In this paper, an image restoration method using the Wiener filter is proposed. In order to bring the theory of the Wiener filter consistent with images that have spatially varying statistics, the proposed method adopts the locally adaptive Wiener filter (AWF) based on the universal Gaussian mixture distribution model (UNI-GMM) previously proposed for denoising. Applying the UNI-GMM-AWF for deconvolution problem, the proposed method employs the stationary Wiener filter (SWF) as a pre-filter. The SWF in the discrete cosine transform domain shrinks the blur point spread function and facilitates the modeling and filtering at the proceeding AWF. The SWF and UNI-GMM are learned using a generic training image set and the proposed method is tuned toward the image set. Simulation results are presented to demonstrate the effectiveness of the proposed method.

In this letter, we remark a well-known nonlinear filtering technique realize immediate effect to suppress the influence of the additive measurement noise in the input to a set theoretic linear blind deconvolution scheme. Numerical examples show ε-separating nonlinear pre-filtering techniques work suitably to this noisy blind deconvolution problem.

The purpose of this paper is to deal with the problem of recovering a signal from its noisy version. One example is to restore old images degraded by noise. The recovery solution is given within the framework of series expansion and we shall show that for the general case the recovery functions have to be elements of an extended pseudo biorthogonal basis (EPBOB) in order to suppress efficiently the corruption noise. After we discuss the different situations of noise, we provide some methods to construct the optimal EPBOB in order to deal with these situations.