Robust variational bayesian kernel based blind image deconvolution

In this paper we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelties of this model are two. First, a sparse kernel based representation of the point spread function (PSF) that allows for the first time estimation of both PSF shape and support. Second, a non Gaussian heavy tail prior for the model noise to make it robust to large errors encountered in BID when little prior knowledge is available about both image and PSF. Sparseness and robustness are achieved by introducing Student-t priors both for the PSF and the noise. A Variational methodology is proposed to solve this Bayesian model. Numerical experiments are presented both with real and simulated data that demonstrate the advantages of this model as compared to previous Gaussian based ones.

[1]  Nikolas P. Galatsanos,et al.  Large Scale Multikernel RVM for Object Detection , 2006, SETN.

[2]  Nikolas P. Galatsanos,et al.  Variational Bayesian blind image deconvolution based on a sparse kernel model for the point spread function , 2006, 2006 14th European Signal Processing Conference.

[3]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevan e Ve tor Ma hine , 2001 .

[4]  Neil D. Lawrence,et al.  A variational approach to robust Bayesian interpolation , 2003, 2003 IEEE XIII Workshop on Neural Networks for Signal Processing (IEEE Cat. No.03TH8718).

[5]  Geoffrey J. McLachlan,et al.  Robust mixture modelling using the t distribution , 2000, Stat. Comput..

[6]  Deepa Kundur,et al.  Blind Image Deconvolution , 2001 .

[7]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[8]  Michael I. Jordan,et al.  An Introduction to Variational Methods for Graphical Models , 1999, Machine Learning.

[9]  Aggelos K. Katsaggelos,et al.  Blind Deconvolution Using a Variational Approach to Parameter, Image, and Blur Estimation , 2006, IEEE Transactions on Image Processing.

[10]  Nikolas P. Galatsanos,et al.  A variational approach for Bayesian blind image deconvolution , 2004, IEEE Transactions on Signal Processing.

[11]  Deepa Kundur,et al.  Blind image deconvolution revisited , 1996 .

[12]  Brian D. Jeffs,et al.  Blind Bayesian restoration of adaptive optics telescope images using generalized Gaussian Markov random field models , 1998, Astronomical Telescopes and Instrumentation.

[13]  Nikolas P. Galatsanos,et al.  Hyperparameter estimation in image restoration problems with partially known blurs , 2002 .