A unified Bayesian framework for algorithms to recover blocky signals

Daniela Calvetti; Erkki Somersalo

doi:10.1117/12.740193

21 September 2007 A unified Bayesian framework for algorithms to recover blocky signals

Daniela Calvetti, Erkki Somersalo

Proceedings Volume 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII; 669704 (2007) https://doi.org/10.1117/12.740193
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

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.

Citation Download Citation

Daniela Calvetti and Erkki Somersalo "A unified Bayesian framework for algorithms to recover blocky signals", Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 669704 (21 September 2007); https://doi.org/10.1117/12.740193

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