A Fast Zigzag-Pruned 4×4 DTT Algorithm for Image Compression

The Discrete Tchebichef Transform (DTT) is a linear orthogonal transform which has higher energy compactness property like other orthogonal transform such as Discrete Cosine Transform (DCT). It is recently found applications in image analysis and compression. This paper proposes a new approach of fast zigzag pruning algorithm of 4x4 DTT coefficients. The principal idea of the proposed algorithm is to make use of the distributed arithmetic and symmetry property of 2-D DTT, which combines the similar terms of the pruned output. Normalization of each coefficient is done by merging the multiplication terms with the quantization matrix so as to reduce the computation. Equal number of zigzag pruned coefficients and block pruned coefficients are used for comparison to test the efficiency of our algorithm. Experimental method shows that our method is competitive with the block pruned method. Specifically for 3x3 block pruned case, our method provides lesser computational complexity and has higher peak signal to noise ratio (PSNR). The proposed method is implemented on a Xilinx XC2VP30 FPGA device to show its efficient use of hardware resources. Key-Words: Discrete Cosine Transform, DiscreteTchebichef Transform, Image compression, Peak signal to noise ratio, Zigzag Prune.