Framelet Algorithms for De-Blurring Images Corrupted by Impulse Plus Gaussian Noise

This paper studies a problem of image restoration that observed images are contaminated by Gaussian and impulse noise. Existing methods for this problem in the literature are based on minimizing an objective functional having the l
¹
fidelity term and the Mumford-Shah regularizer. We present an algorithm on this problem by minimizing a new objective functional. The proposed functional has a content-dependent fidelity term which assimilates the strength of fidelity terms measured by the l
¹
and l
²
norms. The regularizer in the functional is formed by the l
¹
norm of tight framelet coefficients of the underlying image. The selected tight framelet filters are able to extract geometric features of images. We then propose an iterative framelet-based approximation/sparsity deblurring algorithm (IFASDA) for the proposed functional. Parameters in IFASDA are adaptively varying at each iteration and are determined automatically. In this sense, IFASDA is a parameter-free algorithm. This advantage makes the algorithm more attractive and practical. The effectiveness of IFASDA is experimentally illustrated on problems of image deblurring with Gaussian and impulse noise. Improvements in both PSNR and visual quality of IFASDA over a typical existing method are demonstrated. In addition, Fast_IFASDA, an accelerated algorithm of IFASDA, is also developed.