1998): 15–24. http://dx.doi.org/10.1006/jvci.1997.0369.

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Al-Fayadh, Ali Hassan, Hind Rostom Mohammed, and Raghad Sahib Al-shimsah. "Gabor Wavelet Transform in Image Compression." Journal of Kufa for Mathematics and Computer 1, no. 6 (2012): 107–13. https://doi.org/10.31642/jokmc/2018/010613.

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In the present paper, an important mathematical transform which is called Gabor transform be used to develop a method for image compression. Gabor transform is a type of wavelet-based transform. It is embedded in the standard compression algorithm (JPEG2000) as a mother wavelet. Based on the obtained results we believe that Gabor wavelet transform can provide the optimal resolution in both the time and frequency domains, as well as it seems to be the optimal basis to extract local features such as discontinuities. These advantages of Gabor wavelet transform make it an efficient transform for compression.Â The proposed compression system is a new approach that achieves a high compression ratio with acceptable visual quality by exploiting the advantages of Gabor wavelets .The simulation results show that the proposed model gives a good compression images that could be competitive to JPEG2000 using Haar wavelet.

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Hidayat, Syahroni, Habib Ratu P. N., and Danang Tejo Kumoro. "Determination of the Optimum Wavelet Basis Function for Indonesian Vowel Voice Recognition." Jurnal Elektronika dan Telekomunikasi 17, no. 2 (2017): 42. http://dx.doi.org/10.14203/jet.v17.42-47.

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Nowadays, wavelet has been widely applied in extracting features of the signal for automatic speech recognition system. Wavelets have many families that are determined by their mother function and order. The use of different wavelets to analyze the same signal would bring different results. In many cases, a trial and error procedure is used to select the optimal wavelet family. That is because there are no particular wavelet basis functions that can be applied to the entire speech signals. Therefore, it is necessary to analyze the similarity between the speech signal and the wavelet base function. One of the methods that can be used is cross-correlation. In this study, the degree of correlation is determined between wavelet base function and Indonesian vowels. The influence of gender and consistencies of the results are also used in the analysis. The results show that db45 and db44 are most similar to male and female vowels utterance, respectively. For consistencies, only vowel e gives a consistent result. Overall, db44 is most similar to all Indonesian vowels utterance.

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Zhong, Jian Jun, Sheng Nan Fang, and Chang Ying Linghu. "Research on Application of Wavelet Denoising Method Based on Signal to Noise Ratio in the Bench Test." Applied Mechanics and Materials 457-458 (October 2013): 1156–62. http://dx.doi.org/10.4028/www.scientific.net/amm.457-458.1156.

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During the tests of the vehicle automatic transmission bench, the acceleration signal is needed to be denoised. As a means of denoising, wavelet threshold denoising method has small amount of calculation and better filtering effect. However, adopting different wavelet basis functions as well as different threshold rules might have a direct effect on the signal denoising. In this paper, we firstly construct the simulated noisy signal approximated to the observed signal, and then do the signal denoising experiment of parameter matching. Secondly, seven Symlets wavelet basis functions and four classical wavelet threshold rules are selected and tested one by one. Signal to noise ratio (SNR) and root mean square error (RMSE) of the denoised signal, the evaluation indicators, are calculated and carried out in accordance with the merits of denoising effect. Thus the optimal combination of the fixed threshold rule and sym8 wavelet basis function is obtained. Finally, this combination is used in the bench test to denoise the angular acceleration signal, and good filtering effect is achieved.

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Bhavsar, Jignesh, Amrutbhai Patel, and Kalpesh Patel. "Improved Sparse Representation of Image from Inferred Angles of Steerable Wavelet." Indian Journal Of Science And Technology 17, no. 26 (2024): 2698–707. http://dx.doi.org/10.17485/ijst/v17i26.1385.

