Adaptive image restoration in signal-dependent noise

An image distribution is modeled as a non-stationary stochastic process. The presence of signal-dependent noise further renders the noisy observation to be spatially nonstationary. As a consequence, spatially adaptive estimators outperform estimators based on global statistics. A number of spatially adaptive Bayesian estimators are derived using (1) maximum a posteriori probability and (2) minimization of mean square error as the optimality criteria. An estimator that compensates for the low pass filtering effects of adaptive estimators is also obtained, as is a simple nonlinear contrast manipulation technique suitable for images corrupted by signal-dependent noise. In addition to the just mentioned point estimators, multiple parameter estimators using several Markovian image covariance models are derived. Estimators for images degraded by Poisson noise are also obtained. Simple transformations that render the noise signal-independent, followed by the application of classical Wiener filtering techniques to restore the degraded images are investigated. Under low signal-to-noise ratio conditions the additional signal information contained in signal-dependent noise is recovered to obtain an estimate from the degraded image. Extensive computer simulations are carried out to evaluate the performances of the estimators on several images corrupted by different types of signal-dependent noise. In addition to the qualitative comparisons of the restored images, quantitative evaluations using several measures of image quality, some of which are based on simple models of the human visual system, are presented.