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1

Novamizanti, Ledya, Irma Safitri, Hafizhan Bhamakerti Arindaka, and Iwan Iwut Tritoasmoro. "Watermarking berbasis Redundant Discrete Wavelet Transform dan Arnold Transform pada Citra Medis." Jurnal Teknik Elektro 13, no. 2 (2021): 48–55. http://dx.doi.org/10.15294/jte.v13i2.31691.

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In telemedicine, data transmission in digital medical images and electronic medical records through the internet is vulnerable to various threats of theft and manipulation. Image watermarking is needed to provide authentication and security to medical images. This paper proposes an image watermarking scheme based on Redundant Discrete Wavelet Transform (RDWT) and Discrete Cosine Transform (DCT) with watermark encryption using Arnold transform. First, the original host medical image was decomposed into four subbands using RDWT. Then, DCT is applied to the LH subband of the RDWT. On the other hand, the watermark is scrambled using Arnold transform to ensure identity security. The singular value of the watermarked image is obtained by modifying the singular value of the host image and the watermark. Tests were carried out on different medical images, namely X-ray, MRI, CT, and ultrasound, with a watermark in a proprietary logo. The host medical image is the same size as the watermark image. The result of this study can provide high authentication, imperceptibility and security in medical images, with an average PSNR value of 65.67 dB, SSIM 1, BER 0, NC 1. This scheme is resistant to JPEG compression, noise addition, filtering, image sharpening, image enhancement, geometric operations, motion blur, image sharpening, and histogram equalization.
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Roa’a M. Al_airaji, Ibtisam A. Aljazaery, and Haider TH Salim ALRikabi. "Adaptive HDR Image Blind Watermarking Approach Based on Redundant Discrete Wavelet Transform." International Journal of Interactive Mobile Technologies (iJIM) 17, no. 10 (2023): 136–54. http://dx.doi.org/10.3991/ijim.v17i10.38795.

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Remarkable success has been recorded in the usage of digital watermarking which is aimed at protecting the intellectual property of multimedia content. In this paper, a new tone mapping attack-resistant high dynamic range (HDR) image zero-watermarking algorithm is proposed. In this algorithm extraction of stable and invariant features are extracted for efficient zero-watermarking through the application of the redundant discrete wavelet transform (RDWT) to the HDR image. The first step involves transforming the HDR image to HVS color space, and RDWT is implemented using the V-channel so that the LL sub-band which contains the strong structure contents of the image is obtained. The second step involves dividing the LL sub-band into non-overlapping blocks, which are afterwards subjected to the process of transformation through the use of the singular value decomposition (SVD) so that the U matrix can be extracted. Third, the use of an Auto-Regressive (AR) prediction technique was employed in generating a local relationship model and comparison is done to facilitate the production of a binary feature mask. In the fourth process, hybrid chaotic mapping (HCM) is used to generate blended watermark so that the security of the watermark can be fortified. Lastly, the computation of an effective zero-watermark is achieved through the implementation of an exclusive-or operation on the blended watermark and the binary feature mask. Based on the results, the approach presented in this study demonstrated superior performance in terms of withstanding TM attacks and other attacks associated with image processing.
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Al-Dossary, Saleh. "Preconditioning seismic data for channel detection." Interpretation 3, no. 1 (2015): T1—T4. http://dx.doi.org/10.1190/int-2014-0031.1.

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Random seismic noise, present in all 3D seismic data sets, hampers manual interpretation by geoscientists and automatic analysis by a computer program. As a result, many noise-suppression techniques have been developed to enhance image quality. Accurately suppressing seismic noise without damaging image details is crucial in preserving small-scale geologic features for channel detection. The automatic detection of channel patterns theoretically should be easy because of their unique spatial signatures and scales, which differentiate them from other common 3D geobodies. For example, one notable channel characteristic has high local linearity: Spatial coherency is much greater in one direction than in other directions. A variety of techniques, such as spatial filters, can be used to enhance this “slender” channel feature in areas of high signal-to-noise ratio (S/N). Unfortunately, these spatial filters may also reduce the edge detectability in areas of low S/N. In this paper, I compared the effectiveness of three noise reduction filters: (1) running average, (2) redundant wavelet transform (RWT), and (3) polynomial fitting. I demonstrated the usefulness of these filters prior to edge detection to enhance channel patterns in seismic data collected from Saudi Arabia. The data examples demonstrated that RWT and polynomial fitting can successfully preserve, enhance, and delineate channel edges that were not visible in conventional seismic amplitude displays, whereas the running average filter further smeared the detectability of channel edges.
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Zhu, Xuan, Xu Feng Zhang, Qiu Ju Li, Ji Yao Tao, and Ben Yuan Li. "A Novel Image Inpainting Method Based on Sparse Decomposition." Applied Mechanics and Materials 738-739 (March 2015): 573–77. http://dx.doi.org/10.4028/www.scientific.net/amm.738-739.573.

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Redundant Discrete Wavelet Transform (RDWT) and Wavelet Atomic Transform (WAT) are proposed in this paper as a couple of dictionaries to get the structure and texture basing on morphological component decomposition. Then, basing on the fact that the structure and texture have different characteristics, in this paper we use curvature driven diffusion model and Criminisi texture synthesis method to inpaint the structure and texture respectively. At last, compound the inpainted structure and texture and get the inpainting result. The experiment results show the new method can not only decompose the image very well, but also inpaint the image with strong and fairing edge, complete and clear texture .This method shows better results in image inpainting compared to the classical ones.
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Gao, Lin, Tiegang Gao, Jie Zhao, and Yonglei Liu. "Reversible Watermarking in Digital Image Using PVO and RDWT." International Journal of Digital Crime and Forensics 10, no. 2 (2018): 40–55. http://dx.doi.org/10.4018/ijdcf.2018040103.

