Prospective Digital Processing Methods of Multidimensional Signals with the Use of Irregular Meshes

Abstract

The article considers sparse representation of signals based on using irregular meshes, which is one of prospective lines in digital processing of multidimensional signals. Application of irregular meshes has been seen for several decades as a promising field of investigations opening the possibility of using high efficiency of representing a signal carrier in combination with well-developed approximation methods used in solving boundary-value problems. However, lack of tools suitable for solving typical digital signal processing problems with the use of irregular meshes (e.g., for computing orthogonal discrete transforms) had resulted in that any noticeable and practically significant results are lacking in this area. Nevertheless, the recent years have seen a growth of interest in using irregular meshes.

The article presents the results of investigations in this field that were carried out at the MPEI Chair for Computers, Systems and Networks. Matters concerned with generation of irregular meshes adapted to the specific features of multidimensional signals are addressed. Algorithms intended for carrying out interpolation, for making a shift from a regular carrier (a uniform regular mesh) to an irregular one, and for computing discrete transformations for a signal with an irregular carrier are presented. Solutions for arranging intellectual signal processing, such as pattern recognition and motion detection, are suggested.