Wavelet Transform-based Fractal Image Compression Algorithm

One of the primary problems we are confronted with in information age is how to effectively store and transmit huge amounts of digital images and videos. Some popular international standards such as JPEG, MPEG and H.26X are not so perfect and still need to be improved. Fractal image compression (FIC) takes advantage of self-similarities which exist in the images commonly. It uses the self-similarity in different scales of image to find the corresponding fractal description and remove the geometry redundance. FIC is one of the most competitive schemes in recent research, and it has the capable of achieving good image quality at a very high compression ratio. Wavelet transform coding can remove the statistical redundance in images effectively. At the same time, its property of multi-resolution transform adapts to human visual system very well. In this thesis, we combine FIC and wavelet transform and clear the relationship between different wavelet scales significantly, so we can get much higher compression rate and shorter encoding time. The main drawbacks of FIC are the expensive computational cost in the encoding process, the convergence in decoding process, the block-effect in decoded image, etc.In this thesis, we focuses on how to reduce the huge coding time of fractal image compression, and the main contributions are some new fractal image compression algorithms:(1) A new searchless fractal image compression algorithm based on wavelet decomposition is proposed to decrease the encoding time significantly with little decline of PSNR.(2) Two fast fractal image compression algorithms based on K-mean clustering optimization are proposed to accelerate the matching process between range and domain blocks.(3) A new fractal image compression algorithm based on progressive neighbor searching strategy is proposed, and the correlation among adjacent parts is fully used to organize the domain pool, which enhances the encoding efficiency greatly.The organization of this thesis is as follows: Chapter 1 introduces the research background of image compression briefly; Chapter 2 introduces the mathematical background and the theory foundation of the fractal encoding, and realize the classic Jacquin fractal image encoding algorithm, which is the foundation of this thesis; Chapter 3 introduces the wavelet multi-resolution analysis theory and the EZW...