Efficiency of analytical transforms for image compression

Digital image transforms, for decorrelating image pixels, have received wide spread interest in the literature. Analytical transforms play a great role in the gray level decorrelation and energy compaction of the image and hardly affect the performance of the image compression technique. This paper provides a comparison of the bit rate reduction capability and signal to noise ratio among five transforms; namely, Karhunen-Loeve transform (KLT), discrete cosine transform (DCT), discrete Hartley transform (DHT), discrete Gabor transform (DGT), and the discrete wavelet transform (DWT), where they have shown the most promise in image compression coding systems. The coefficients of the transform are truncated with a specified threshold and the bit rate is computed after Huffman coding. The image is reconstructed from the truncated version of the coefficient matrix. Peak signal to noise ratio and compression ratio are considered to evaluate the efficiency of the analytical transform. The error image between the original and the reconstructed image is computed to follow the error distribution over the image.