Sparsity order estimation for single snapshot compressed sensing

Romer F, Lavrenko A, Del Galdo G, Hotz T, Arikan O, Thoma RS (2015)

Publication Type: Conference contribution

Publication year: 2015

Journal

Conference Record of the Asilomar Conference on Signals, Systems and Computers Institute of Electrical and Electronics Engineers

Publisher: IEEE Computer Society

Book Volume: 2015-April

Pages Range: 1220-1224

Conference Proceedings Title: Conference Record - Asilomar Conference on Signals, Systems and Computers

Event location: Pacific Grove, CA, USA

ISBN: 9781479982974

DOI: 10.1109/ACSSC.2014.7094653

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.

Involved external institutions

Technische Universität Ilmenau DE Germany (DE) Bilkent University / Bilkent Üniversitesi TR Turkey (TR)

How to cite

APA:

Romer, F., Lavrenko, A., Del Galdo, G., Hotz, T., Arikan, O., & Thoma, R.S. (2015). Sparsity order estimation for single snapshot compressed sensing. In Michael B. Matthews (Eds.), Conference Record - Asilomar Conference on Signals, Systems and Computers (pp. 1220-1224). Pacific Grove, CA, USA: IEEE Computer Society.

MLA:

Romer, F., et al. "Sparsity order estimation for single snapshot compressed sensing." Proceedings of the 48th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015, Pacific Grove, CA, USA Ed. Michael B. Matthews, IEEE Computer Society, 2015. 1220-1224.

BibTeX: Download