Adaptive Non-uniform Compressive Sampling for Time-varying Signals

TL;DR

This paper introduces an adaptive non-uniform compressive sampling method for time-varying sparse signals, improving measurement efficiency by using Bayesian inference without prior knowledge.

Contribution

It proposes a novel ANCS technique that adaptively allocates sensing energy based on previous measurements, enhancing recovery of sparse signals without prior sparsity information.

Findings

Achieves desired non-uniform signal recovery

Reduces measurements for signals sparse in canonical basis

Demonstrates effectiveness through numerical simulations

Abstract

In this paper, adaptive non-uniform compressive sampling (ANCS) of time-varying signals, which are sparse in a proper basis, is introduced. ANCS employs the measurements of previous time steps to distribute the sensing energy among coefficients more intelligently. To this aim, a Bayesian inference method is proposed that does not require any prior knowledge of importance levels of coefficients or sparsity of the signal. Our numerical simulations show that ANCS is able to achieve the desired non-uniform recovery of the signal. Moreover, if the signal is sparse in canonical basis, ANCS can reduce the number of required measurements significantly.