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Sensors 2015, 15(1), 234-247; doi:10.3390/s150100234

Modified OMP Algorithm for Exponentially Decaying Signals

1
Centre of New Technologies, University of Warsaw, Banacha 2C 02-097, Poland
2
Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw 02-093, Poland
*
Author to whom correspondence should be addressed.
Received: 12 September 2014 / Accepted: 15 December 2014 / Published: 24 December 2014
(This article belongs to the Section Sensor Networks)
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Abstract

A group of signal reconstruction methods, referred to as compressed sensing (CS), has recently found a variety of applications in numerous branches of science and technology. However, the condition of the applicability of standard CS algorithms (e.g., orthogonal matching pursuit, OMP), i.e., the existence of the strictly sparse representation of a signal, is rarely met. Thus, dedicated algorithms for solving particular problems have to be developed. In this paper, we introduce a modification of OMP motivated by nuclear magnetic resonance (NMR) application of CS. The algorithm is based on the fact that the NMR spectrum consists of Lorentzian peaks and matches a single Lorentzian peak in each of its iterations. Thus, we propose the name Lorentzian peak matching pursuit (LPMP). We also consider certain modification of the algorithm by introducing the allowed positions of the Lorentzian peaks’ centers. Our results show that the LPMP algorithm outperforms other CS algorithms when applied to exponentially decaying signals. View Full-Text
Keywords: compressed sensing; orthogonal matching pursuit; exponentially decaying signal; nuclear magnetic resonance; non-uniform sampling; Lorentzian peaks matching pursuit compressed sensing; orthogonal matching pursuit; exponentially decaying signal; nuclear magnetic resonance; non-uniform sampling; Lorentzian peaks matching pursuit
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Kazimierczuk, K.; Kasprzak, P. Modified OMP Algorithm for Exponentially Decaying Signals. Sensors 2015, 15, 234-247.

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