The problem of restoration of digital images plays a central role in multitude important applications. A particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modelled by ill-conditional operator. In such situation, the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some priori information called as simply priors is essential for image restoration, rendering it stable and robust to noise. Particularly, if the original image is known to be a piecewise smooth function, a total variation (TV) based image restoration can be applied. This paper proposes an algorithm for unconstrained optimization problem where the objective function includes a data fidelity term and a nonsmooth regulaizer.Total Variation method is employed to find solution of the problem based on the Improved Iterative Shrinkage Thresholding Algorithm (IISTA). IISTA is performed through a recursive application of two simple procedures linear filtering and soft thresholding. An experimental result shows that proposed algorithm performs well when compared with the existing methods.

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The aim of this paper is to apply the regularization functions namely TV norm, l 1 norm and l 0 norm and regularization parameters with these norms in image restoration. This class of problems results from combining a linear observation model with a non-quadratic regularizer. Improved Iterative Shrinkage Thresholding algorithm (IISTA) and Iterative Shrinkage Thresholding algorithm (ISTA) are employed for comparison. These algorithms are performed through a recursive application of two simple procedures such as linear filtering and soft thresholding.