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This article proposed a reversible digital image watermarking scheme using PVO and Redundant Discrete Wavelet Transform (RDWT). The PVO was introduce to the proposed scheme to enhance the embedding capacity. By embedding the watermark in the RDWT coefficients, the proposed scheme exploited the visual masking property of RDWT to achieve better visual quality. Also, the proposed scheme has better performance on embedding capacity because the RDWT has several sub-band coefficients for embedding. The experimental results on natural and medical images suggests that the proposed scheme could meet the demand of perceptional quality with better embedding capacity than former schemes.
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Gao, Lin, Yunjie Zhang, and Guoyan Li. "Reversible Watermarking in Medical Images Using Sub-Sample and Multiple Histogram Modification." Journal of Information Technology Research 13, no. 4 (2020): 75–90. http://dx.doi.org/10.4018/jitr.2020100106.

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This paper proposed a reversible medical image watermarking scheme using multiple histogram modification (MHM) and redundant discrete wavelet transform (RDWT). The MHM was introduced to the proposed scheme to enhance the embedding capacity. By embedding the watermark in the RDWT coefficients, the proposed scheme exploited the visual masking property of RDWT to guarantee the visual quality. Also, the proposed scheme has better performance on embedding capacity because the RDWT has several sub-band coefficients for embedding. The experimental results on medical images suggests that the proposed scheme could meet the demand of perceptional quality with better embedding capacity than former schemes.
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Ren, Dianwei, and Mohamed G. Abdelsalam. "Tracing along-strike structural continuity in the Neoproterozoic Allaqi-Heiani Suture, southern Egypt using principal component analysis (PCA), fast Fourier transform (FFT), and redundant wavelet transform (RWT) of ASTER data." Journal of African Earth Sciences 44, no. 2 (2006): 181–95. http://dx.doi.org/10.1016/j.jafrearsci.2005.10.010.

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Singh, Siddharth, and Tanveer J. Siddiqui. "Robust Image Data Hiding Technique for Copyright Protection." International Journal of Information Security and Privacy 7, no. 2 (2013): 44–56. http://dx.doi.org/10.4018/jisp.2013040103.

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A robust image data-hiding scheme for copyright protection is proposed and simulated. The scheme uses a combination of redundant discrete wavelet transform (RDWT), singular value decomposition (SVD) and spread spectrum technique. The embedding is done by spreading the copyright mark into the singular values of middle frequency sub-bands of RDWT coefficients of the cover image. Chaotic sequence is used for spreading. The use of chaotic sequence and RDWT increases security and robustness of the proposed scheme. Simulation results show that the proposed scheme achieves higher security and robustness against filtering, addition of noise, JPEG compression, sharpening, gamma correction, resizing, rotation, and histogram equalization than other existing techniques for copyright protection.
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Gao, Lin, Tiegang Gao, and Jie Zhao. "Reversible Watermarking in Medical Image Using RDWT and Sub-Sample." International Journal of Digital Crime and Forensics 7, no. 4 (2015): 1–18. http://dx.doi.org/10.4018/ijdcf.2015100101.

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This paper proposed a reversible medical image watermarking scheme using Redundant Discrete Wavelet Transform (RDWT) and sub-sample. To meet the highly demand of the perceptional quality, the proposed scheme embedding the watermark by modifying the RDWT coefficients. The sub-sample scheme is introduced to the proposed scheme for the enhancement of the embedding capacity. Moreover, to meet the need of security, a PWLCM based image encryption algorithm is introduced for encrypting the image after the watermark embedding. The experimental results suggests that the proposed scheme not only meet the highly demand of the perceptional quality, but also have better embedding capacity than former DWT based scheme. Also the encryption scheme could protect the image contents efficiently.
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Subramaniam, Jalab, Ibrahim, and Mohd Noor. "Improved Image Splicing Forgery Detection by Combination of Conformable Focus Measures and Focus Measure Operators Applied on Obtained Redundant Discrete Wavelet Transform Coefficients." Symmetry 11, no. 11 (2019): 1392. http://dx.doi.org/10.3390/sym11111392.

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The image is the best information carrier in the current digital era and the easiest to manipulate. Image manipulation causes the integrity of this information carrier to be ambiguous. The image splicing technique is commonly used to manipulate images by fusing different regions in one image. Over the last decade, it has been confirmed that various structures in science and engineering can be demonstrated more precisely by fractional calculus using integrals or derivative operators. Many fractional-order-based techniques have been used in the image-processing field. Recently, a new specific fractional calculus, called conformable calculus, was delivered. Herein, we employ the combination of conformable focus measures (CFMs), and focus measure operators (FMOs) in obtaining redundant discrete wavelet transform (RDWT) coefficients for improving the image splicing forgery detection. The process of image splicing disorders the content of tampered image and causes abnormality in the image features. The spliced region’s boundaries are usually blurring to avoid detection. To make use of the blurred information, both CFMs and FMOs are used to calculate the degree of blurring of the tampered region’s boundaries for image splicing detection. The two public image datasets IFS-TC and CASIA TIDE V2 are used for evaluation of the proposed method. The obtained results of the proposed method achieved accuracy rate 98.30% for Cb channel on IFS-TC image dataset and 98.60% of the Cb channel on CASIA TIDE V2 with 24-D feature vector. The proposed method exhibited superior results compared with other image splicing detection methods.
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Devi, Kilari Jyothsna, Priyanka Singh, Jatindra Kumar Dash, et al. "A New Robust and Secure 3-Level Digital Image Watermarking Method Based on G-BAT Hybrid Optimization." Mathematics 10, no. 16 (2022): 3015. http://dx.doi.org/10.3390/math10163015.

