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Proceedings Paper

A unified Bayesian framework for algorithms to recover blocky signals
Author(s): Daniela Calvetti; Erkki Somersalo
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Paper Abstract

We consider the problem of recovering signals from noisy indirect observations under the additional a priori information that the signal is believed to be slowly varying except at an unknown number of points where it may have discontinuities of unknown size. The model problem is a linear deconvolution problem. To take advantage of the qualitative prior information available, we use a non-stationary Markov model with the variance of the innovation process also unknown, and apply Bayesian techniques to estimate both the signal and the prior variance. We propose a fast iterative method for computing a MAP estimates and we show that, with a rather standard choices of the hyperpriors, the algorithm produces the fixed point iterative solutions of the total variation and of the Perona-Malik regularization methods. We also demonstrate that, unlike the non-statistical estimation methods, the Bayesian approach leads to a very natural reliability assessment of edge detection by a Markov Chain Monte Carlo (MCMC) based analysis of the posterior.

Paper Details

Date Published: 21 September 2007
PDF: 10 pages
Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 669704 (21 September 2007); doi: 10.1117/12.740193
Show Author Affiliations
Daniela Calvetti, Case Western Reserve Univ. (United States)
Erkki Somersalo, Helsinki Univ. of Technology (Finland)

Published in SPIE Proceedings Vol. 6697:
Advanced Signal Processing Algorithms, Architectures, and Implementations XVII
Franklin T. Luk, Editor(s)

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