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arXiv · 1210.7506

Convolutional Compressed Sensing Using Deterministic Sequences

Kezhi Li·Lu Gan·Cong Ling
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Abstract

In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the \textit{m}-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain.

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Kezhi Li, Lu Gan, Cong Ling. 2012-10-28. Convolutional Compressed Sensing Using Deterministic Sequences. https://doi.org/10.1109/tsp.2012.2229994

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