Spatial Autoregressions in Digital Image Restoration: Simultaneous Models.
MARYLAND UNIV COLLEGE PARK COMPUTER VISION LAB
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We consider the application of spatial autoregressive random field models in the restoration of degraded images. The degradation is assumed to be due to a space invariant, periodic, nonseparable point spread function and additive noise, colored or white. We assume that the images are represented by two-dimensional spatial autoregressive models and we develop fast, optimal, non-recursive filters, the optimality criterion being the minimum mean squared error MMSE. Within the class of spatial autoregressive models, there are two nonequivalent classes of random field RF models, the so-called simultaneous autoregressive SAR models and the conditional Markov CM models. In this paper, we develop restoration algorithms and give examples of restoration using the SAR models. The restoration filter is optimal, if the parameters characterizing the RF models are known exactly. In practice, however, they are estimated from the images. An iterative scheme is used for the estimation of parameters in SAR models. Performance bounds of restoration algorithms are calculated. In a subsequent paper, the case of CM models will be considered. Author
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