Median Filter Based Digital Image Restoration Using Joint Statistical Modeling

Image restoration involves the reduction or complete removal of image degradation in an effort to enhance an image and recover its original form. One of the main methods of image restoration is Joint Statistical Modeling (JSM). This thesis proposes method for image restoration based on JSM and the statistical characterization of the nonlocal self-similarity and local smoothness of natural images. In an effort to improve the image restoration results through JSM, the proposed method involves the addition of a Switching Median Filter (SMF) to JSM and a Median Filter (MF) at the end of every iteration in the restoration process. Overall, the proposed image restoration method makes the following contributions: it establishes JSM in a domain for hybrid space-transformation; using JSM, it develops a new type of minimization function to be used in solving inverse problems in image processing; and JSM is developing a new rule-based in the Split Bregman method, which is intended to solve any prospective image problems related to a theoretical proof of convergence. The proposed method was experimentally tested for three kinds of image restoration: image deblurring, image inpainting (text removal), and the removal of mixed Gaussian and salt-and-pepper noise. The results of these experiments indicate that image restoration using the proposed method is a significant improvement compared to conventional JSM. Furthermore, the convergence of the proposed method was also considerably improved relative to JSM.