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Image Decomposition and Separation Using Sparse Representations: An Overview

Fadili, M. Jalal and Starck, Jean-Luc and Bobin, Jérôme and Moudden, Yassir (2010) Image Decomposition and Separation Using Sparse Representations: An Overview. Proceedings of the IEEE, 98 (6). pp. 983-994. ISSN 0018-9219. https://resolver.caltech.edu/CaltechAUTHORS:20100608-082431957

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Abstract

This paper gives essential insights into the use of sparsity and morphological diversity in image decomposition and source separation by reviewing our recent work in this field. The idea to morphologically decompose a signal into its building blocks is an important problem in signal processing and has far-reaching applications in science and technology. Starck , proposed a novel decomposition method—morphological component analysis (MCA)—based on sparse representation of signals. MCA assumes that each (monochannel) signal is the linear mixture of several layers, the so-called morphological components, that are morphologically distinct, e.g., sines and bumps. The success of this method relies on two tenets: sparsity and morphological diversity. That is, each morphological component is sparsely represented in a specific transform domain, and the latter is highly inefficient in representing the other content in the mixture. Once such transforms are identified, MCA is an iterative thresholding algorithm that is capable of decoupling the signal content. Sparsity and morphological diversity have also been used as a novel and effective source of diversity for blind source separation (BSS), hence extending the MCA to multichannel data. Building on these ingredients, we will provide an overview the generalized MCA introduced by the authors in and as a fast and efficient BSS method. We will illustrate the application of these algorithms on several real examples. We conclude our tour by briefly describing our software toolboxes made available for download on the Internet for sparse signal and image decomposition and separation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/JPROC.2009.2024776 DOIUNSPECIFIED
Additional Information:© 2009 IEEE. Manuscript received March 10, 2009; revised May 29, 2009; accepted June 1, 2009. Date of publication September 29, 2009; date of current version May 19, 2010. This work was supported by NatImages ANR under Grant ANR-08-EMER-009.
Funders:
Funding AgencyGrant Number
NatImages ANR ANR-08-EMER-009
Subject Keywords:Blind source separation; image decomposition; morphological component analysis; sparse representations
Issue or Number:6
Record Number:CaltechAUTHORS:20100608-082431957
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100608-082431957
Official Citation:Fadili, M. J.; Starck, J.-L.; Bobin, J.; Moudden, Y.; , "Image Decomposition and Separation Using Sparse Representations: An Overview," Proceedings of the IEEE , vol.98, no.6, pp.983-994, June 2010 doi: 10.1109/JPROC.2009.2024776
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18599
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jun 2010 18:46
Last Modified:03 Oct 2019 01:45

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