Analysis of hard-thresholding for distributed compressed sensing with one-bit measurements

Abstract

A simple hard-thresholding operation is shown to be able to uniformly recover L signals x1, ..., xL ∈ R n that share a common support of size s from m = O(s) one-bit measurements per signal if L ≥ ln(en/s). This result improves the single signal recovery bounds with m = O(s ln(en/s)) measurements in the sense that asymptotically fewer measurements per non-zero entry are needed. Numerical evidence supports the theoretical considerations. * The authors gratefully acknowledge the support by the DFG project "Information Theory and Recovery Algorithms for Quantized and Distributed Compressed Sensing" in context of SPP 1798.