On a simple derivation of the complementary matching pursuit

• Published in: Signal processing Vol. 90; no. 2; pp. 702 - 706
• Main Authors: Rath, Gagan, Guillemot, Christine
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2010; Elsevier
• Subjects: Algorithms; Applied sciences; Approximation; Chemical-mechanical polishing; Complementary matching pursuit; Derivation; Error analysis; Exact sciences and technology; Greedy algorithms; Information, signal and communications theory; Matching; Matching pursuit; Mathematical analysis; Miscellaneous; Orthogonal matching pursuit; Signal processing; Sparse approximation; Telecommunications and information theory; Vectors (mathematics); Orthogonal matching pursuit; Greedy algorithms; Sparse approximation; Complementary matching pursuit; Matching pursuit; Performance evaluation; Linear equation; Greedy algorithm; Signal processing; Iterative method; Sparse representation
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2009.07.030

Sparse approximation in a redundant basis has attracted considerable attention in recent years because of many practical applications. The problem basically involves solving an under-determined system of linear equations under some sparsity constraint. In this paper, we present a simple interpretation of the recently proposed complementary matching pursuit (CMP) algorithm. The interpretation shows that the CMP, unlike the classical MP, selects an atom and determines its weight based on a certain sparsity measure of the resulting residual error. Based on this interpretation, we also derive another simple algorithm which is seen to outperform CMP at low sparsity levels for noisy measurement vectors.