  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: $\Sigma \Delta$ 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.
