Monte Carlo methods for compressed sensing
Monte Carlo methods for compressed sensing
In this paper we study Monte Carlo type approaches to Bayesian sparse inference under a squared error loss. This problem arises in Compressed Sensing, where sparse signals are to be estimated and where recovery performance is measured in terms of the expected sum of squared error. In this setting, it is common knowledge that the mean over the posterior is the optimal estimator. The problem is however that the posterior distribution has to be estimated, which is extremely difficult. We here contrast approaches that use a Monte Carlo estimate for the posterior mean. The randomised Iterative Hard Thresholding algorithm is compared to a new approach that is inspired by sequential importance sampling and uses a bootstrap re-sampling step based on importance weights.
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead
July 2014
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead
Blumensath, Thomas
(2014)
Monte Carlo methods for compressed sensing.
IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014), Florence, Italy.
04 - 09 May 2014.
5 pp
.
(doi:10.1109/ICASSP.2014.6853747).
Record type:
Conference or Workshop Item
(Poster)
Abstract
In this paper we study Monte Carlo type approaches to Bayesian sparse inference under a squared error loss. This problem arises in Compressed Sensing, where sparse signals are to be estimated and where recovery performance is measured in terms of the expected sum of squared error. In this setting, it is common knowledge that the mean over the posterior is the optimal estimator. The problem is however that the posterior distribution has to be estimated, which is extremely difficult. We here contrast approaches that use a Monte Carlo estimate for the posterior mean. The randomised Iterative Hard Thresholding algorithm is compared to a new approach that is inspired by sequential importance sampling and uses a bootstrap re-sampling step based on importance weights.
Text
ICASSP14_IHT_02.pdf
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e-pub ahead of print date: 1 May 2014
Published date: July 2014
Venue - Dates:
IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2014), Florence, Italy, 2014-05-04 - 2014-05-09
Organisations:
Signal Processing & Control Grp
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Local EPrints ID: 364847
URI: http://eprints.soton.ac.uk/id/eprint/364847
PURE UUID: 15c20442-3176-40c2-b473-6b2ac999675f
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Date deposited: 13 May 2014 10:10
Last modified: 15 Mar 2024 03:34
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