MAP Approach to Blind Deconvolution by Means of Inverse Filtering

O. Michailovich and A. Tannenbaum (USA)


Blind deconvolution, inverse filtering, Bayesian estimation, and shift invariant spaces.


The problem of blind deconvolution (BD) has long been recognized as one of the most intricate problems in signal and image processing. This problem has been addressed via a multitude of approaches, most of which are based on constructing an inverse operator that is applied to the observed data in either explicit or implicit manner. In the focus of the current study are explicit deconvolution meth ods, in which an estimate of the original signal/image is ob tained as a result of convolving the observed (i.e., blurred) data with an inverse filter. Since for the case of BD, the blur (commonly referred to as a point spread function (PSF)) is not a priori known, the inverse filter needs to be estimated from the available data. In the current study, a novel ap proach to estimating the inverse filter is proposed, in which the latter is computed as a maximum-a-posteriori (MAP) estimate. It is shown that the property of MAP estima tion of being capable of incorporating a priori information on the parameters of inverse filtering allows one to obtain solutions which are considerably more stable as compared to maximum likelihood (ML) estimates, the properties of which depend on the observed data only. Some key ad vantages of the proposed BD method are demonstrated in a series of both in silico and real-life experiments.

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