Abstract-In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolutionbased 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-ZadoffChu (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.
Kezhi Li et al. proposed a new class of orthogonal circulant matrices built from deterministic sequences for convolution-based compressed sensing REF .
Convolutional Compressed Sensing Using Deterministic Sequences
ArXiv
ArXiv
Mathematics Computer Science