Random Acquisition in Compressive Sensing

Compressive sensing has the ability of reconstruction of signal/image from the compressive measurements which are sensed with a much lower number of samples than a minimum requirement by Nyquist sampling theorem. The random acquisition is widely suggested and used for compressive sensing. In the random acquisition, the randomness of the sparsity structure has been deployed for compressive sampling of the signal/image. The article goes through all the literature up to date and collects the main methods, and simply described the way each of them randomly applies the compressive sensing. This article is a comprehensive review of random acquisition techniques in compressive sensing. Theses techniques have reviews under the main categories of (1) random demodulator, (2) random convolution, (3) modulated wideband converter model, (4) compressive multiplexer diagram, (5) random equivalent sampling, (6) random modulation pre-integration, (7) quadrature analog-to-information converter, (8) randomly triggered modulated-wideband compressive sensing (RT-MWCS).

Review of analog-to-information converters

The implementation of high‑throughput systems with the traditional approach to the discretization of the analog signal according to the Kotelnikov theorem is faced with the problems of high power consumption and the need to store and transfer large amounts of data. An alternative approach to sampling and processing information is based on advances in the compressed sampling theory. The paper provides a brief overview of the main provisions of this theory and considers examples of its use in practice for the implementation of information reading systems – analog‑to‑information converters. The purpose of these devices is to reduce the pressure on conventional analog‑to‑digital converters, to reduce the sampling rate and the amount of output data. The main architectures of analog‑information converters are considered: non‑uniform sampling, random filter, random demodulator, modulated wideband converter, compressive multiplexer, random modulator pre‑integrator, spread spectrum random modulator pre‑integrator.

Design of a Multi-Channel Random Demodulator for Wideband Signals

The wideband signals in most important applications are sparse or compressible in some sense. A multi-channel scheme for random demodulator without integrator is introduced in this paper. This architecture is based on compressive sensing (CS) and random demodulator (RD), and overcomes the problem of the integrator’s switching scheme injects noise into the signal and deteriorates the reconstructed signal of the RD, which has the same reconstruction guarantees by similar algorithms with the basic RD because the measurement matrix between their is identical, and which resolves some of the practical issues present in prior work. The results of simulation indicate that multi-tone signal can be successful reconstructed at sampling rate downs to 1/10 of the Nyquist-rate, which represents an up to 90% savings in the bandwidth and the storage memory.