The Research Of Fractal Coding Combined With Compressive Sensing

With the vigorous development of information technology, digital image becomesone of the main forms of information. However, the huge redundancy in the originalimage causes the waste of resource in image transmission and storage process.Therefore, image compression is a necessary step in image processing. More and moreimage compression technologies have been proposed since1960s. The fractal imagecoding method attracts the scholars’ attention for its novel thought and high potentialcompression ratio. Fractal coding, wavelet coding and model-based coding areconsidered as the most potential encoding technologies. Although fractal coding can gethigh compression ratio, the quality of compression is not so good and it needs too muchtime. These disadvantages make fractal coding can’t be widely used. In order toovercome the shortcomings of the fractal coding, domestic and foreign scholars haveproposed many improved algorithms, the fractal coding combined with waveletalgorithm is the most success. This paper takes it as a background, launching research.Firstly, the significance of image compression and the image compressiontechnology development history are introduced. And then a brief classification ofexisting image compression algorithms is presented and some typical codingtechnologies and their characteristics are analyzed.Secondly, this paper introduces the research background and the significance of thefractal coding, elaborates the fractal coding theoretical basis and the principle oftraditional fractal coding and describes the traditional fractal steps with theoreticalknowledge in detail. We discuss the characteristics of fractal coding and the key factorof reconstruction through experimental results. Then, through the argument of the affineinvariant of the inner product, we propose an improved fractal coding algorithm basedon the inner product and variance.Finally, according to the research of compressive sensing and fractal coding whichis based on the wavelet transform, this paper proposes a fractal coding combined withcompressive sensing algorithm which includes two parts: low frequency coding anddifferential image coding. At first, the image is decomposed by wavelet transform,fractal compression algorithm based on the variance and inner product is used to codethe low-frequency sub-image, for differential image and other sub-image, we usecompressive sensing coding algorithm to sample and code the difference image and other sub-figure, to ease distortion and recover the detail of the image after fractalcoding. Compressive sensing samples from sparse signal using low sampling rate, andgets accurate reconstruction images. Because the differential image and high-frequencysub-image are sparse, it is feasible to use compressive sensing algorithm in coding them.The experimental results show that the proposed algorithm not only improves the speedof coding, but also obtains high quality reconstructed image.