# $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

@article{Aharon2006rmKA, title={\$rm K\$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation}, author={Michal Aharon and Michael Elad and Alfred Marcel Bruckstein}, journal={IEEE Transactions on Signal Processing}, year={2006}, volume={54}, pages={4311-4322} }

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…

## 7,335 Citations

K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation

- Computer Science
- 2005

A novel algorithm for adapting dictionaries in order to achieve sparse signal representations, K-SVD, 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.

K-SVD and its non-negative variant for dictionary design

- Computer ScienceSPIE Optics + Photonics
- 2005

A simple and yet efficient variation of the K-SVD that handles such extraction of non-negative dictionaries is presented, and its generalization to nonnegative matrix factorization problem that suits signals generated under an additive model with positive atoms is described.

Dictionary Optimization for Block-Sparse Representations

- Computer ScienceIEEE Transactions on Signal Processing
- 2012

This paper proposes an algorithm for learning a block-sparsifying dictionary of a given set of signals that does not require prior knowledge on the association of signals into groups, and develops a method that automatically detects the underlying block structure given the maximal size of those groups.

Orthogonal Procrustes Analysis for Dictionary Learning in Sparse Linear Representation

- Computer SciencePloS one
- 2017

R-SVD is presented, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups and its robustness and wide applicability are confirmed.

Submodular Dictionary Selection for Sparse Representation

- Computer ScienceICML
- 2010

An efficient learning framework to construct signal dictionaries for sparse representation by selecting the dictionary columns from multiple candidate bases is developed and it is shown that if the available dictionary column vectors are incoherent, the objective function satisfies approximate submodularity.

Dictionary design for sparse signal representations using K-SVD with sparse Bayesian learning

- Computer Science2012 IEEE 11th International Conference on Signal Processing
- 2012

This paper proposes to counter this problem by using Sparse Bayesian Learning in the initial stage of the K-SVD algorithm, offering gradual convergence of the learning algorithm from a non-sparse representation of the signals to a sparse representation as the iterations progress, giving the training vectors a good enough chance to “spread out” over the dictionary.

Bayesian K-SVD Using Fast Variational Inference

- Computer ScienceIEEE Transactions on Image Processing
- 2017

A fully-automated Bayesian method is proposed that considers the uncertainty of the estimates and produces a sparse representation of the data without prior information on the number of non-zeros in each representation vector and develops an efficient variational inference framework that reduces computational complexity.

Greedy Dictionary Selection for Sparse Representation

- Computer ScienceIEEE Journal of Selected Topics in Signal Processing
- 2011

An efficient learning framework to construct signal dictionaries for sparse representation by selecting the dictionary columns from multiple candidate bases is developed and it is shown that if the available dictionary column vectors are incoherent, the objective function satisfies approximate submodularity.

K-SVD dictionary-learning for the analysis sparse model

- Computer Science2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2012

The goal is to learn the analysis dictionary from a set of signal examples, and the approach taken is parallel and similar to the one adopted by the K-SVD algorithm that serves the corresponding problem in the synthesis model.

Overcomplete Dictionary Design by Empirical Risk Minimization

- Computer Science
- 2007

This paper presents a new approach for dictionary learning based on minimizing the empirical risk, and offers incorporation of non-injective and nonlinear operators, where the data and the recovered parameters may reside in different spaces.

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