Identification of image and blur parameters for the restoration of noncausal blurs

Abstract

An optimal statistical parameter estimation technique is presented for the identification of unknown image and blur model parameters. The development leads to an autoregressive moving average (ARMA) model identification problem, where the image model coefficients define the AR part, and the blur parameters define the MA part. Conditional maximum-likelihood estimates of the unknown parameters are derived both in the absence and in the presence of observation noise. The proposed algorithms constitute a generalization of previous work on blur identification in that they are able to locate the zero loci of the blurred image spectrum on the entire z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> - z <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> plane. Simulation results, as well as photographically blurred images processed with the proposed algorithms, are shown as examples.