Image Restoration Techniques: A Novel Approach using an Iterative Procedure using an Iterative Procedure

Abstract

The problem of reconstruction of digital images from their corrupted measurements is observed as a problem of central significance in numerous fields of engineering and imaging sciences. This paper addresses the problem of how to recover degraded images with partial image pixels being missing during transmission or damaged by impulsive noise. A wide range of image restoration tasks is covered in the mathematical model considered in this paper, e.g. image deblurring, image inpainting and super-resolution imaging. In those cases, the degradation is typically initiated by the resolution limitations of an imaging device in use and/or by the destructive influence of measurement noise. A novel and influential perspective on image modernization and restoration is to regard the computational objective as the classification of corrupt (disorganized) pixels using the classification of the nearest uncorrupted (classified) pixels. Based on the assumption that nature images are likely to have a sparse representation in the wavelet tight frame domain, we propose a regularization based approach to recover degraded images by enforcing the analysis-based sparsely prior of images in the tight frame domain. We use a split Bregman method to solve the resulting minimization problem efficiently. Numbers of experiments have been carried out for various image restoration tasks: simultaneously image de-blurring and in-painting, super resolution imaging and image de-blurring under impulsive noise, demonstrated the effectiveness of our proposed algorithm and the robustness to misdetection errors of missing/damaged pixels, and are compared favourably against existing algorithms.