Advances in Image Coding Based on Multiscale Geometric Analysis

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.