Proceedings ArticleDOI
Image Denoising Via Learned Dictionaries and Sparse representation
Michael Elad,Michal Aharon +1 more
- Vol. 1, pp 895-900
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TLDR
This work addresses the image denoising problem, where zeromean white and homogeneous Gaussian additive noise should be removed from a given image, by defining a global image prior that forces sparsity over patches in every location in the image.Abstract:
We address the image denoising problem, where zeromean white and homogeneous Gaussian additive noise should be removed from a given image. The approach taken is based on sparse and redundant representations over a trained dictionary. The proposed algorithm denoises the image, while simultaneously trainining a dictionary on its (corrupted) content using the K-SVD algorithm. As the dictionary training algorithm is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm, with state-of-the-art performance, equivalent and sometimes surpassing recently published leading alternative denoising methods.read more
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Book ChapterDOI
On single image scale-up using sparse-representations
TL;DR: This paper deals with the single image scale-up problem using sparse-representation modeling, and assumes a local Sparse-Land model on image patches, serving as regularization, to recover an original image from its blurred and down-scaled noisy version.
Journal ArticleDOI
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
TL;DR: The aim of this paper is to introduce a few key notions and applications connected to sparsity, targeting newcomers interested in either the mathematical aspects of this area or its applications.
Journal ArticleDOI
Sparse Representation for Color Image Restoration
TL;DR: This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to state-of-the-art results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper.
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Journal ArticleDOI
Fields of Experts
Stefan Roth,Michael J. Black +1 more
TL;DR: The approach provides a practical method for learning high-order Markov random field models with potential functions that extend over large pixel neighborhoods with non-linear functions of many linear filter responses.
References
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TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
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De-noising by soft-thresholding
TL;DR: The authors prove two results about this type of estimator that are unprecedented in several ways: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures.
Journal ArticleDOI
$rm K$ -SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
TL;DR: A novel algorithm for adapting dictionaries in order to achieve sparse signal representations, the K-SVD algorithm, an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data.
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.