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This contribution applies tools from the information theory and soft computing (SC) paradigms to the embedding and extraction of watermarks in aerial remote sensing (RS) images to protect copyright. By the time 5G came along, Internet usage had already grown exponentially. Regarding copyright protection, the most important responsibility of the digital image watermarking (DIW) approach is to provide authentication and security for digital content. In this paper, our main goal is to provide authentication and security to aerial RS images transmitted over the Internet by the proposal of a hybrid approach using both the redundant discrete wavelet transform (RDWT) and the singular value decomposition (SVD) schemes for DIW. Specifically, SC is adopted in this work for the numerical optimization of critical parameters. Moreover, 1-level RDWT and SVD are applied on digital cover image and singular matrices of LH and HL sub-bands are selected for watermark embedding. Further selected singular matrices SLH and SHL are split into 3×3 non-overlapping blocks, and diagonal positions are used for watermark embedding. Three-level symmetric encryption with low computational cost is used to ensure higher watermark security. A hybrid grasshopper–BAT (G-BAT) SC-based optimization algorithm is also proposed in order to achieve high quality DIW outcomes, and a broad comparison against other methods in the state-of-the-art is provided. The experimental results have demonstrated that our proposal provides high levels of imperceptibility, robustness, embedding capacity and security when dealing with DIW of aerial RS images, even higher than the state-of-the-art methods.
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Yadav, Arun Singh, Surendra Kumar, Girija Rani Karetla, et al. "A Feature Extraction Using Probabilistic Neural Network and BTFSC-Net Model with Deep Learning for Brain Tumor Classification." Journal of Imaging 9, no. 1 (2022): 10. http://dx.doi.org/10.3390/jimaging9010010.

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Background and Objectives: Brain Tumor Fusion-based Segments and Classification-Non-enhancing tumor (BTFSC-Net) is a hybrid system for classifying brain tumors that combine medical image fusion, segmentation, feature extraction, and classification procedures. Materials and Methods: to reduce noise from medical images, the hybrid probabilistic wiener filter (HPWF) is first applied as a preprocessing step. Then, to combine robust edge analysis (REA) properties in magnetic resonance imaging (MRI) and computed tomography (CT) medical images, a fusion network based on deep learning convolutional neural networks (DLCNN) is developed. Here, the brain images’ slopes and borders are detected using REA. To separate the sick region from the color image, adaptive fuzzy c-means integrated k-means (HFCMIK) clustering is then implemented. To extract hybrid features from the fused image, low-level features based on the redundant discrete wavelet transform (RDWT), empirical color features, and texture characteristics based on the gray-level cooccurrence matrix (GLCM) are also used. Finally, to distinguish between benign and malignant tumors, a deep learning probabilistic neural network (DLPNN) is deployed. Results: according to the findings, the suggested BTFSC-Net model performed better than more traditional preprocessing, fusion, segmentation, and classification techniques. Additionally, 99.21% segmentation accuracy and 99.46% classification accuracy were reached using the proposed BTFSC-Net model. Conclusions: earlier approaches have not performed as well as our presented method for image fusion, segmentation, feature extraction, classification operations, and brain tumor classification. These results illustrate that the designed approach performed more effectively in terms of enhanced quantitative evaluation with better accuracy as well as visual performance.
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Petrov, Miroslav. "Multiscale Spectral Methods for Data Indexing in a Radon Space." Information Technologies and Control 13, no. 3-4 (2015): 2–6. http://dx.doi.org/10.1515/itc-2016-0011.

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Abstract This paper presents three methods for multiscale indexing of the content of projection data of computed tomography images in the CBIR-systems for medical database search. The feature spaces in the developed algorithms have been created by means of, respectively: Discrete Stationary Wavelet Transform (DSWT), Shearlet Transform (ST) and Repagulum Wavelet Transform (RWT). A comparative analysis and assessment of the proposed algorithms have been carried out based on experimental studies with computed tomography images.
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Li, Ning, and Rui Zhou. "Rolling Element Bearing Fault Detection Using Redundant Second Generation Wavelet Packet Transform." Advanced Materials Research 199-200 (February 2011): 931–35. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.931.

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Wavelet transform has been widely used for the vibration signal based rolling element bearing fault detection. However, the problem of aliasing inhering in discrete wavelet transform restricts its further application in this field. To overcome this deficiency, a novel fault detection method for roll element bearing using redundant second generation wavelet packet transform (RSGWPT) is proposed. Because of the absence of the downsampling and upsampling operations in the redundant wavelet transform, the aliasing in each subband signal is alleviated. Consequently, the signal in each subband can be characterized by the extracted features more effectively. The proposed method is applied to analyze the vibration signal measured from a faulty bearing. Testing results confirm that the proposed method is effective in extracting weak fault feature from a complex background.
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YAMAGUCHI, TOMONARI, MITSUHIKO FUJIO, and KATSUHIRO INOUE. "REDUNDANT MORPHOLOGICAL WAVELET AND LOCAL PATTERN SPECTRUM." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (2013): 1360001. http://dx.doi.org/10.1142/s0219691313600011.

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Time-frequency analysis methods such as wavelet analysis are applied to investigate characteristic from non-stationary signals. In this study, we proposed redundant morphological wavelet analysis that was a kind of nonlinear discrete wavelet and redundant wavelet. This method analyzes a transition of shape information from signals in detail since this method keeps property of shift invariance though information of decomposition includes redundancy. Local pattern spectrum which corresponds to nonlinear short time Fourier transform is derived from this nonlinear wavelet. The characteristics of these methods were confirmed by applying to simulation data and actual data.
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Li, X., M. He, and M. Roux. "Multifocus image fusion based on redundant wavelet transform." IET Image Processing 4, no. 4 (2010): 283. http://dx.doi.org/10.1049/iet-ipr.2008.0259.

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Fowler, J. E. "The redundant discrete wavelet transform and additive noise." IEEE Signal Processing Letters 12, no. 9 (2005): 629–32. http://dx.doi.org/10.1109/lsp.2005.853048.

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Zhang, Si Yang, Ri Xin Wang, Yong Bo Li, Min Qiang Xu, and Zi Qian Cui. "The Reciprocating Compressor Fault Analysis Based on ORSGWT." Advanced Materials Research 1037 (October 2014): 125–28. http://dx.doi.org/10.4028/www.scientific.net/amr.1037.125.

