NMF with Sparse Regularizations in Transformed Domains

Published in

SIAM Journal of Imaging Sciences(2014)

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TL;DR

This work shows how a sparse NMF algorithm called nonnegative generalized morphological component analysis (nGMCA) can be extended to impose nonnegativity in the direct domain along with sparsity in a transformed domain, with both analysis and synthesis formulations.

Abstract

Nonnegative blind source separation, which is also referred to as nonnegative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing, and biomedical signal processing. In this context, the efficient retrieval of the sources requires the use of signal priors such as sparsity. Although NMF has been well studied with sparse constraints in the direct domain, only very few algorithms can encompass nonnegativity together with sparsity in a transformed domain since simultaneously dealing with two priors in two different domains is challenging. In this paper, we show how a sparse NMF algorithm called nonnegative generalized morphological component analysis (nGMCA) can be extended to impose nonnegativity in the direct domain along with sparsity in a transformed domain, with both analysis and synthesis formulations. To the best of our knowledge, this work presents the first comparison of analysis and synthesis priors---as well as their reweighted versions---in t...

Authors

Jean-Luc Starck

4 papers

J. Rapin

3 papers

J. Bobin

3 papers

References48 items

Sparse redundant formulations and non-negativity in Blind Source Separation

Sparse and Non-Negative BSS for Noisy Data

A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints

Weighted NMF for high-resolution mass spectrometry analysis

Sparse and unique nonnegative matrix factorization through data preprocessing

NMF with Sparse Regularizations in Transformed Domains

Published in

SIAM Journal of Imaging Sciences(2014)

External Links:

Generate Graph DownloadPDF

TL;DR

Abstract

Authors

Jean-Luc Starck

4 papers

J. Rapin

3 papers

J. Bobin

3 papers

References48 items

Sparse redundant formulations and non-negativity in Blind Source Separation

Sparse and Non-Negative BSS for Noisy Data

A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints

TL;DR

Abstract

Authors

References48 items

Sparse redundant formulations and non-negativity in Blind Source Separation

Sparse and Non-Negative BSS for Noisy Data

A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints

Weighted NMF for high-resolution mass spectrometry analysis

Sparse and unique nonnegative matrix factorization through data preprocessing

TL;DR

Abstract

Authors

References48 items

Sparse redundant formulations and non-negativity in Blind Source Separation

Sparse and Non-Negative BSS for Noisy Data

A new iterative firm-thresholding algorithm for inverse problems with sparsity constraints

Weighted NMF for high-resolution mass spectrometry analysis

Sparse and unique nonnegative matrix factorization through data preprocessing

A Generalized Forward-Backward Splitting

Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization

The Cosparse Analysis Model and Algorithms

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Non-negative Matrix Factorization with Sparseness Constraints

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Sparse Image and Signal Processing: Frontmatter

Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity, by Jean-Luc Starck, Fionn Murtagh, and Jalal M. Fadili

Constrained Nonnegative Matrix Factorization for Hyperspectral Unmixing

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NMF WITH SPARSE REGULARIZATIONS IN TRANSFORMED DOMAINS

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