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Convolutional Compressed Sensing Using Deterministic Sequences

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3 Author(s)
Li, K. ; Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK ; Lu Gan ; Cong Ling

In this paper, a new class of orthogonal 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 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.

Published in:

Signal Processing, IEEE Transactions on  (Volume:61 ,  Issue: 3 )