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It can be found that the redundant second generation wavelet function had more accurate analysis ability compared with the other wavelets and wavelet packets through simulation signals analyses. The analyses of the industrial signals may be more difficult due to its complex character. The de-noising ability of the redundant second generation wavelet to the industrial noise was confirmed by comparing with wavelet packets. But the signal after de-noising still expresses confused and makes analysis difficult. The optimized redundant second generation wavelet transform (ORSGWT) method was established with Newton interpolation and scale thresholds. Then the fault signals of valve block gap being processed with ORSGWT method were smoother and more apparent about the fault characters comparing with the normal state signals.
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An, Zhi Yong, Pei Qiang Liu, and Hai Lan Jiang. "Dynamic Textures Retrieval Using the Integrated Wavelet-Based Surfacelet Transform." Applied Mechanics and Materials 263-266 (December 2012): 227–30. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.227.

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To reduce the redundancy, a new integrated wavelet-based surfacelet transform(WBST) is proposed. The integrated WBST is constructed by combining the integrated 3D non-redundant wavelet with nonsubsampled directional filter banks. For 3D non-redundant wavelet transform, there are seven high frequency sub-bands and one high frequency sub-bands. Therefore, we design the integrated scheme with three high frequency sub-bands. In order to get the texture-spatial features, 3D local binary pattern (3D LBP) is used to describe the dynamic texture feature of low frequency sub-band. The mean and standard deviation of coefficients in each sub bands can be used as the high frequency features. Experiments show that the proposed algorithm using the integrated WBST outperforms the 3D WT.
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Liu, Jianhua, Peng Geng, and Hongtao Ma. "Multifocus image fusion based on coefficient significance of redundant discrete wavelet transform." Industrial Robot: the international journal of robotics research and application 46, no. 3 (2019): 377–83. http://dx.doi.org/10.1108/ir-11-2018-0229.

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Purpose This study aims to obtain the more precise decision map to fuse the source images by Coefficient significance method. In the area of multifocus image fusion, the better decision map is very important the fusion results. In the processing of distinguishing the well-focus part with blur part in an image, the edge between the parts is more difficult to be processed. Coefficient significance is very effective in generating the better decision map to fuse the multifocus images. Design/methodology/approach The energy of Laplacian is used in the approximation coefficients of redundant discrete wavelet transform. On the other side, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient. Findings Due to the shift-variance of the redundant discrete wavelet and the effectiveness of fusion rule, the presented fusion method is superior to the region energy in harmonic cosine wavelet domain, pixel significance with the cross bilateral filter and multiscale geometry analysis method of Ripplet transform. Originality/value In redundant discrete wavelet domain, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient of source images.
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Shen, Min Fen, Zhi Fei Su, Jin Yao Yang, and Li Sha Sun. "An Image Fusion Algorithm Based on Redundant Wavelet Transform." Applied Mechanics and Materials 687-691 (November 2014): 3656–61. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.3656.

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Because of the limit of the optical lens’s depth, the objects of different distance usually cannot be at the same focus in the same picture, but multi-focus image fusion can obtain fusion image with all goals clear, improving the utilization rate of the image information ,which is helpful to further computer processing. According to the imaging characteristics of multi-focus image, a multi-focus image fusion algorithm based on redundant wavelet transform is proposed in this paper. For different frequency domain of redundant wavelet decomposition, the selection principle of high-frequency coefficients and low-frequency coefficients is respectively discussed .The fusion rule is that,the selection of low frequency coefficient is based on the local area energy, and the high frequency coefficient is based on local variance combining with matching threshold. As can be seen from the simulation results, the method given in the paper is a good way to retain more useful information from the source image , getting a fusion image with all goals clear.
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Brassarote, Gabriela De Oliveira Nascimento, Eniuce Menezes de Souza, and João Francisco Galera Monico. "Multiscale Analysis of GPS Time Series from Non-decimated Wavelet to Investigate the Effects of Ionospheric Scintillation." TEMA (São Carlos) 16, no. 2 (2015): 119. http://dx.doi.org/10.5540/tema.2015.016.02.0119.

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Due to the numerous application possibilities, the theory of wavelets has been applied in several areas of research. The Discrete Wavelet Transform is the most known version. However, the downsampling required for its calculation makes it sensitive to the origin, what is not ideal for some applications,mainly in time series. On the other hand, the Non-Decimated Discrete Wavelet Transform (or Maximum Overlap Discrete Wavelet Transform, Stationary Wavelet Transform, Shift-invariant Discrete Wavelet Transform, Redundant Discrete Wavelet Transform) is shift invariant, because it considers all the elements of the sample, by eliminating the downsampling and, consequently, represents a time series with the same number of coefficients at each scale. In the present paper, the objective is to present the theorical aspects of the a multiscale/multiresolution analysis of non-stationary time series from non-decimated wavelets in terms of its implementation using the same pyramidal algorithm of the decimated wavelet transform. An application with real time series of the effect of the ionospheric scintillation on artificial satellite signals is investigated. With this analysis some information and hidden patterns which can not be detected in the time domain, may therefore be explained in the space-frequency domain.
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van de Walle, A. "Merging Fractal Image Compression and Wavelet Transform Methods." Fractals 05, supp01 (1997): 3–15. http://dx.doi.org/10.1142/s0218348x97000590.

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Fractal image compression and wavelet transform methods can be combined into a single compression scheme by using an iterated function system to generate the wavelet coefficients. The main advantage of this approach is to significantly reduce the tiling artifacts: operating in wavelet space allows range blocks to overlap without introducing redundant coding. Our scheme also permits reconstruction in a finite number of iterations and lets us relax convergence criteria. Moreover, wavelet coefficients provide a natural and efficient way to classify domain blocks in order to shorten compression times. Conventional fractal compression can be seen as a particular case of our general algorithm if we choose the Haar wavelet decomposition. On the other hand, our algorithm gradually reduces to conventional wavelet compression techniques as more and more range blocks fail to be properly approximated by rescaled domain blocks.
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Huang, Bin Wen, and Yuan Jiao. "A New Adaptive Image Denoising Method Based on Wavelet Packet Transform and Neighbor Dependency." Applied Mechanics and Materials 433-435 (October 2013): 301–5. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.301.

