Optimization also has important roles in this era of digitalization and artificial vision, specifically for image and data processing. After introducing fundamental image processing techniques, the chapter considers image deblurring via the Lucy-Richardson algorithm (RLA). Then, image decomposition into texture+cartoon parts is treated with the Mumford-Shah approach for image segmentation, and the use of Chan-Vese model. Next, the total variation analysis of images, and the Rudin, Osher and Fatemi (ROF) model are introduced, for image denoising. Now, there is a section devoted to Bregman-related algorithms (including the split Bregman iteration); and another section for the Douglas-Rachford splitting algorithm. A surprising and motivating application is introduced next: matrix completion (that can be used for picture recovery, text removal from images, and marketing recommendations). After all this, another part of the chapter comes, focusing on sparsity optimization for signal processing. A series of optimization methods, which should be fast, are introduced. The chapter ends with two experiments: the elimination of salt and pepper noise from pictures, and image restoring (damaged pictures) by inpainting techniques. The chapter includes several MATLAB programs for assessment of the methods.