Recovery of Binary Sparse Signals with Biased Measurement Matrices

TL;DR

This paper investigates conditions for accurately recovering sparse binary signals using biased measurement matrices and box-constrained basis pursuit, showing that under certain conditions, solutions can be efficiently obtained via boxed-constrained least-squares.

Contribution

It introduces probabilistic conditions ensuring successful recovery of binary signals with biased matrices and links basis pursuit solutions to least-squares under these conditions.

Findings

Recovery conditions are probabilistically established.

Basis pursuit solutions can be obtained via least-squares.

Applicable to both sparse and saturated binary signals.

Abstract

This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary signals is very likely. In fact, we also show that under the same condition, the solution of the boxed-constrained basis pursuit program can be found using boxed-constrained least-squares.