Practical compressive sensing with Toeplitz and circulant matrices

Wotao Yin; Simon Morgan; Junfeng Yang; Yin Zhang

doi:10.1117/12.863527

14 July 2010 Practical compressive sensing with Toeplitz and circulant matrices

Wotao Yin, Simon Morgan, Junfeng Yang, Yin Zhang

Proceedings Volume 7744, Visual Communications and Image Processing 2010; 77440K (2010) https://doi.org/10.1117/12.863527
Event: Visual Communications and Image Processing 2010, 2010, Huangshan, China

Abstract

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.

Citation Download Citation

Wotao Yin, Simon Morgan, Junfeng Yang, and Yin Zhang "Practical compressive sensing with Toeplitz and circulant matrices", Proc. SPIE 7744, Visual Communications and Image Processing 2010, 77440K (14 July 2010); https://doi.org/10.1117/12.863527

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