Proceedings ArticleDOI
Generalized multivariate exponential power prior for wavelet-based multichannel image restoration
Yosra Marnissi,Amel Benazza-Benyahia,Emilie Chouzenoux,Jean-Christophe Pesquet +3 more
- pp 2402-2406
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TLDR
This paper addresses the problem of recovering the image components in a wavelet domain by adopting a variational approach and addresses the challenging issue of computing the Maximum A Posteriori estimate by using a Majorize-Minimize optimization strategy.Abstract:
In multichannel imaging, several observations of the same scene acquired in different spectral ranges are available. Very often, the spectral components are degraded by a blur modelled by a linear operator and an additive noise. In this paper, we address the problem of recovering the image components in a wavelet domain by adopting a variational approach. Our contribution is twofold. First, an appropriate multivariate penalty function is derived from a novel joint prior model of the probability distribution of the wavelet coefficients located at the same spatial position in a given subband through all the channels. Secondly, we address the challenging issue of computing the Maximum A Posteriori estimate by using a Majorize-Minimize optimization strategy. Simulation tests carried out on multispectral satellite images show that the proposed method outperforms conventional techniques.read more
Citations
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Journal ArticleDOI
Sparse Regularization via Convex Analysis
TL;DR: A class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized, and avoids the systematic underestimation characteristic of L1 norm regularization are proposed.
Journal ArticleDOI
Total Variation Denoising via the Moreau Envelope
TL;DR: This letter describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals and involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function.
Journal ArticleDOI
Sparse Signal Approximation via Nonseparable Regularization
Ivan Selesnick,Masoud Farshchian +1 more
TL;DR: A type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization.
Journal ArticleDOI
Total Variation Denoising Via the Moreau Envelope
TL;DR: In this paper, a nonconvex penalty is introduced to maintain the convexity of the cost function, based on the Moreau envelope, which can yield more accurate estimation of piecewise constant signals.
Journal ArticleDOI
Enhanced Sparsity by Non-Separable Regularization
Ivan Selesnick,Ilker Bayram +1 more
TL;DR: An algorithm is presented (an instance of forward-backward splitting) for sparse deconvolution using the new penalty, designed to enable the convex formulation of ill-conditioned linear inverse problems with quadratic data fidelity terms.
References
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Journal ArticleDOI
Ideal spatial adaptation by wavelet shrinkage
TL;DR: In this article, the authors developed a spatially adaptive method, RiskShrink, which works by shrinkage of empirical wavelet coefficients, and achieved a performance within a factor log 2 n of the ideal performance of piecewise polynomial and variable-knot spline methods.
Proceedings ArticleDOI
A non-local algorithm for image denoising
TL;DR: A new measure, the method noise, is proposed, to evaluate and compare the performance of digital image denoising methods, and a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image is proposed.
Journal ArticleDOI
Adapting to Unknown Smoothness via Wavelet Shrinkage
TL;DR: In this article, the authors proposed a smoothness adaptive thresholding procedure, called SureShrink, which is adaptive to the Stein unbiased estimate of risk (sure) for threshold estimates and is near minimax simultaneously over a whole interval of the Besov scale; the size of this interval depends on the choice of mother wavelet.
Journal ArticleDOI
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
L. Sendur,Ivan Selesnick +1 more
TL;DR: This work proposes new non-Gaussian bivariate distributions, and corresponding nonlinear threshold functions (shrinkage functions) are derived from the models using Bayesian estimation theory, but the new shrinkage functions do not assume the independence of wavelet coefficients.
Journal ArticleDOI
Image Compression Using Block Truncation Coding
Edward J. Delp,O. Mitchell +1 more
TL;DR: In this paper, a new technique for image compression called block truncation coding (BTC) is presented and compared with transform and other techniques, which uses a two-level (one-bit) nonparametric quantizer that adapts to local properties of the image.