<title>Fractal image compression based on wavelet transform</title>

Abstract

It is well known that images can be greatly compressed by exploiting the self-similar redundancies. In this paper, the self-similarities of wavelet transform are analyzed, and it is discovered that corresponding subbands of different scale detail signals are similar. An image coding method is proposed according to this property. The typical self-affirm transform is modified such that it is adapted to DWT coefficient encoding. An adaptive quantization method of the transform parameters s, is given. Firstly, a J-order discrete wavelet transform of the original image, denoted by LL₀, is performed. That is, LL is decomposed into LL_{j + 1}, LH_{j + 1, HL$_j + 1}, for 0 <EQ j <EQ J - 1. Secondly, LL_{J$. is encoded based on DCT. Thirdly, HL(subscript J} LH_J and HH_J are quantized and run- length coded. Fourthly, HL_j, LH_j and HH_j for 1 <EQ j <EQ J - 1, are encoded with modified self- similar transforms. HL_j, LH_j, and HH_j are divided into non-overlapping range blocks. For each range block R_{i (epsilon} HL_j, a domain block D_j (epsilon) HL_{j + 1}, which best matches R_j, is found, and the parameter s₁ of the corresponding transform is determined and adaptively quantized. Several kinds of images are compressed with this method. Experimental results demonstrate that this method can compress images significantly while keeping a very good fidelity. Besides, the algorithm is faster than typical fractal image coding methods because less searching is needed.