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In image processing, removal of noise without blurring the image edges is a difficult problem. Aiming at orthogonal wavelet transform and traditional thresholds shortage, a new adaptive threshold image de-noising method which is based on wavelet packet transform and neighbor dependency is proposed. Low frequency part and high frequency part can be decomposed at the same time in wavelet packet transform and the information contained in wavelet coefficients is redundant. Using this kind of relativity in wavelet packet coefficients, we use a new variance neighbor estimation method and then neighbor dependency adaptive threshold is produced. From the experiment result, we see that compared with traditional methods, this method can not only effectively eliminate noise, but can also well keep original images information and the quality after image de-noising is very well.
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Sharkova, S. B., and V. A. Faerman. "Wavelet transform-based cross-correlation in the time-delay estimation applications." Journal of Physics: Conference Series 2142, no. 1 (2021): 012019. http://dx.doi.org/10.1088/1742-6596/2142/1/012019.

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Abstract The article discusses the application of wavelet analysis for the time-frequency time-delay estimation. The proposed algorithm is wavelet transform-based cross-correlation time delay estimation that applies discrete time wavelet transform to filter the input signal prior to computation of cross-correlation function. The distinguishing feature of the algorithm that it uses the variation of continuous wavelet transform to process the discrete signals instead of dyadic wavelet transform that is normally applied to the case. Another feature that the implication of convolution theorem is used to compute coefficients of the wavelet transform. This makes possible to omit redundant discrete Fourier transforms and significantly reduce the computational complexity. The principal applicability of the proposed method is shown in the course of a computational experiments with artificial and real-world signal. So the method demonstrated expected selectivity for the signals localized in the different frequency bands. The application of the method to practical case of pipeline leak detection was also successful. However, the study concluded that this method provides no specific advantages in comparison with the conventional one. In the future, alternative applications in biological signal processing will be considered.
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B.Mantale, Umesh, and Vishwajit B. Gaikwad. "Image Fusion of Brain Images using Redundant Discrete Wavelet Transform." International Journal of Computer Applications 74, no. 4 (2013): 7–11. http://dx.doi.org/10.5120/12871-8797.

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Bhatnagar, Gaurav, and Q. M. Jonathan Wu. "A new logo watermarking based on redundant fractional wavelet transform." Mathematical and Computer Modelling 58, no. 1-2 (2013): 204–18. http://dx.doi.org/10.1016/j.mcm.2012.06.002.

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Subhedar, Mansi S., and Vijay H. Mankar. "Image steganography using redundant discrete wavelet transform and QR factorization." Computers & Electrical Engineering 54 (August 2016): 406–22. http://dx.doi.org/10.1016/j.compeleceng.2016.04.017.

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Arrais Junior, Ernano, Ricardo Alexandro de Medeiros Valentim, and Glaucio Bezerra Brandao. "Real Time QRS Detection Based on Redundant Discrete Wavelet Transform." IEEE Latin America Transactions 14, no. 4 (2016): 1662–68. http://dx.doi.org/10.1109/tla.2016.7483498.

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Zhao, Wen Jing, Ming Jun Zhao, and Jian Pan. "The Image Compression Technology Based on Wavelet Transform." Advanced Materials Research 1078 (December 2014): 370–74. http://dx.doi.org/10.4028/www.scientific.net/amr.1078.370.

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Image compression is a data compression technology used in the digital image, its purpose is to reduce redundant information of the image data, and provide a more efficient format to store and transmit data. Due to the huge image data and the existing relatively low transport conditions, the image compression has become an inevitable. The key technology of image compression is how to transform image data, how to quantify image data, and how to entropy code the quantized data. Using two-dimensional Mallat image wavelet compression algorithm is a new method of image compression, and it is the core technology of the wavelet image compression.
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Hussain F. Mahdi. "AN EFFICIENT REARRANGEMENT OF DATA FOR GRAY IMAGE COMPRESSION BASED ON WAVELET TRANSFORM." Diyala Journal of Engineering Sciences 4, no. 2 (2011): 29–38. http://dx.doi.org/10.24237/djes.2011.04203.

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In this paper a new method is a proposed for gray image compression based on re-ordering the data of image before applying a wavelet transform. The advantage of converting the color image into luminance-chrominance color space is that the luminance and chrominance components are very much decorrelated between each other. Moreover, the chrominance signals contain much redundant information and can easily be subsampled without sacrificing any visual quality for the reconstructed image
 In this paper a rearrangement of the gray image data is done by dividing it into three components (similar the RGB components of the color image) and convert color space from RGB to YCbCr (Y: luminance, Cb chrominance/blue, and Cr is chrominance/red) then apply wavelet transform. This method can return information more than wavelet method therefore very good result and high PSNR are obtained when it is compared with wavelet transform
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32

FENG, L., C. Y. SUEN, Y. Y. TANG, and L. H. YANG. "EDGE EXTRACTION OF IMAGES BY RECONSTRUCTION USING WAVELET DECOMPOSITION DETAILS AT DIFFERENT RESOLUTION LEVELS." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 06 (2000): 779–93. http://dx.doi.org/10.1142/s0218001400000519.