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Objectives: Presenting images with sparse coefficients has a wide variety of real-time applications in compressive sensing. However, sparse representations of images present challenges due hidden similarities in the higher order moments. Literature suggests that the applications that involve natural images present a high level of similarity. Steerable basis, due to their rotational invariant property, have shown potential in sparse representation of natural images. Hence, the objective of the proposed study is to identify steerable basis that maximize the sparse representation of natural images. Method: Prior studies have used the angle of steerable basis either from the random assignment or derived from Hough transform. In this study, we propose the selection of steerable basis angle derived from maximum a prior method. Exploiting a steerable basis for better sparse representation requires the knowledge of proper steerable angles. Hence, we propose using MAP learning approach to identify this angle. Findings: The proposed method resulted in optimal steerable angle without the need for calculation of Hough Transform. In addition, the method also resulted in almost 10 percent improvement in sparse representation as indicated by higher Kurtosis. Novelty: We compare the measure of sparsity to evaluate the effectiveness of the proposed method. The results indicate the optimal sparsity from the proposed method as indicated from the maximum values of kurtosis compared to the previous related methods. In addition, the proposed method relaxes the requirement of manipulating Hough transform for optimal steerable angle. Keywords: Sparsity, Steerable Basis, Wavelet Pyramid Structure, Image Compression, Hough Transform

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Voskoboinikov, Yuri E. "А locally adaptive wavelet filtering algorithm for images". Analysis and data processing systems, № 1 (29 березня 2023): 25–36. http://dx.doi.org/10.17212/2782-2001-2023-1-25-36.

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The algorithms based on the decomposition of a noisy image in an orthogonal basis of wavelet functions have been widely used to filter images (especially contrasting ones) over the past four decades. In this case, most wavelet filtering algorithms are of a threshold nature, namely: the decomposition coefficient smaller in an absolute value of a certain threshold value is reset to zero; otherwise the coefficient undergoes some (most often nonlinear) transformation. A certain (and very significant) drawback of threshold algorithms is that all coefficients of a certain decomposition level are processed with one identical threshold value (i.e., a constant value for all de-composition coefficients). This does not allow taking into account the “individual energy” of each decomposition coefficient for its more optimal processing. Therefore, we propose its own filtering factor for each coefficient, built on the basis of the optimal Wiener filtering and where a filtering parameter is introduced to compensate for incomplete a priori information on the value of the processed decomposition coefficients. In order to select a filtering parameter, a statistical approach has been proposed that makes it possible to estimate the optimal value of this parameter with acceptable accuracy. The performed computational experiment has shown the developed algorithm effectiveness for wavelet filtering of images.

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Jignesh, Bhavsar, Patel Amrutbhai, and Patel Kalpesh. "Improved Sparse Representation of Image from Inferred Angles of Steerable Wavelet." Indian Journal of Science and Technology 17, no. 26 (2024): 2698–707. https://doi.org/10.17485/IJST/v17i26.1385.

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Abstract Objectives: Presenting images with sparse coefficients has a wide variety of real-time applications in compressive sensing. However, sparse representations of images present challenges due hidden similarities in the higher order moments. Literature suggests that the applications that involve natural images present a high level of similarity. Steerable basis, due to their rotational invariant property, have shown potential in sparse representation of natural images. Hence, the objective of the proposed study is to identify steerable basis that maximize the sparse representation of natural images. Method: Prior studies have used the angle of steerable basis either from the random assignment or derived from Hough transform. In this study, we propose the selection of steerable basis angle derived from maximum a prior method. Exploiting a steerable basis for better sparse representation requires the knowledge of proper steerable angles. Hence, we propose using MAP learning approach to identify this angle. Findings: The proposed method resulted in optimal steerable angle without the need for calculation of Hough Transform. In addition, the method also resulted in almost 10 percent improvement in sparse representation as indicated by higher Kurtosis. Novelty: We compare the measure of sparsity to evaluate the effectiveness of the proposed method. The results indicate the optimal sparsity from the proposed method as indicated from the maximum values of kurtosis compared to the previous related methods. In addition, the proposed method relaxes the requirement of manipulating Hough transform for optimal steerable angle. Keywords: Sparsity, Steerable Basis, Wavelet Pyramid Structure, Image Compression, Hough Transform

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Gu, Yajing, and Yuanguo Zhu. "Optimal Control for Parabolic Uncertain System Based on Wavelet Transformation." Axioms 11, no. 9 (2022): 453. http://dx.doi.org/10.3390/axioms11090453.

