基于小波变换的分形压缩方法研究

【作者】 司徽东；

【导师】 付永生；

【作者基本信息】 山东大学 ， 信号与信息处理， 2005， 硕士

【摘要】 图像是人们生活中信息交流的最为重要的载体,也是蕴涵信息量最大的媒体。众所周知,数字图像的数据量非常庞大,必须经过有效的压缩,才能满足数字图像的高速传输和存储。所以图像压缩作为通信及多媒体领域中的一项关键技术,对于信息技术的发展具有很强的现实意义和广阔的发展前景。 近年来,随着许多新理论、新方法的不断涌现,出现了一大批新的图像压缩编码方法。 分形图像压缩算法是热点之一。分形编码是在Mandelbrot分形几何理论的基础上发展起来的一种编码方法。其关键在于寻找图像的IFS(迭代函数系统),利用它来达到压缩图像的目的。分形压缩的本质是由于图像中存在高度的仿射冗余度,即图像中包含有许多自我参考物。它有许多部分是自相似的,经过适当变换,各区域可以互相表达。分形图像压缩技术的核心是拼接定理。 基于小波分析的压缩算法在静态和动态图像压缩领域得到广泛的应用,并且已经成为某些图像压缩国际标准(如JPEG2000)的重要环节。小波变换用于图像编码的基本思想就是把图像进行多分辨率分解,分解成不同空间、不同频率的子图像,然后再对子图像进行系数编码。系数编码是小波变换用于压缩的核心,压缩的实质是对系数的量化压缩。根据Mallat的塔式分解算法,图像经过小波变换后被分割成四个频带:水平、垂直、对角线和低频,低频部分还可以继续分解。然而,采用何种策略对小波变换后的数据进行处理仍是图像压缩领域的一个研究热点。 本文研究的重点是图像小波分解后分形压缩编码方法。基于对传统的小波域分形方法的分析,本文提出了一种改进的压缩方案,即分步采用智能螺旋搜索法(IHSM)和同位元素对应法(EEPM)相结合的方法对原有方案进行改进。智能螺旋搜索法的提出是将空间域图像的局部自相似特性尝试用于小波域的分析,打破了传统的搜索方法,将分形方法概念进一步延伸。同位元素对应法则是利用了图像小波分解后的子带相似性,用低频块的分形码经过运算对比来代替高频块的分形码,既减少了运算时间,又提高了图像的压缩比,使图像小波分解的优势得到了更多还原

【Abstract】 Image is the most important carrier among the information intercommunion in people’s life, and it is the biggest media containing information. As we all know, the data quantity is very large in a digital image. If the data couldn’t be compressed efficiently, it will be a great obstacle to the development of communication and multimedia technologies when high transmission speed and large memory are needed in multimedia communication system. Image compression technology, as a crucial technology in the fields of communication and multimedia, is very important to information technology nowadays and future.Along with many new theorieses and new method flows out, many new image compression methods have been proposed in recent years.The fractal compression scheme is one of the focus methods. Fractal coding is a compression scheme which based on the Mandelbrot’s fractal geometry theory. The key of this scheme is to find IFS of the image, and then utilize the IFS to compress the image. The genius of the fractal coding is the high redundancy degree. In other words, the image contains many self- frame of reference, which has many self- resemblanced parts. Each region can express the other one through appropriate transformation. The core of this compression scheme is Collage Theorem.Wavelet-based compression scheme has been put into practice in the areas of compression of static images and motive images as well as a key part in some international standards such as JPEG2000. The basic ideology of the wavelet-based compression scheme is multi-resolution. Analyzing the image in the different space and different frequency is the first process, then we carry coefficient coding on the sub-block. Coefficient coding is the core of wavelet-based compression scheme,and the substance of the compression is carry quantiti- compression on coefficient. One image is divided into four frequency thought wavelet-transformation. However, it is still a research hotspot that how to deal with the coefficients transformed from adigital image with wavelet in a more efficient way.This paper focuses on fractal compression coding method after image wavelet decomposition. Based on the analysis of the traditional fractal method of the wavelet field, it presents an improved compression approach that it respectively takes the method of combining the intelligent helix search method (IHSM) and the equivalent element parallelism method (EEPM) to improve the original approach. The presentation of the IHSM is trying to put the use of part of the similarities of its own of the space field image into the analysis of the wavelet field, and it has broken the traditional searching method and has better expanded the concept of the fractal method. However, the EEPM just utilizes the similarity of the sub-band after the image wavelet decomposition, by calculating and contrasting the fractal coding in low frequency block to take place of the one in high. It not only reduced the calculating time but also advanced the image compression rate so that the advantage of the image wavelet decomposition can better embodiment.The mock computer test shows that by taking the above-mentioned improved approach the subjective effect of the reconstructed image has little difference between the one via original calculating method, but the calculating efficiency and the compression rate both get great improvement Then this explains that the improved approach mentioned in this essay has got fine effect, and it makes full combination of the wavelet transformation and the advantage of the fractal coding so that it has formed an image compression approach which is effective in operation and excellent in capability.更多还原