Image Compression Based On Fractal And Wavelet

These years, image coding methods based on fractal theories and wavelet transform are showing its advantages, in which wavelet based image coding methods have been adopted by JPEG2000 as its core algorithm. These theories and technologies have their own characteristics, and they can solve problems in some extent. In the meanwhile, fractal image coding methods and wavelet based image coding methods have strong correlation. If we can make full use of the correlation, we are able to solve above problems better. In this paper, the author has done some researches of image compression based on fractal and wavelet transform. The works mainly contain three parts:(1) The fractal image coding algorithm is an irreversible coding method. Its exhaustive inherent encoding time has limited its applications in the image coding field. In this paper, based on the no search fractal image coding algorithm, the author introduces a modified grey-level transform to fully exploit the advantages of the no search fractal image coding algorithm. The modified grey-level transform can greatly reduce the matching error between the range blocks and the domain blocks. Thus, it can reduce the level of the quadtree partitioning and the number of the range blocks. The proposed algorithm can reduce the encoding time while get a little gains for the reconstructed image.(2) The idea behind most hybrid fractal wavelet coders is to apply a discrete wavelet transform to the image and then use fractal methods in the wavelet domain. It is well-known that the wavelet energy concentration is located primarily in the lowest frequency subband. Thus, if the lowest frequency subband is encoded more effectively, the encoder performance can be enhanced. In this paper, the author uses the fast fractal image coding method to encode the lowest subband and uses the set partitioning in hierarchical trees(SPIHT) to encode the error of the fractal coding and other subbands. Due to the small size of the lowest subband and the fractal decoding speed, the proposed method can greatly reduce the encoding time of the fractal coding. Compare with the SPIHT, the proposed methods can better maintain the details of the image because it can set more bitbudget to the SPIHT. Thus, the reconstructed image quality is enhanced.(3) The SPIHT algorithm has been a benchmark in the image coding field. In this paper, the author analyzes the disadvantages and the characters of the SPIHT, and then proposes a modified algorithm based on the block space orientation tree and the adjustment of the order of the output information. The proposed algorithm can reduce the requirement of the memory and enhance the quality of the reconstructed image in the meanwhile.