2019/11/18 by Arian, Arman, Yilmaz, Ozgur
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1911.07525
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still take on values in the continuum. In today's "digital" world, a subsequent quantization step, where these measurements are replaced with elements from a finite set is crucial. We focus on one of the approaches that yield efficient quantizers for CS: ΣΔ quantization, followed by a one-stage tractable reconstruction method, which was developed by Saab et al. with theoretical error guarantees in the case of sub-Gaussian matrices. We propose two alternative approaches that extend this result to a wider class of measurement matrices including (certain unitary transforms of) partial bounded orthonormal systems and deterministic constructions based on chirp sensing matrices.