Lattice Implementation of Nonuniform Filter Banks and Its Applications

近年来，小波变换被应用到图像编码中，JPEG2000和MPEG4分别将小波变换作为静止图像编码和视频编码的标准技术。小波变换实现为双通道滤波器组的倍频连接。然而，与DCT相比，该方法的计算量增加，且对图像编码的最优性不明确。在这个项目中，我们的目的是实现非均匀滤波器组，这是小波变换的广义版本，同时使用晶格结构保持完美的重构结构。为了实现完美的重构，将非均匀滤波器组转换为均匀滤波器组。将非均匀滤波器组分为抽取比为整数的滤波器组和抽取比为有理数的滤波器组两类。对这两种情况进行了讨论，提出了广义线性相位非均匀滤波器组的设计方法和晶格结构，以实现结构上的完美重构。并将得到的非均匀滤波器组应用于图像编码应用，验证了该方案的有效性。

Recently, Wavelet transforms have been used in the image coding, which are adopted as standard technology in JPEG2000 for still images and MPEG4 for video. The wavelet transforms are implemented as octave connection of 2-channel filter banks. However the computational complexity increases than DCT and the optimality is not clear for image coding. In this project, our purpose is to implement the nonuniform filter banks which is the generalized version of wavelet transform, while keeping the perfect reconstruction structurely using lattice stracture. To achieve the perfect reconstruction, the nonuniform filter banks are transformed into the uniform banks. The nonuniform filter banks are divided into two classes, one is the case that the decimation ratio is integer and other is the case that the decimation ratio is rarional. We discussed the both cases and presented the design method of generalized linear phase nonuniform filter banks and the lattice structure to achieve the perfect reconstruction structurely. Also we adapt the resulting nonuniform filter banks to image coding applications and confirm the validity of our project.