Orthogonal U transform and its application in image compression

In this paper, a new unitary transform called U transform is constructed in recursion way. The U transform matrix contains piecewise constant basis vectors, piecewise linear basis vectors and piecewise second order polynomial basis vectors, and therefore U transform is a generalization of Walsh transform and Slant transform. A fast computational algorithm has been found for the transformation. The U transform is applied to digital image compression with quantization table based on Human Visual System (HVS). The experimental results indicate that U transform outperforms Slant transform in image compression.