Journal ArticleDOI
$rm K$ -SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
TLDR
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.Abstract:
In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is 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. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image dataread more
Citations
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Image Super-Resolution Using Deep Convolutional Networks
TL;DR: Zhang et al. as discussed by the authors proposed a deep learning method for single image super-resolution (SR), which directly learns an end-to-end mapping between the low/high-resolution images.
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Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
Michael Elad,Michal Aharon +1 more
TL;DR: This work addresses the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image, and uses the K-SVD algorithm to obtain a dictionary that describes the image content effectively.
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Image Super-Resolution Via Sparse Representation
TL;DR: This paper presents a new approach to single-image superresolution, based upon sparse signal representation, which generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods.
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Learning a Deep Convolutional Network for Image Super-Resolution
TL;DR: This work proposes a deep learning method for single image super-resolution (SR) that directly learns an end-to-end mapping between the low/high-resolution images and shows that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network.
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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.
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Journal ArticleDOI
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.
Journal ArticleDOI
An information-maximization approach to blind separation and blind deconvolution
TL;DR: It is suggested that information maximization provides a unifying framework for problems in "blind" signal processing and dependencies of information transfer on time delays are derived.
Book
Vector Quantization and Signal Compression
Allen Gersho,Robert M. Gray +1 more
TL;DR: The author explains the design and implementation of the Levinson-Durbin Algorithm, which automates the very labor-intensive and therefore time-heavy and expensive process of designing and implementing a Quantizer.