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This paper describes a novel method for edge feature detection of document images based on wavelet decomposition and reconstruction. By applying the wavelet decomposition technique, a document image becomes a wavelet representation, i.e. the image is decomposed into a set of wavelet approximation coefficients and wavelet detail coefficients. Discarding wavelet approximation, the edge extraction is implemented by means of the wavelet reconstruction technique. In consideration of the mutual frequency, overlapping will occur between wavelet approximation and wavelet details, a multiresolution-edge extraction with respect to an iterative reconstruction procedure is developed to ameliorate the quality of the reconstructed edges in this case. A novel combination of this multiresolution-edge results in clear final edges of the document images. This multi-resolution reconstruction procedure follows a coarser-to-finer searching strategy. The edge feature extraction is accompanied by an energy distribution estimation from which the levels of wavelet decomposition are adaptively controlled. Compared with the scheme of wavelet transform, our method does not incur any redundant operation. Therefore, the computational time and the memory requirement are less than those in wavelet transform.
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33

Li, N., R. Zhou, and X. Z. Zhao. "Mechanical faulty signal denoising using a redundant non-linear second-generation wavelet transform." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 4 (2011): 799–808. http://dx.doi.org/10.1243/09544062jmes2410.

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Denoising and extraction of the weak signals are crucial to mechanical equipment fault diagnostics, especially for early fault detection, in which cases fault features are very weak and masked by the noise. The wavelet transform has been widely used in mechanical faulty signal denoising due to its extraordinary timefrequency representation capability. However, the mechanical faulty signals are often non-stationary, with the structure varying significantly within each scale. Because a single wavelet filter cannot mimic the signal structure of an entire scale, the traditional wavelet-based signal denoising method cannot achieve an ideal effect, and even worse some faulty information of the raw signal may be lost in the denoising process. To overcome this deficiency, a novel mechanical faulty signal denoising method using a redundant non-linear second generation wavelet transform is proposed. In this method, an optimal prediction operator is selected for each transforming sample according to the selection criterion of minimizing each individual prediction error. Consequently, the selected predictor can always fit the local characteristics of the signals. The signal denoising results from both simulated signals and experimental data are presented and both support the proposed method.
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34

G., Thirugnanam, and Arulselvi S. "ICA BASED DIGITAL IMAGE WATERMARKING BASED ON REDUNDANT DISCRETE WAVELET TRANSFORM." ICTACT Journal on Image and Video Processing 02, no. 03 (2012): 375–81. http://dx.doi.org/10.21917/ijivp.2012.0053.

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35

Kittisuwan, Pichid, Sanparith Marukatat, Thitiporn Chanwimaluang, and Widhyakorn Asdornwised. "Image Denoising Employing Two-Sided Gamma Random Vectors with Cycle-Spinning in Wavelet Domain." ECTI Transactions on Electrical Engineering, Electronics, and Communications 9, no. 2 (2009): 255–63. http://dx.doi.org/10.37936/ecti-eec.201192.172503.

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In this work, we present new Bayesian estimator for circularly-contoured Two-Sided Gamma random vector in additive white Gaussian noise (AWGN). This PDF is used in view of the fact that it is more peaked and the tails are heavier to be incorporated in the probabilistic modeling of the wavelet coefficients. One of the cruxes of the Bayesian image denoising methods is to estimate statistical parameters for a shrinkage function. We employ maximum a posterior (MAP) estimation to calculate local variances with Rayleigh density prior for local observed variances and Gaussian distribution for noisy wavelet coefficients. Several denoising methods (ProbShrink with redundant wavelet transform) using undecimated wavelet transforms provide good results. The undecimated wavelet transforms can also be viewed as applying an orthogonal wavelet transform to a set of shifted versions of the signal. This procedure wasfirst suggested by Coifman and Donoho where they termed it cycle-spinning method. We apply cycle spinning with orthogonal wavelet transforms in our work. The experimental results show that the proposed method yields good denoising results.
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36

Addison, Paul S. "Introduction to redundancy rules: the continuous wavelet transform comes of age." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (2018): 20170258. http://dx.doi.org/10.1098/rsta.2017.0258.

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Redundancy: it is a word heavy with connotations of lacking usefulness. I often hear that the rationale for not using the continuous wavelet transform (CWT)—even when it appears most appropriate for the problem at hand—is that it is ‘redundant’. Sometimes the conversation ends there, as if self-explanatory. However, in the context of the CWT, ‘redundant’ is not a pejorative term, it simply refers to a less compact form used to represent the information within the signal. The benefit of this new form—the CWT—is that it allows for intricate structural characteristics of the signal information to be made manifest within the transform space, where it can be more amenable to study: resolution over redundancy. Once the signal information is in CWT form, a range of powerful analysis methods can then be employed for its extraction, interpretation and/or manipulation. This theme issue is intended to provide the reader with an overview of the current state of the art of CWT analysis methods from across a wide range of numerate disciplines, including fluid dynamics, structural mechanics, geophysics, medicine, astronomy and finance. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.
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ARIVAZHAGAN, S., D. GNANADURAI, J. R. ANTONY VANCE, K. M. SAROJINI, and L. GANESAN. "IMPLEMENTATION OF ZERO TREE WAVELET CODERS IN DSP PROCESSOR." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 01 (2004): 75–86. http://dx.doi.org/10.1142/s0219691304000366.

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With the fast evolution of Multimedia systems, Image compression algorithms are very much needed to achieve effective transmission and compact storage by removing the redundant information of the image data. Wavelet transforms have received significant attention, recently, due to their suitability for a number of important signal and image compression applications and the lapped nature of this transform and the computational simplicity, which comes in the form of filter bank implementations. In this paper, the implementation of image compression algorithms based on discrete wavelet transform such as embedded zero tree wavelet (EZW) coder, set partitioning in hierarchical trees coder without lists (SPIHT — No List) and packetizable zero tree wavelet (PZW) coder in DSP processor is dealt in detail and their performance analysis is carried out in terms of different compression ratios, execution timing and for different packet losses. PSNR is used as the criteria for the measurement of reconstructed image quality.
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38

Xiang, Wenzhao, Chang Liu, Hongyang Yu, and Xilin Chen. "Wavelet-Driven Masked Image Modeling: A Path to Efficient Visual Representation." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 8 (2025): 8611–19. https://doi.org/10.1609/aaai.v39i8.32930.

