Multidimensional Geometrical Signal Representation: Constructions and Applications
Yue Lu · 2007
One of the key differences between one-dimensional (1-D) and N-D (N ≥ 2) signals is the geometrical information, an important and unique feature of multidimensional signals. The goal of this research is to develop a new set of theories and techniques in signal processing that can make better use of the intrinsic geometrical information in multidimensional data in a robust and efficient way. The primary technique we employ to approach this problem is multidimensional filter banks, due to their computational advantages, their design flexibilities, and very importantly, their direct connection with the theory of basis (nonredundant) and frame (redundant) decomposition of multidimensional signals. Directional information is an important geometric feature of multidimensional signals. As a result of a separable extension from 1-D bases, multidimensional wavelet transforms have very limited directionality. Furthermore, different directions are mixed in certain wavelet subbands. To solve this problem, we propose a simple Directional Extension for Wavelets (DEW) that fixes this subband mixing problem and improves the directionality. In a nutshell, the proposed