Convolutional Compressed Sensing Using Deterministic Sequences
This work addresses compressed sensing for signal processing applications, offering a deterministic alternative to random convolution methods, but it appears incremental as it builds on existing sequence-based approaches.
The paper tackles the problem of compressed sensing by proposing a new class of circulant matrices based on deterministic sequences, such as Frank-Zadoff-Chu and Golay sequences, to enable uniform and non-uniform recovery of sparse signals in time, frequency, or DCT domains.
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.