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—In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcom-plete 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,… (More)

We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are… (More)

- Michal Aharon, Michael Elad, Alfred Bruckstein, Yana Katz
- 2005

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,… (More)

In recent years there is a growing interest in the study of sparse representation for signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Recent activity in this field concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a… (More)

- Michal Aharon, Michael Elad, Alfred M Bruckstein
- 2005

In recent years there is a growing interest in the study of sparse representation for signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described as sparse linear combinations of these atoms. Recent activity in this field concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a… (More)

We address the image denoising problem, where zero-mean 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… (More)

- Michal Aharon, Michael Elad, Alfred M Bruckstein
- 2006

A full-rank under-determined linear system of equations Ax = b has in general infinitely many possible solutions. In recent years there is a growing interest in the sparsest solution of this equation—the one with the fewest non-zero entries, measured by x 0. Such solutions find applications in signal and image processing, where the topic is typically… (More)

Modeling signals by sparse and redundant representations has been drawing considerable attention in recent years. Coupled with the ability to train the dictionary using signal examples, these techniques have been shown to lead to state-of-the-art results in a series of recent applications. In this paper we propose a novel structure of such a model for… (More)

Understanding facial expressions in image sequences is an easy task for humans. Some of us are capable of lipreading by interpreting the motion of the mouth. Automatic lipreading by a computer is a challenging task, with so far limited success. The inverse problem of synthesizing real looking lip movements is also highly non-trivial. Today, the technology… (More)