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HONS 04/06

A Fast Discrete Tchebichef Transform Algorithm for Image Compression

Kiyoyuki Nakagaki
Department of Computer Science
University of Canterbury

Abstract

The Discrete Tchebichef Transform (DTT) is a transform method based on the scaled orthogonal Tchebichef polynomials, which have applications recently found in image compression and pattern recognition. This report summarises the research carried out for the development of a fast DTT algorithm. The mathematical properties and the related algorithmic details of the Discrete Cosine Transform (DCT) have been studied in order to develop a fast DTT algorithm. A novel DTT algorithm suitable for 4 × 4 image blocks is proposed in this report. A theoretical analysis of the proposed method, the method using the direct application of the definition and the method using the separability and the symmetry shows that the proposed method requires the smallest number of operations while the direct application of the definition performs badly. Presented experimental results also show the improved performance of the proposed algorithm.