基于多尺度几何分析的图像编码研究进展

Advances in Image Coding Based on Multiscale Geometric Analysis

近10年来,在小波变换的理论基础之上,产生了一系列新的能够更加有效地表示和处理高维数据奇异的数学变换,统称为"多尺度几何分析".它们不仅具有多分辨率特性、时频局部性、多方向性和各向异性,而且克服了小波变换表示边缘、轮廓等高维奇异时存在的局限性.目前,有关多尺度几何分析的理论和应用方法的研究已经成为一个新的热点.首先探讨了小波变换的方向特性及其局限性;其次,以多尺度几何分析的发展为主线,对基于各种多尺度几何分析工具的静态图像编码算法进行概述阐述和比较研究,同时分析和讨论了各类算法的优势和不足;最后,对基于多尺度几何分析的图像编码算法的未来发展进行展望.

Recently built upon the theory of wavelet analysis, a series of mathematical transforms have been explored that can effectively represent and process high-dimensional singularities. These novel transforms are generally referred to as ＂multiscale geometric analysis （MGA）＂. The objective of MGA is to establish an optimal transform that provides multiscale and multidirectional representation for high-dimensional functions. They have many good characteristics such as multiresolution, time-frequency localization, multi-directionality, as well as anisotropy. Meanwhile, MGA overcomes the limitations of wavelet in representing higher-dimensional singularities, such as edges and contours. So far, the theory and application of MGA have attracted extensive attention from different disciplines of image processing. Among these disciplines, MGA shows great potential for image coding since it can provide a sparser representation than wavelet. Research on MGA-based approach thus has become a focus in the field of image coding in recent years. In this paper, the authors first discuss the directionality of wavelet transform and its limitations. Then taking the development of MGA as thread, they summarize state-of-the-art image coding methods based on MGA. By comparative study, the advantages and drawbacks of each kind of methods are analyzed and discussed. Finally, they state the possible new directions of MGA-based image coding in further developments.