多尺度脊波字典的构造及其在图像编码中的应用

在变换域图像编码技术中，图像的稀疏表示是编码的关键。该文在分析了脊波函数的缺陷的基础上，首先提出了一种多尺度脊波字典的构造方法，并通过树形结构对原子进行组织，加快了图像稀疏分解中最匹配原子的搜索速度；然后提出了一种基于树形多尺度脊波字典的匹配追踪静态图像编码方法；最后通过对量化失真与编码速率的分析，结合稀疏分解系数的分布，提出了系数的自适应量化和编码方案。实验结果表明，多尺度脊波字典能够对图像进行有效的稀疏表示；与JPEG2000相比，新的编码算法具有更好的编码性能，尤其在低比特率条件下。

Construction of Multiscale Ridgelet Dictionary and Its Application for Image Coding

The sparse representation of image is the key to the image coding technique in transform domain. In this paper, based on the analysis of the limitation of ridgelet function, a new construction method of multiscale ridgelet dictionary is firstly proposed. The speed of search of the most matching atoms is improved based on the tree structured organization of atoms. And then a tree structure multiscale ridgelet dictionary based matching pursuit image coding scheme is proposed. In the last the decomposed coefficients are adaptively quantized and encoded based on the distribution of coefficients and the rate-distortion analysis. Experiment results show that the new multiscale ridgelet dictionary can represent the images sparsely. On the other hand, the performances of the new method are shown to compare favorably against those of JPEG2000 scheme, especially at low bit rate.