A support vector machine (SvM) with the auto-correlation of a compactly supported wavelet as a kernel is proposed in this paper. The authors prove that this kernel is an admissible support vector kernel. The main adva...
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A support vector machine (SvM) with the auto-correlation of a compactly supported wavelet as a kernel is proposed in this paper. The authors prove that this kernel is an admissible support vector kernel. The main advantage of the auto-correlation of a compactly supported wavelet is that it satisfies the translation invariance property, which is very important for its use in signalprocessing. Also, we can choose a better wavelet by selecting from different wavelet families for our auto-correlation wavelet kernel. This is because for different applications we should choose wavelet filters selectively for the autocorrelation kernel. We should not always select the same wavelet fllters independent of the application, as we demonstrate. Experiments on signal regression and pattern recognition show that this kernel is a feasible kernel for practical applications. (C) 2008 Elsevier B.v. All rights reserved.
25 years after the seminal work of Jean Morlet, the wavelet transform, multiresolution analysis, and other space frequency or space scale approaches are considered standard tools by researchers in imageprocessing, an...
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ISBN:
(纸本)9780819464514
25 years after the seminal work of Jean Morlet, the wavelet transform, multiresolution analysis, and other space frequency or space scale approaches are considered standard tools by researchers in imageprocessing, and many applications have been proposed that point out the interest of these techniques. This paper proposes a review of the recent published works dealing with industrial applications of wavelet and, more generally speaking, multiresolution analysis. More than 180 recent papers are presented.
This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into pred...
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ISBN:
(纸本)0819432997
This paper develops new algorithms for adapted multiscale analysis and signal adaptive wavelet transforms. We construct our adaptive transforms with the lifting scheme, which decomposes the wavelet transform into prediction and update stages. We adapt the prediction stage to the signal structure and design the update stage to preserve the desirable properties of the wavelet transform. The resulting scale and spatially adaptive transforms are extended to the image estimation problem;our new image transforms show improved denoising performance over existing (non-adaptive) orthogonal transforms.
This article presents the construction and various properties of complex Daubechies wavelets with a special emphasis on symmetric solutions. Such solutions exhibit interesting relationships between the real and imagin...
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This article presents the construction and various properties of complex Daubechies wavelets with a special emphasis on symmetric solutions. Such solutions exhibit interesting relationships between the real and imaginary components of the complex scaling function and the complex wavelet. We present those properties in the context of imageprocessing. Within the framework of statistical modelling, we focus on the redundant description of real images given by the complex multiresolution representation. A hierarchical Markovian Graphical model is then explored. We present an Expectation Maximization algorithm for optimizing the model with observational complex wavelet data. This model is then applied to image estimation and texture classification. In both applications, we demonstrate the benefit brought by the Markovian hypothesis and the performance of the real images's complex multiscale representation. (C) 2003 Elsevier B.v. All rights reserved.
Nonlinearities are often encountered in the analysis and processing of real-world signals. This paper develops new signal decompositions for nonlinear analysis and processing. The theory of tensor norms is employed to...
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ISBN:
(纸本)0819422134
Nonlinearities are often encountered in the analysis and processing of real-world signals. This paper develops new signal decompositions for nonlinear analysis and processing. The theory of tensor norms is employed to show that wavelets provide an optimal basis for the nonlinear signal decompositions. The nonlinear signal decompositions are also applied to signalprocessing problems.
作者：
Starck, JLCEA
SEI SAP DAPNIA F-91191 Gif Sur Yvette France
We present in this paper a new way to measure the information in a signal, based on noise modeling. We show that the use of such an entropy-related measure leads to good results for signal restoration.
ISBN:
(纸本)0819432997
We present in this paper a new way to measure the information in a signal, based on noise modeling. We show that the use of such an entropy-related measure leads to good results for signal restoration.
In this contribution a preprocessing technique for information flow control in compressed video sequences is presented. It consists of resolution adaptation in spatial and temporal domains and is based on a wavelet mu...
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ISBN:
(纸本)0819425915
In this contribution a preprocessing technique for information flow control in compressed video sequences is presented. It consists of resolution adaptation in spatial and temporal domains and is based on a wavelet multiresolution representation. The technique allows to reduce information peaks during frames sequences characterized by large motion and to reduce artifacts introduced by coders operating at high compression rates. Extending previous works(1,2), the contribution exploits the decreasing perceptive resolution versus the angular distance from the visual line of sight (foveal zone) providing additional features related to motion activity.
In this paper, an adaptive separable 2D wavelet transform is proposed. wavelet transforms are widely used in signal and imageprocessing due to its energy compaction property. Sparser representation corresponds to bet...
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In this paper, an adaptive separable 2D wavelet transform is proposed. wavelet transforms are widely used in signal and imageprocessing due to its energy compaction property. Sparser representation corresponds to better performance in compression, denoising, compressive sensing, sparse component analysis and many other applications. The proposed scheme results in more compact representation then fixed wavelet. Instead of the commonly used least squares criterion, least absolute deviation (LAD) is introduced. It results in more accurate adaptation resistant to outliers. The advantages of the proposed method have been shown on synthetic and real-world images.
We present a regularized method for wavelet thresholding in a multiresolution framework. For astronomical applications, classical methods perform a standard thresholding by setting to zero non-significant coefficients...
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ISBN:
(纸本)0819425915
We present a regularized method for wavelet thresholding in a multiresolution framework. For astronomical applications, classical methods perform a standard thresholding by setting to zero non-significant coefficients. The regularized thresholding uses a Tikhonov regularization constraint to give a value for the non-significant coefficients. This regularized multiresolution thresholding;is used for various astronomical applications. In image filtering, the significant coefficients are kept, and we compute the new value for each non-significant coefficients according to the regularization constraint. In image compression, only the most significant wavelet coefficients are coded. With lossy compression algorithms such as hcompress, the compressed image has a block-like appearance because of coefficients that are set to zero over large areas. We apply the Tikhonov constraint to restore the coefficients lost during the compression. By this way the distortion is decreasing and the blocking: effect is removed. This regularization applies with any kind of wavelet functions. We compare the performances of the regularized and non-regularized compression algorithms for Haar and spline filters. We show that the point spread function can be used;Is an additional constraint in the restoration of astronomical objects with complex shape. We present a regularized decompression scheme that includes filtering, compression and image deconvolution in a multiresolution framework.
We propose a new image compression scheme based on fractal coding of a wavelet transform coefficients using a fast non-iterative algorithm for the codebook generation. The original image is first decomposed into subba...
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ISBN:
(纸本)0818679204
We propose a new image compression scheme based on fractal coding of a wavelet transform coefficients using a fast non-iterative algorithm for the codebook generation. The original image is first decomposed into subbands containing information indifferent spatial directions and different scales, using an orthogonal wavelet filter bank. Subbands are encoded using local Iterated Function Systems (LIFS) with range and domain blocks presenting horizontal or vertical directionalities. Their sizes are estimated according to the correlation lengths and resolution of each subband. The computational complexity is greatly decreased by using subband decomposition. In addition a fast non-iterative algorithm is implemented for the blocks classification. This algorithm creates progressively the codebook during only one scanning of the training set. We proves the efficiency of the proposed approach both in terms of PSNR/bit rate and computation time.
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