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In this paper, we study a new type of optimal control problem subject to a parabolic uncertain partial differential equation where the expected value criterion is adopted in the objective function. The basic idea of Haar wavelet transformation is to transform the proposed problem into an approximate uncertain optimal control problem with arbitrary accuracy because the dimension of Haar basis tends to infinity. The relative convergence theorem is proved. An application to an optimal control problem with an uncertain heat equation is dealt with to illustrate the efficiency of the proposed method.

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Zhang, Zhong, Jin Ohtaki, Hiroshi Toda, Takashi Imamura, and Tetsuo Miyake. "A novel variable filter band discrete wavelet transform: Application." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (2014): 1460007. http://dx.doi.org/10.1142/s0219691314600078.

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In this study, in order to verify the effectiveness of the variable filter band discrete wavelet transform (VFB-DWT) and construction method of the variable-band filter (VBF), a fetal ECG extraction has been carried out and the main results obtained are as follows. The approach to configuration VBF by selecting the frequency band only where the fetal ECG component is present was effective to configure the optimal base sensible signal. The extraction of the fetal ECG was successful by applying the wavelet shrinkage to VFB-DWT, which used the constructed VBF. The information entropy was selected as an evaluation index, and two kinds of ECG signals are used to evaluate the wavelet transform basis between the wavelet packet transform (WPT) and the VFB-DWT. One is a synthesized signal composed of white noise, the maternal ECG and the fetal ECG. The other signal is the real target signal separated by independent component analysis (ICA) and has the mother's body noise, the maternal ECG and the fetal ECG. The result shows that the basis by VBF of the VFB-DWT is better than the basis of the WPT that was chosen by the best basis algorithm (BBA).

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Yu, Zhentao, Jie Chen, Baoqiang Zhang, Dan Wang, and Hao Jiang. "Selection Method of Optimal Wavelet Basis Function for Aeromagnetic Anomaly Signal Processing." Journal of Coastal Research 115, sp1 (2020): 530. http://dx.doi.org/10.2112/jcr-si115-145.1.

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WENG, Hao, and Jinji GAO. "Wavelet Packet Basis Optimal Selection in Compressing Vibration Signals of a Gearbox." Recent Patents on Computer Science 6, no. 3 (2013): 218–26. http://dx.doi.org/10.2174/22132759113069990010.

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Goldschneider, J. R., and E. A. Riskin. "Optimal bit allocation and best-basis selection for wavelet packets and TSVQ." IEEE Transactions on Image Processing 8, no. 9 (1999): 1305–9. http://dx.doi.org/10.1109/83.784444.

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PONT, ORIOL, ANTONIO TURIEL, and CONRAD J. PÉREZ-VICENTE. "ON OPTIMAL WAVELET BASES FOR THE REALIZATION OF MICROCANONICAL CASCADE PROCESSES." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (2011): 35–61. http://dx.doi.org/10.1142/s0219691311003943.

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Multiplicative cascades are often used to represent the structure of turbulence. Under the action of a multiplicative cascade, the relevant variables of the system can be understood as the result of a successive transfer of information in cascade from large to small scales. However, to make this cascade transfer explicit (i.e. being able to decompose each variable as the product of larger scale contributions) is only achieved when signals are represented in an optimal wavelet basis. Finding such a basis is a data-demanding, highly-complex task. In this paper, we propose a formalism that allows to find the optimal wavelet of a signal in an efficient, little data-demanding way. We confirm the appropriateness of this approach by analyzing the results on synthetic signals constructed with prescribed optimal bases. We show the validity of our approach constrained to given families of wavelets, though it can be generalized for a continuous unconstrained search scheme.

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Cheng, Liwei, Duanling Li, Xiang Li, and Shuyue Yu. "The Optimal Wavelet Basis Function Selection in Feature Extraction of Motor Imagery Electroencephalogram Based on Wavelet Packet Transformation." IEEE Access 7 (2019): 174465–81. http://dx.doi.org/10.1109/access.2019.2953972.

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Zhao, Kai, Ben Wei Li, and Jing Chen. "Study on the Method of Vibration Signal De-Noising Using Wavelet Packet Based on QPSO." Applied Mechanics and Materials 599-601 (August 2014): 1738–44. http://dx.doi.org/10.4028/www.scientific.net/amm.599-601.1738.

