Some properties and fast algorithms of slant transform in image processing

Abstract A first order stationary Markov process model has been considered for image processing problems. A relative performance measure of unitary transforms to image data has been defined. It has been proved that the slant transform is superior to Walsh-Hadamard transform in this relative performance measure for positive correlation under the assumed model. A lower bound of relative performance has also been found. Furthermore, fast algorithms for computing diagonal elements of any slant transformed matrix have been presented. Finally, it has been shown how slant transform can be modified to improve the relative performance.