Practical compressive sensing with Toeplitz and circulant matrices | Zendy

Wotao Yin | Zendy; Simon P. Morgan | Zendy; Junfeng Yang | Zendy; Yin Zhang | Zendy

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Practical compressive sensing with Toeplitz and circulant matrices

Author(s) -

Wotao Yin,

Simon P. Morgan,

Junfeng Yang,

Yin Zhang

Publication year - 2010

Publication title -

proceedings of spie, the international society for optical engineering/proceedings of spie

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.192

H-Index - 176

eISSN - 1996-756X

pISSN - 0277-786X

DOI - 10.1117/12.863527

Subject(s) - toeplitz matrix , circulant matrix , compressed sensing , decoding methods , algorithm , computer science , random matrix , matrix (chemical analysis) , linear system , mathematics , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , composite material

Compressive sensing encodes a signal into a relatively small number of incoherent linear measurements. In theory, the optimal incoherence is achieved by completely random measurement matrices. However, such matrices are often difficult and costly to implement in hardware realizations. Random Toeplitz and circulant matrices can be easily (or even naturally) realized in various applications. This paper introduces fast algorithms for reconstructing signals from incomplete Toeplitz and circulant measurements. Computational results are presented to show that Toeplitz and circulant matrices are not only as effective as random matrices for signal encoding, but also permit much faster decoding. © 2010 SPIE.

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