Estimating sparse signals using integrated wide-band dictionaries

Abstract

In this paper, we present a technique for reducing the size of the dictionary in sparse signal reconstruction by formulating an initial dictionary containing elements that spans bands of the considered parameter space. We allow for the use of this banded dictionary in a first-stage estimation procedure, in which large parts of the parameter space is discarded for further analysis, thereby reducing the overall computationally complexity required to allow for a reliable signal reconstruction. We illustrate the presented principle on the problem of estimating sinusoidal components corrupted by white noise.