Multidimensional Nonseparable Subband Coding

这项研究提供了一个参数化的整个家庭的多维完美重建子带编码滤波器组。 这样做的动机在于图像（视频）类型信号的有效编码和压缩的实际应用。 这样得到的多维滤波器组的族的参数描述被用于设计具有期望的频率分离特性的完美重构滤波器组。 整个家庭的不可分离的多维光滑小波，这些滤波器组的迭代产生的也完全参数化，以这种方式。 所采用的技术基本上包括那些从多维系统理论。 双正交问题正在接近制定他们作为矩阵扩展或矩阵完成问题的多维多项式或稳定适当的合理功能的环;和paraunitary问题的描述，或等价地，合成多维无损系统。 类似的策略正在使用的因果制定，以及在处理特殊类别的解决方案，如线性相位的解决方案。

This research is providing a parameterization of the entire family of multidimensional perfect reconstruction subband coding filter banks. The motivation for doing this lies in practical application of efficient coding and compression of image (video) type signals. The parametric description of the family of multidimensional filter banks so obtained is being used to design perfect reconstruction filter banks having desirable frequency separation properties. The entire family of nonseparable multidimensional smooth wavelets resulting from iterations of these filter banks is also being completely parameterized in this way. The techniques being adopted essentially consist of those from multidimensional system theory. The biorthogonal problems are being approached by formulating them as matrix extension or matrix completion problems in the ring of multidimensional polynomials or stable proper rational functions; and the paraunitary problems as problems of describing, or equivalently, synthesizing multidimensional lossless systems. Similar strategies are being used in the acausal formulation as well as in dealing with special classes of solutions such as the linear phase solutions.