A jointly optimal fractal/DCT compression scheme

In this paper a hybrid fractal and discrete cosine transform (DCT) coder is developed. Drawing on the ability of DCT to remove inter-pixel redundancies and on the ability of fractal transforms to capitalize on long-range correlations within the image, the hybrid coder performs an operationally optimal, in the rate-distortion sense, bit allocation among coding parameters. An orthogonal basis framework is used within which an image segmentation and a hybrid block-based transform are selected jointly. The selection of coefficients in the DCT component of the overall block transform is made a part of the optimization procedure. A Lagrangian multiplier approach is used to optimize the hybrid transform parameters together with the segmentation. Differential encoding of the DC coefficient is employed, with the scanning path based on a 3rd-order Hilbert curve. Simulation results show a significant improvement in quality with respect to the JPEG standard, an approach based on optimization of DCT basis vectors, as well as, the purely fractal techniques.