Lattice Implementation of Nonuniform Filter Banks and Its Applications

近年来，小波变换被用于图像编码，JPEG2000对静止图像和MPEG4视频采用小波变换作为标准技术。小波变换被实现为2通道滤波器组的倍频程连接。然而，与DCT相比，DCT的计算复杂度增加了，图像编码的最优性还不是很清楚。在这个项目中，我们的目的是实现非均匀滤波器组，它是小波变换的推广形式，同时利用格子结构保持完美的重构。为了实现完美重构，将非均匀滤波器组变换为均匀滤波器组。将非均匀滤波器组分为两类，一类是抽取比为整数的情况，另一类是抽取比为稀疏数的情况。我们讨论了这两种情况，并给出了广义线性相位非均匀滤波器组的设计方法和实现结构上的完美重构的格子结构。此外，我们还将得到的非均匀滤波器组应用于图像编码应用中，并验证了我们方案的有效性。

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.