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Although many wavelet de-noising methods have been studied and proposed, the parameters of them are obtained by experience mostly, which makes the de-noising effect instable. To solve the issues, the solutions, such as the selection of wavelet function and threshold function, the calculation of decomposition levels, the optimal wavelet packet basis and the thresholds obtained based on QPSO, have been studied in this paper. Every parameter is obtained by calculation. This method is applied to the de-noising experiment of sine and vibration signals. Through the experimental verification, the effect of this de-noising method is obvious.

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Salankar, Nilima, Sangita B. Nemade, and Varsha P. Gaikwad. "Classification of seizure and seizure free EEG signals using optimal mother wavelet and relative power." Indonesian Journal of Electrical Engineering and Computer Science 20, no. 1 (2020): 197. http://dx.doi.org/10.11591/ijeecs.v20.i1.pp197-205.

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This paper presents an approach for the selection of mother wavelet for classification of EEG epilepsy signals .Wavelet transform is very popular for analyzing signals in time and frequency domain. But as there are various wavelet families exist and not a one fits to all, in this study author have experimented with 51 wavelets from six different families Haar(haar), Daubechies(Db), Symlet(Sym), Coiflets(Coif), Biorthogonal(Bior) and Discrete Meyer(Dmey). Optimal mother wavelet is selected on the basis of highest correlation between input signal and reconstructed signal. With Discrete wavelet transform four levels of decomposition have been used to create the five EEG rhythms delta, theta, alpha, beta and gamma. Five features kurtosis, skew, mean, standard deviation and relative power have been extracted from each decomposed level by using the optimal mother wavelet. Statistical significance of the extracted features has been computed by Mann Whitney U test with significance level p&lt;0.05 and statistical parameters sensitivity, specificity and accuracy for performance evaluation of the classifier have been computed. Results shown that out of six experimented wavelet families, five families with eight wavelets have qualified the correlation test. Out of five extracted feature relative power is more statistically significant for all type of classification and all EEG bands .Classifier used is support vector machine and accuracy of classifier lies in the range of 74% to 100 % for 14 classifications between different subsets.

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Nilima, Salankar, B. Nemade Sangita, and P. Gaikwad Varsha. "Classification of seizure and seizure free EEG signals using optimal mother wavelet and relative power." Indonesian Journal of Electrical Engineering and Computer Science 20, no. 1 (2020): 197–205. https://doi.org/10.11591/ijeecs.v20.i1.pp197-205.

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This paper presents an approach for the selection of mother wavelet for classification of EEG epilepsy signals. Wavelet transform is very popular for analyzing signals in time and frequency domain. But as there are various wavelet families exist and not a one fits to all, in this study author have experimented with 51 wavelets from six different families Haar(haar), Daubechies(Db), Symlet(Sym), Coiflets(Coif), Biorthogonal(Bior) and Discrete Meyer(Dmey). Optimal mother wavelet is selected on the basis of highest correlation between input signal and reconstructed signal. With Discrete wavelet transform four levels of decomposition have been used to create the five EEG rhythms delta, theta, alpha, beta and gamma. Five features kurtosis, skew, mean, standard deviation and relative power have been extracted from each decomposed level by using the optimal mother wavelet. Statistical significance of the extracted features has been computed by Mann Whitney U test with significance level p<0.05 and statistical parameters sensitivity, specificity and accuracy for performance evaluation of the classifier have been computed. Results shown that out of six experimented wavelet families, five families with eight wavelets have qualified the correlation test. Out of five extracted feature relative power is more statistically significant for all type of classification and all EEG bands. Classifier used is support vector machine and accuracy of classifier lies in the range of 74% to 100 % for 14 classifications between different subsets.

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Idris, Rasyidah, and Nadzir Anas Lim. "Optimal Methods for Fault Detection and Classification." ELEKTRIKA- Journal of Electrical Engineering 22, no. 1 (2023): 75–82. http://dx.doi.org/10.11113/elektrika.v22n1.439.

