Combined DCT-HAAR transforms for image compression

Abstract

Discrete Cosine Transform (DCT) and Haar wavelet transform are very important transforms in image compression. While DCT works extremely well for highly correlated data, the Haar transform gives superior results for images exhibiting rapid gradient variations. The objective of this project is to combine the advantages of these 2 transforms into one transform in order to get better peak-signal-to-noise-ratio (PSNR) and keeping good compression ratio. Following the JPEG, our first approach was to apply separately on each 8x8 block the Haar and the DCT transforms. A signaling bit along the transform which gave better PSNR are quantized and transmitted. This approach gave better PSNR than each one separately. Our second approach was to construct a new hybrid transform which is a combination of these 2 transforms. We mixed both DCT and Haar transforms into one transform. We derived the new transform coding formulas. Our last approach was to divide the image into non-equal size blocks based on a modification of the quadtree decomposition. We applied our hybrid transform on each block obtained. Results show that our approach outperforms the existing DCT and Haar methods, keeping good quality of the image even for high compression ratios, giving a higher PSNR than DCT for the same compression ratio, and permitting better edge recovery than the Haar transform.