Noise-Resilient Unlimited Sampling and Recovery of Sparse Signals

Abstract

In this paper, we investigate the use of modulo-ADCs in compressed sensing to handle the issue of the limited dynamic range of standard ADCs. The current state-of-the-art algorithm for modulo-compressed sensing uses an ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm-based approximation of the sparsity constraint, resulting in a computationally demanding mixed-integer linear optimization. Handling noisy measurements further complicates the problem, requiring mixed-integer quadratic programming, a problem known to be NP-hard. We present an alternative iterative hard-thresholding approach to address this issue. Our solution is computationally simpler and capable of handling noisy measurements. Additionally, we provide theoretical guarantees that the algorithm can successfully recover sparse vectors if the sampling operator satisfies the integer augmented-restricted isometry property, which holds when the number of measurements is sufficiently large.