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Detecting fault in transmission line is very important in order to have a well-functioned power system. This is due to the fact that the system will be distorted if there is fault in the transmission line. Occurrence of fault causes the significant difference in terms of the value of current or voltage in the system. There are a few approaches that can be used in order to detect and classify fault in the transmission line. Two methods of fault detection and classification have been used to be analyzed in order to identify both method accuracy and reliability. The two methods are the Wavelet Transform method and the Fuzzy Logic based method. Both methods show their own advantages and disadvantages after simulation have been done. These methods are later being utilized by combining both to create a better version of fault detection and classification method. In this paper, a combined method of Wavelet Transform and Fuzzy Logic based for fault detection and classification model for power systems is developed and simulated. This combined method is later compared to other method under the same category but different perspective and aspect namely the Radial Basis Function Neural Network. Fuzzy Logic Based method and Radial Basis Function Neural Network falls under Artificial Intelligence category for fault classification method. However, the approach used for both method is significantly different.

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Moradi, L., F. Mohammadi, and D. Baleanu. "A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets." Journal of Vibration and Control 25, no. 2 (2018): 310–24. http://dx.doi.org/10.1177/1077546318777338.

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The aim of the present study is to present a numerical algorithm for solving time-delay fractional optimal control problems (TDFOCPs). First, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet functions and their properties are implemented to derive some operational matrices. Then, the fractional derivative of the state function in the dynamic constraint of TDFOCPs is approximated by means of the Chelyshkov wavelets. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration TDFOCPs into an algebraic system. Moreover, some illustrative examples are considered and the obtained numerical results were compared with those previously published in the literature.

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Lavrynenko, Oleksandr, Denys Bakhtiiarov, Georgiy Konakhovych, and Vitalii Kurushkin. "Method for Adaptive Wavelet Filtering of Speech Signals Based on Daubechies Filters with Minimization of Errors in Finding Optimal Thresholds." Electronics and Control Systems 3, no. 77 (2023): 60–68. http://dx.doi.org/10.18372/1990-5548.77.18005.

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The paper deals with the problem of adaptive wavelet filtering of speech signals based on Daubechies filters with minimization of errors in finding optimal threshold values. This approach is similar to estimating a speech signal by averaging it using a kernel that is locally adapted to the smoothness of the signal. In this case, a set of coupled mirror filters decomposes the speech signal in a discrete domain according to the orthogonal Daubechies wavelet basis into several frequency bands. Noise removal of speech signals is performed as a complete cutoff of the wavelet transform coefficients based on the assumption that their small amplitude values are noise. Thus, in the Daubechies wavelet basis, where coefficients with large amplitude correspond to abrupt changes in the speech signal, such processing preserves only the intermittent components originating from the input speech signal without adding other components caused by noise. In general, by equating small coefficients to zero, we perform adaptive smoothing that depends on the smoothness of the input speech signal. By keeping the coefficients of large amplitude, we avoid smoothing out sharp drops and preserve local features. Performing this procedure on several scales leads to a gradual reduction of the noise effect on both piecewise smooth and discontinuous parts of the speech signal. In view of this, the main task of the study is to adaptively generate micro-local thresholds, which will reduce the impact of additive noise on the pure form of the speech signal, and preserve significant wavelet coefficients of large amplitude that characterize the local features of the speech signal. Thus, as a result of our work, we have proved the feasibility of developing the presented method of wavelet filtering of speech signals with adaptive thresholds based on Daubechies wavelet analysis, which minimizes the loss of speech intelligibility and allows for noise removal depending on the properties and physical nature of the processed data.

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Zadiraka, Valeriy, Liliya Luts, and Inna Shvidchenko. "Invariants of optimal integration of rapidly oscillatory functions." Physico-mathematical modelling and informational technologies, no. 32 (July 8, 2021): 121–25. http://dx.doi.org/10.15407/fmmit2021.32.121.

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The paper presents some common elements (invariants) of optimal integration of rapidly oscillatory functions for the different types of oscillations, in particular, for calculating the Fourier transform from finite functions, wavelet transform, and Bessel transform. Their brief description is given. The application of the invariants allows to increase the potential of quadrature formulas due to the fullest use of apriori information. Invariants form the basis of computer technology of integration of rapidly oscillatory functions with a given accuracy with limited computational resources.

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