Lattice Modeling Approach to Multidimensional Signal Processing

一维随机过程的格参数刻画 已成为一个发展良好的理论，有许多应用，以线性 估计，频谱分析，语音编码与合成，系统 识别和控制系统。 这项研究旨在 将该理论扩展到二维标量像场， 多维随机场 特别是， 非常丰富的散射/逆散射问题的理论和 将检查网格截面结构。 这种联系的核心 是格型滤波器的级联和嵌套特性，其中 增加新的部分并不改变先前的部分。 这项工作奠定了基础的理论晶格建模， 对于多维数据处理、模式 识别和数字滤波。

Lattice parameter characterization of one-dimensional random processes has become a well developed theory with many applications to linear estimation, spectral analysis, speech coding and synthesis, system identification, and control systems. This research is directed towards the extension of this theory to two-dimensional scalar image fields and multidimensional random fields. In particular, the connection between the very rich theory of scattering/inverse scattering problems and the lattice section structure will be examined. Central to this connection is the cascade and the nesting properties of the lattice filter where the addition of a new section does not change the previous sections. This work lays the basis for a theory of lattice modeling which is crucial to applications to multidimensional data processing, pattern recognition, and digital filtering.