Compressive Signal Processing with Circulant Sensing Matrices
Abstract
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises of processing the random projections directly, without first reconstructing the signal. In this paper, we show that circulant sensing matrices allow to perform a variety of classical signal processing tasks such as filtering, interpolation, registration, transforms, and so forth, directly in the compressed domain and in an exact fashion, \emph{i.e.}, without relying on estimators as proposed in the existing literature. The advantage of the techniques presented in this paper is to enable direct measurement-to-measurement transformations, without the need of costly recovery procedures.
Cite
@article{arxiv.1403.2835,
title = {Compressive Signal Processing with Circulant Sensing Matrices},
author = {Diego Valsesia and Enrico Magli},
journal= {arXiv preprint arXiv:1403.2835},
year = {2014}
}