Regularized Fractal Image Decoding

The goal of this paper is to present a new recipe for the fractal image decoding process. In this paper, we explain how fractal-based methods can be internally combined with regularization schemes, e.g., Tikhonov, total variation (TV), or hard-constrained regularization. Although the regularization procedure is very common in context of algebraic image restoration, it has not yet been thought directly in the context of fractal-based methods. This implication can be advantageous in many ways to improve the quality of the decoded image depending on the regularization functional. We develop the theory and apply the standard iterative methods of steepest descent and projected Landweber. We apply our technique to the under-determined missing fractal code problem as verification to the theory presented