Hierarchical Bayesian image restoration from partially known blurs

Nikolas P. Galatsanos, Vladimir Z. Mesarović, Rafael Molina, Aggelos K. Katsaggelos

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


In this paper, we examine the restoration problem when the point-spread function (PSF) of the degradation system is partially known. For this problem, the PSF is assumed to be the sum of a known deterministic and an unknown random component. This problem has been examined before; however, in most previous works the problem of estimating the parameters that define the restoration filters was not addressed. In this paper, two iterative algorithms that simultaneously restore the image and estimate the parameters of the restoration filter are proposed using evidence analysis (EA) within the hierarchical Bayesian framework. We show that the restoration step of the first of these algorithms is in effect almost identical to the regularized constrained total leastsquares (RCTLS) filter, while the restoration step of the second is identical to the linear minimum mean square-error (LMMSE) filter for this problem. Therefore, in this paper we provide a solution to the parameter estimation problem of the RCTLS filter. We further provide an alternative approach to the expectation-maximization (EM) framework to derive a parameter estimation algorithm for the LMMSE filter. These iterative algorithms are derived in the discrete Fourier transform (DFT) domain; therefore, they are computationally efficient even for large images. Numerical experiments are presented that test and compare the proposed algorithms.

Original languageEnglish (US)
Pages (from-to)1784-1797
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number10
StatePublished - Oct 2000

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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