Certain smoothing techniques and their applications to image processing

This thesis consists of five chapters. The first chapter is devoted to the introduction. In this chapter, the concepts of noise and denoising in image processing are introduced first, then the types and history of these terms are mentioned and some required preliminary informations are also presented. In the second chapter, some definitions are given that is needed further. In the third chapter, a global smoothing approximation technique is proposed to make the total variation function smooth (continuous and differentiable) to facilitate its use in denoising. In Chapter 4, an application of the given algorithm in Chapter 3 is represented, proposed algorithm is applied to a set of test images to show its effectiveness. The fifth and the last chapter is devoted to the conclusion and recommendations.