Implementation of an Image Compression Algorithm Based on Low Complexity Integer Approximate Discrete Tchebichef Transform

Abstract

The discrete cosine transform (DCT) is used widely in the area of image compression. Recently, the Discrete Tchebichef Transform (DTT) is reported to be superior to DCT in terms of coding performance. In this paper, DTT is presented first. Then a scheme of deriving the integer approximate DTT is introduced. The integer approximate DTT is used to compress a gray-scale image. Since the resulting integer approximate DTT matrix is not normal, we need to multiply a diagonal matrix to its left. When we use the integer matrix to perform the transform, the diagonal matrix have to be merged into the quantization process. We derive the equivalent quantization matrix and the inverse quantization matrix. Compared with JPEG and exact DTT, the integer approximated DTT shows a bit lower reconstructed image quality but with extreme low complexity.