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Masked Image Modeling (MIM) has garnered significant attention in self-supervised learning, thanks to its impressive capacity to learn scalable visual representations tailored for downstream tasks. However, images inherently contain abundant redundant information, leading the pixel-based MIM reconstruction process to focus excessively on finer details such as textures, thus prolonging training times unnecessarily. Addressing this challenge requires a shift towards a compact representation of features during MIM reconstruction. Frequency domain analysis provides a promising avenue for achieving compact image feature representation. In contrast to the commonly used Fourier transform, wavelet transform not only offers frequency information but also preserves spatial characteristics and multi-level features of the image. Additionally, the multi-level decomposition process of wavelet transformation aligns well with the hierarchical architecture of modern neural networks. In this study, we leverage wavelet transform as a tool for efficient representation learning to expedite the training process of MIM. Specifically, we conduct multi-level decomposition of images using wavelet transform, utilizing wavelet coefficients from different levels to construct distinct reconstruction targets representing various frequencies and scales. These reconstruction targets are then integrated into the MIM process, with adjustable weights assigned to prioritize the most crucial information. Extensive experiments demonstrate that our method achieves comparable or superior performance across various downstream tasks while exhibiting higher training efficiency.
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39

Arrais Junior, Ernano, Ricardo Alexsandro de Medeiros Valentim, and Gláucio Bezerra Brandão. "Real-time premature ventricular contractions detection based on Redundant Discrete Wavelet Transform." Research on Biomedical Engineering 34, no. 3 (2018): 187–97. http://dx.doi.org/10.1590/2446-4740.01618.

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40

Zoe M., Fowler, Fowler James E., and Miguel Agnieszka. "Multiresolution DECOLOR for camouflaged moving foreground detection using a redundant wavelet transform." Electronic Imaging 34, no. 14 (2022): 229–1. http://dx.doi.org/10.2352/ei.2022.34.14.coimg-229.

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41

Lai, Zongying, Xiaobo Qu, Yunsong Liu, et al. "Image reconstruction of compressed sensing MRI using graph-based redundant wavelet transform." Medical Image Analysis 27 (January 2016): 93–104. http://dx.doi.org/10.1016/j.media.2015.05.012.

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42

Zhou, Rui, Wen Bao, Ning Li, Xin Huang, and Daren Yu. "Mechanical equipment fault diagnosis based on redundant second generation wavelet packet transform." Digital Signal Processing 20, no. 1 (2010): 276–88. http://dx.doi.org/10.1016/j.dsp.2009.04.005.

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43

LIANG, YANYAN, ZHANCHUAN CAI, DONGXU QI, and ZESHENG TANG. "SCALE-INVARIANT V-TRANSFORM AND ITS APPLICATION TO SIGNAL DE-NOISING." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 05 (2013): 1350038. http://dx.doi.org/10.1142/s0219691313500380.

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An aporia of signal de-noising is that the local signal reconstruction at the singular points. Based on the analysis for the signal singular points, combining signal scaling and orthogonal transform, This paper present a novel method called Scale-Invariant V-Transform (SIVT) for signal de-noising based on V-System, which is polynomial multi-wavelets in invariant set. SIVT employs multiple redundant basis of various scale to suppress the artifacts appearing in the singular points of denoised signal. The test results reveal the SIVT reconstructions exhibit higher visual quality and numerical measurement of SNR than wavelet-based reconstructions. Existing theory of SIVT suggests that these new approaches can perform significantly better than wavelet methods in certain signal reconstruction problems.
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44

Babajanian Bisheh, Hossein, Gholamreza Ghodrati Amiri, and Ehsan Darvishan. "Ensemble Classifiers and Feature-Based Methods for Structural Damage Assessment." Shock and Vibration 2020 (December 19, 2020): 1–14. http://dx.doi.org/10.1155/2020/8899487.

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In this paper, a new structural damage detection framework is proposed based on vibration analysis and pattern recognition, which consists of two stages: (1) signal processing and feature extraction and (2) damage detection by combining the classification result. In the first stage, discriminative features were extracted as a set of proposed descriptors related to the statistical moment of the spectrum and spectral shape properties using five competitive time-frequency techniques including fast S-transform, synchrosqueezed wavelet transform, empirical wavelet transform, wavelet transform, and short-time Fourier transform. Then, forward feature selection was employed to remove the redundant information and select damage features from vibration signals. By applying different classifiers, the capability of the feature sets for damage identification was investigated. In the second stage, ensemble-based classifiers were used to improve the overall performance of damage detection based on individual classifiers and increase the number of detectable damages. The proposed framework was verified by a suite of numerical and full-scale studies (a bridge health monitoring benchmark problem, IASC-ASCE SHM benchmark structure, and a cable-stayed bridge in China). The results showed that the proposed framework was superior to the existing single classifier and could assess the damage with reduced false alarms.
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45

Aghayan, Afshin, Priyank Jaiswal, and Hamid Reza Siahkoohi. "Seismic denoising using the redundant lifting scheme." GEOPHYSICS 81, no. 3 (2016): V249—V260. http://dx.doi.org/10.1190/geo2015-0601.1.

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Separating linear coherent noise, such as ground roll from reflections, remains a key challenge in seismic processing. By adapting the redundant lifting scheme (RLS), a wavelet transform method, to seismic data, we have determined how the wavelet domain can be used to suppress coherent and random noise. The RLS operates on a trace-by-trace basis decomposing each time series into wavelet-coefficient (WC) time series and consequently a single gather (in a shot, receiver, or common depth point domain) into a series of WC subgathers (SGs). The decomposition changes the relative magnitude of WCs of various events (reflection, head wave, ground roll, etc.) from one SG to another without affecting their moveout. In SG(s) in which the WCs of undesired events were significantly stronger than the desired events, the WCs can be surgically muted. Selective muting in carefully chosen SGs attenuates undesired events while having minimal effects on frequency spectra of the desired events. In addition, random noise can be suppressed in the individual SGs by designing a local thresholding mechanism (we have used modified Otsu thresholding) in combination with adaptive Wiener filtering. We have developed this approach of suppressing coherent and random noise in a step-by-step manner first using a synthetic shot gather, followed by demonstration on two real gathers. Our RLS-based denoising method has minimal effects on the lower end of signal frequency spectra, and it could be a valuable tool in a processor’s toolbox when data preconditioning for advanced processing such as waveform inversion, which benefits from low frequencies, is desired.
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46

Padmanabhan, S. Anantha, and Krishna Kumar. "An Efficient Video Compression Encoder Based on Wavelet Lifting Scheme in LSK." Journal of Computational and Theoretical Nanoscience 13, no. 10 (2016): 7581–91. http://dx.doi.org/10.1166/jctn.2016.5756.

