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K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation (2006)
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BibTeX
@MISC{Aharon06k-svd:an,
author = {Michal Aharon and et al.},
title = {K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation},
year = {2006}
}
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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 u-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 data.
Keyphrases
sparse representation designing overcomplete dictionary training signal u-svd algorithm basis pursuit new method feature extraction inverse problem current dictionary gain-shape vq novel algorithm u-means clustering process recent activity prototype signal-atoms real image data strict sparsity constraint dictionary column linear transforms dictionary atom include compression index term atom decomposition pursuit method prespecified set sparse linear combination overcomplete dictionary vector quantization recent year decompose signal pursuit algorithm sparse coding iterative method synthetic test sparse signal representation
