Fast pyramidal search for perceptually based fractal image compression

In this paper, we present a fast algorithm for perceptually based fractal image compression. The algorithm is based on a refinement of the fractal code from an initial coarse level of a pyramid. Assuming the block matching error is modeled as a first order Laplacian autoregressive process, we derive the threshold sequence for the objective function in each pyramidal level. Computational efficiency depends on the depth of the pyramid and the search step size, and could be improved by up to two orders of magnitude over the computational effort required for a full search of the original image. The algorithm is quasi-optimal, in terms of minimizing the weighted least absolute error. Its main advantage is the greatly decreased computational complexity, when compared to full search algorithms.