Compressive sensing of a superposition of pulses

Chinmay Hegde, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Compressive Sensing (CS) has emerged as a potentially viable technique for the efficient acquisition of high-resolution signals and images that have a sparse representation in a fixed basis. The number of linear measurements M required for robust polynomial time recovery of S-sparse signals of length N can be shown to be proportional to S logN. However, in many real-life imaging applications, the original S-sparse image may be blurred by an unknown point spread function defined over a domain Ω; this multiplies the apparent sparsity of the image, as well as the corresponding acquisition cost, by a factor of |Ω|. In this paper, we propose a new CS recovery algorithm for such images that can be modeled as a sparse superposition of pulses. Our method can be used to infer both the shape of the two-dimensional pulse and the locations and amplitudes of the pulses. Our main theoretical result shows that our reconstruction method requires merely M = O(S + |Ω|) linear measurements, so that M is sublinear in the overall image sparsity S|Ω|. Experiments with real world data demonstrate that our method provides considerable gains over standard state-of-the-art compressive sensing techniques in terms of numbers of measurements required for stable recovery.

Original languageEnglish (US)
Title of host publication2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Proceedings
Pages3934-3937
Number of pages4
DOIs
StatePublished - Nov 8 2010
Event2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010 - Dallas, TX, United States
Duration: Mar 14 2010Mar 19 2010

Other

Other2010 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010
CountryUnited States
CityDallas, TX
Period3/14/103/19/10

Keywords

  • Blind deconvolution
  • Compressive sensing
  • Sparse approximation

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

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