Image Compression Using a Fast and Efficient Discrete Tchebichef Transform Algorithm

The Discrete Tchebichef Transform (DTT) which based on discrete orthogonal Tchebichef polynomials can be an alternative to the Discrete Cosine Transform (DCT) for image processing such as image compression and image recognition as the properties of the DTT are similar to that of the DCT. The DTT not only has higher energy compactness than the DCT in images that have high illumination value variations such as artificial diagrams but also has the advantage of easily computation using a set of recurrence relations. In this paper, the DTT will be introduced with explanation of its similarity to DCT, also a new fast and efficient 4x4 algorithm for computing the DTT coefficients which can be used in image compression will be proposed. This algorithm reduces computational complexity as measured in terms of the number of arithmetic operations while keeping the accuracy of the reconstructed images.