Regularized signal reconstruction for level-crossing sampling using Slepian functions

Abstract

In this paper, we propose a method for efficient signal reconstruction from non-uniformly spaced samples collected using level-crossing sampling. Level-crossing (LC) sampling captures samples whenever the signal crosses predetermined quantization levels. Thus the LC sampling is a signal-dependent, non-uniform sampling method. Without restriction on the distribution of the sampling times, the signal reconstruction from non-uniform samples becomes ill-posed. Finite-support and nearly band-limited signals are well approximated in a low-dimensional subspace with prolate spheroidal wave functions (PSWF) also known as Slepian functions. These functions have finite support in time and maximum energy concentration within a given bandwidth and as such are very appropriate to obtain a projection of those signals. However, depending on the LC quantization levels, whenever the LC samples are highly non-uniformly spaced obtaining the projection coefficients requires a Tikhonov regularized Slepian reconstruction. The performance of the proposed method is illustrated using smooth, bursty and chirp signals. Our reconstruction results compare favorably with reconstruction from LC-sampled signals using compressive sampling techniques.