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This paper presents a video compression system using wavelet lifting scheme. Video compression algorithms (“codecs”) manipulate video signals to dramatically reduce the storage and bandwidth required while maximizing the perceived video quality. There are four common methods for compression; discrete cosine transforms (DCT), vector quantization (VQ), fractal compression, and discrete wavelet transform (DWT). A gradient based motion estimation algorithm based on shapemotion prediction is used which takes advantage of the correlation between neighboring Binary Alpha Blocks (BABs), to match with the MPEG-4 shape coding case and speed up the estimation process. Then a non-redundant wavelet transform has been implemented as an iterative filter banks with down sampling operations. LSK operates without lists and is suitable for a fast, simple hardware implementation. Here the Set Partitioned Embedded bloCK coder (SPECK) image compression called Improved Listless SPECK (ILSPECK) is used. ILSPECK code a single zero to several insignificant subbands. This reduces the length of the output bit string as well as encoding/decoding time.
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47

Renaud, Olivier, Jean-Luc Starck, and Fionn Murtagh. "Prediction Based on a Multiscale Decomposition." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 02 (2003): 217–32. http://dx.doi.org/10.1142/s0219691303000153.

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A wavelet-based forecasting method for time series is introduced. It is based on a multiple resolution decomposition of the signal, using the redundant "à trous" wavelet transform which has the advantage of being shift-invariant. The result is a decomposition of the signal into a range of frequency scales. The prediction is based on a small number of coefficients on each of these scales. In its simplest form it is a linear prediction based on a wavelet transform of the signal. This method uses sparse modelling, but can be based on coefficients that are summaries or characteristics of large parts of the signal. The lower level of the decomposition can capture the long-range dependencies with only a few coefficients, while the higher levels capture the usual short-term dependencies. We show the convergence of the method towards the optimal prediction in the autoregressive case. The method works well, as shown in simulation studies, and studies involving financial data.
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48

XIE, XIN-PING, XUAN-HAO DING, HONG-QIANG WANG, and YING-CHUN JIANG. "CONTINUOUS WAVELET ANALYSIS OF GENE EXPRESSION SIGNALS FOR CANCER CLASSIFICATION." Journal of Biological Systems 17, no. 03 (2009): 377–96. http://dx.doi.org/10.1142/s0218339009002946.

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This paper proposes a continuous wavelet transform (CWT)-based approach for extracting gene expression patterns associated with cancer. By viewing a particular arrangement of genes as a pseudo-time series and gene expression profile of a patient as a pseud-time signal, CWT can be used to extract hidden expression patterns for cancer classification. Generally, gene expression data are highly redundant and very noisy, and hidden expression patterns play crucial roles for cancer classification rather than any single gene or a simple combination of genes. The CWT can detect consistent patterns in a time-frequency manner, and is more powerful than discrete wavelet transform (DWT) due to the availability of more detail information. Experimental results on four publicly available gene expression datasets show the effectiveness and efficiency of the CWT in extracting useful expression patterns.
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Wang, Yan Yan, Jian Guo Yang, and Zhou Ying Ji. "Study on Gasoline Engine Knock Indicators Based on Wavelet Transform and Rough Set." Advanced Materials Research 651 (January 2013): 625–30. http://dx.doi.org/10.4028/www.scientific.net/amr.651.625.

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In order to improve the knock diagnosis accuracy, knock tests were carried out on a gasoline engine, and the slight knock characteristics from vibration signals of the gasoline engine were extracted by wavelet transform method. Making use of sub-band signals which were generated by wavelet transform of vibration signals as the style signals, 23 time-domain parameters were studied by using rough set theory, and the redundant relationship of the various parameters for describing the knock characteristic was revealed. Finally, the best parameters combination of peak-to-peak value, mean amplitude and mean value was put forward as the knock indicators. The result shows that the indicators obtained by rough set theory can diagnose slight knock combustion, and the diagnostic accuracy is better than single indicator determination knock method.
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50

Ohura, Ryuji, and Teruya Minamoto. "A blind digital image watermarking method based on the dyadic wavelet packet transform and fast interval arithmetic techniques." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 05 (2015): 1550040. http://dx.doi.org/10.1142/s021969131550040x.

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We propose a new digital image watermarking method based on the dyadic wavelet packet transform (DYWPT) and fast interval arithmetic (IA) techniques. Because the DYWPT has a redundant representation, like the dyadic wavelet transform (DYWT), the amount of information that the watermark must contain is greater than in the case of methods based on ordinary discrete wavelet transforms (DWTs) and the discrete wavelet packet transform (DWPT). However, the order of the high frequency components is not necessarily the same as the order of their frequency domain. Therefore, in our approach, we rearrange the order of the high frequency components in descending order of frequency components and embed a watermark selectively into higher frequency components. Our watermark is a ternary-valued logo that is embedded into higher frequency components through use of the DYWPT and fast IA techniques. We describe our watermarking procedure in detail and present experimental results demonstrating that our method produces watermarked images that have better quality and are robust with respect to various types of attacks, including marking, clipping, median filtering, contrast tuning (histeq and imadjust commands in the MATLAB Image Processing Toolbox), addition of Gaussian white noise, addition of salt & pepper noise, JPEG and JPEG 2000 compressions, rotation, and resizing.
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