Iterative Image Restoration with Adaptive Regularization and Parametric Constrains

In this paper the iterative methods of image restoration are considered. These methods are based on the successive approximation algorithm with adaptive regularization and parametric constrains on the solution. The adaptive regularization preserves the global image smoothing and is considered as the combined nonlinear operator for simultaneous removal of additive Gaussian and impulse noises. The corresponded condition of iteration convergence is investigated. The adaptation strategy is based on the generalized noise visibility function which determines the pixel belonging to the flat arias or edges. Noise visibility function is considered as an indicator function and mathematically determined as the intersection of two additional binary images obtained from local variance estimation and edge image. Extending the previous work, it is proposed the new paprametric constrain on the solution in spatial frequency domain. Opposite the above mentioned regularization, which bounds from above the energy of the restored frequency components, the proposed adaptive frequency constrain determines the lower bound of the solution. The introduction of such constrain is conditioned by the inability of the classical regularized iterative algorithms with the existed constrains to restore the strongly depressed or missed frequency components. To overcome this disadvantage the parametric model of image spectrum is used. The model consists of the sum of 3 exponential decays to approximate the whole image magnitude spectrum using available information about low-pass frequency part of the degraded image. The proposed approach has the corresponded analogue in the spatial coordinate domain where well-known parametric model of maximum entropy method is used to obtain high spatial resolution. However, opposite maximum entropy model, which is mostly suitable for impulselike images due to its all-poles character, the proposed frequency parametric model has the higher level of generalization, because the exponential model describes the large amount of real image spectra. The performed computer simulation illustrates the high efficiency of the proposed technique on the examples of images degraded by defocusing.