Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences

TL;DR

This paper introduces a novel approach using Discrete Prolate Spheroidal Sequences (DPSS) to improve compressive sensing of continuous-time multiband signals, providing theoretical guarantees and practical methods for signal recovery.

Contribution

It develops a DPSS-based dictionary tailored for sampled multiband signals, bridging the gap between discrete CS and continuous-time signal acquisition, with theoretical analysis and practical insights.

Findings

High-quality sparse approximations for multiband signals

Theoretical guarantees for signal recovery

Practical implementation of DPSS-based CS

Abstract

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements.