Super-Resolution With Sparse Mixing Estimators
Stéphane Mallat,Guoshen Yu +1 more
TLDR
A class of inverse problem estimators computed by mixing adaptively a family of linear estimators corresponding to different priors corresponding toDifferent priors are introduced, providing state-of-the-art numerical results.Abstract:
We introduce a class of inverse problem estimators computed by mixing adaptively a family of linear estimators corresponding to different priors. Sparse mixing weights are calculated over blocks of coefficients in a frame providing a sparse signal representation. They minimize an l1 norm taking into account the signal regularity in each block. Adaptive directional image interpolations are computed over a wavelet frame with an O(N log N) algorithm, providing state-of-the-art numerical results.read more
Citations
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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
A Survey of Sparse Representation: Algorithms and Applications
TL;DR: A comprehensive overview of sparse representation is provided and an experimentally comparative study of these sparse representation algorithms was presented, which could sufficiently reveal the potential nature of the sparse representation theory.
Journal ArticleDOI
Super-resolution: a comprehensive survey
TL;DR: The current comprehensive survey provides an overview of most of these published works by grouping them in a broad taxonomy, and common issues in super-resolution algorithms, such as imaging models and registration algorithms, optimization of the cost functions employed, dealing with color information, improvement factors, assessment of super- resolution algorithms, and the most commonly employed databases are discussed.
Journal ArticleDOI
Group-based sparse representation for image restoration.
Jian Zhang,Debin Zhao,Wen Gao +2 more
TL;DR: The proposed group-based sparse representation (GSR) is able to sparsely represent natural images in the domain of group, which enforces the intrinsic local sparsity and nonlocal self-similarity of images simultaneously in a unified framework.
Proceedings ArticleDOI
Semi-coupled dictionary learning with applications to image super-resolution and photo-sketch synthesis
TL;DR: The proposed semi-coupled dictionary learning (SCDL) model is applied to image super-resolution and photo-sketch synthesis, and the experimental results validated its generality and effectiveness in cross-style image synthesis.
References
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Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
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TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
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Regularization and variable selection via the elastic net
Hui Zou,Trevor Hastie +1 more
TL;DR: It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.
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Atomic Decomposition by Basis Pursuit
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.
Journal ArticleDOI
Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.