Local regularization and Bayesian hypermodels

Daniela Calvetti; Erkki Somersalo

doi:10.1117/12.623159

16 September 2005 Local regularization and Bayesian hypermodels

Daniela Calvetti, Erkki Somersalo

Proceedings Volume 5910, Advanced Signal Processing Algorithms, Architectures, and Implementations XV; 59100W (2005) https://doi.org/10.1117/12.623159
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

In this paper, we restore a one-dimensional signal that a priori is known to be a smooth function with a few jump discontinuities from a blurred, noisy specimen signal using a local regularization scheme derived in a Bayesian statistical inversion framework. The proposed method is computationally effective and reproduces well the jump discontinuities, thus is an alternative to using total variation (TV) penalty as a regularizing functional. Our approach avoids the non-differentiability problems encountered in TV methods and is completely data driven in the sense that the parameter selection is done automatically and requires no user intervention. A computed example illustrating the performance of the method when applied to the solution of a deconvolution problem is presented.

Citation Download Citation

Daniela Calvetti and Erkki Somersalo "Local regularization and Bayesian hypermodels", Proc. SPIE 5910, Advanced Signal Processing Algorithms, Architectures, and Implementations XV, 59100W (16 September 2005); https://doi.org/10.1117/12.623159

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