Sparsity order estimation for single snapshot compressed sensing

Date
2015-11
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Conference Record - Asilomar Conference on Signals, Systems and Computers
Print ISSN
1058-6393
Electronic ISSN
Publisher
IEEE
Volume
Issue
Pages
1220 - 1224
Language
English
Type
Conference Paper
Journal Title
Journal ISSN
Volume Title
Series
Abstract

In this paper we discuss the estimation of the spar-sity order for a Compressed Sensing scenario where only a single snapshot is available. We demonstrate that a specific design of the sensing matrix based on Khatri-Rao products enables us to transform this problem into the estimation of a matrix rank in the presence of additive noise. Thereby, we can apply existing model order selection algorithms to determine the sparsity order. The matrix is a rearranged version of the observation vector which can be constructed by concatenating a series of non-overlapping or overlapping blocks of the original observation vector. In both cases, a Khatri-Rao structured measurement matrix is required with the main difference that in the latter case, one of the factors must be a Vandermonde matrix. We discuss the choice of the parameters and show that an increasing amount of block overlap improves the sparsity order estimation but it increases the coherence of the sensing matrix. We also explain briefly that the proposed measurement matrix design introduces certain multilinear structures into the observations which enables us to apply tensor-based signal processing, e.g., for enhanced denoising or improved sparsity order estimation. © 2014 IEEE.

Course
Other identifiers
Book Title
Keywords
Additive noise, Product design, Signal processing, Signal reconstruction, Khatri-Rao products, Matrix rank, Measurement matrix, Model-order selection, Observation vectors, Order estimation, Single snapshots, Vandermonde matrix, Compressed sensing
Citation
Published Version (Please cite this version)