Near-Optimal Adaptive Compressed Sensing

TL;DR

This paper introduces CASS, an adaptive compressed sensing algorithm that achieves near-optimal signal recovery at lower SNR levels with reduced computational complexity, outperforming traditional methods.

Contribution

The paper presents CASS, a simple adaptive sensing algorithm with near-optimal theoretical guarantees and practical performance improvements over existing compressed sensing techniques.

Findings

CASS succeeds at lower SNR levels than standard compressed sensing.

CASS requires only k log n measurements for k-sparse signals.

CASS is computationally less intensive and performs better in simulations.

Abstract

This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible signal-to-noise-ratio (SNR) levels, improving on previous work in adaptive compressed sensing. Like traditional compressed sensing based on random non-adaptive design matrices, the CASS algorithm requires only k log n measurements to recover a k-sparse signal of dimension n. However, CASS succeeds at SNR levels that are a factor log n less than required by standard compressed sensing. From the point of view of constructing and implementing the sensing operation as well as computing the reconstruction, the proposed algorithm is substantially less computationally intensive than standard compressed sensing. CASS is also demonstrated to perform considerably better in practice through simulation. To the best of our knowledge, this is the first demonstration of an adaptive compressed sensing algorithm with near-optimal theoretical guarantees and excellent practical performance. This paper also shows that methods like compressed sensing, group testing, and pooling have an advantage beyond simply reducing the number of measurements or tests -- adaptive versions of such methods can also improve detection and estimation performance when compared to non-adaptive direct (uncompressed) sensing.