NMF with Sparse Regularizations in Transformed Domains (2014-07-29T00:00:00.000000Z)

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

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

A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

Bregman iteration algorithm for sparse nonnegative matrix factorizations via alternating l1-norm minimization

Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing

Nonnegative Matrix and Tensor Factorizations - Applications to Exploratory Multi-way Data Analysis and Blind Source Separation

Signal restoration with overcomplete wavelet transforms: comparison of analysis and synthesis priors

Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis

Blind Source Separation: the Sparsity Revolution

Enhancing Sparsity by Reweighted ℓ1 Minimization

Sparsity and Morphological Diversity in Blind Source Separation

Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization

On the Complexity of Nonnegative Matrix Factorization

Nonnegative matrix factorization with constrained second-order optimization

Regularized Alternating Least Squares Algorithms for Non-negative Matrix/Tensor Factorization

Monaural Sound Source Separation by Nonnegative Matrix Factorization With Temporal Continuity and Sparseness Criteria

Analysis versus synthesis in signal priors

Performance measurement in blind audio source separation

Email Surveillance Using Non-negative Matrix Factorization

Non-negative Matrix Factorization with Sparseness Constraints

Sparse coding and NMF

Sparse Representation and Its Applications in Blind Source Separation

Non-negative sparse coding

Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization

Learning the parts of objects by non-negative matrix factorization

Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values†

Singularity detection and processing with wavelets

Advances In Imaging And Electron Physics

Sparse Regularizations and Non-negativity in BSS

A rst-order primal-dual algorithm for convex problems with applications to imaging

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

Sparse Nonnegative Matrix Factorization for Clustering

Blind Image Separation Using Nonnegative Matrix Factorization with Gibbs Smoothing

Signal Recovery by Proximal Forward-Backward Splitting

Independent Component Analysis: Blind source separation by sparse decomposition in a signal dictionary

Algorithms for Non-negative Matrix Factorization

Wave shrink with firm shrinkage

WaveLab and Reproducible Research

Translation-Invariant De-Noising

NMF WITH SPARSE REGULARIZATIONS IN TRANSFORMED DOMAINS

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