Accession Number : ADA266247


Title :   Applications of the Phi-Transform


Descriptive Note : Final rept. 1 Oct 89-Mar 93,


Corporate Author : SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS AND STATISTICS


Personal Author(s) : DeVore, Ronald ; Jawerth, B


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a266247.pdf


Report Date : Mar 1993


Pagination or Media Count : 9


Abstract : Research on this project has centered on the Phi-transform and wavelets and their application to various problems in image/signal processing, differential equations, and computer aided design. Construction of Wavelets - While the Phi-transform and wavelets have been developed in a quite general setting, several applications, most notably in image processing and numerical methods for differential equations, have pointed to several deficiencies in the traditional wavelet constructions. *This has led the researchers to consider alternate constructions of wavelets and related questions. Partial Differential Equations Concentration has been on two of the most prominent problems in partial differential equations: nonlinear equations such as conservation laws which arise in the study of wave propagation and elliptic problems on nonsmooth domains which arise in scattering theory and many aspects of computer aided design. Image Processing - The researchers have investigated algorithms for image and surface compression based on wavelet decompositions. The algorithms developed have been shown by the researchers to be optimal methods for compression in the sense of width or optimal recovery. Computer Aided Design - They have continued their development of the second generation of the CAD system SLIP. They now have a prototype running which allows them to reconstruct a 3D CAD description from photographic images of a manufactured part. Collaboration With Industry - They continue their collaboration with various industries, government laboratories, and university centers.


Descriptors :   *INTEGRAL TRANSFORMS , ALGORITHMS , SIGNAL PROCESSING , IMAGE PROCESSING , PROPAGATION , SCATTERING , SURFACE WAVES , COMPUTER AIDED DESIGN , THEORY , PHOTOGRAPHIC IMAGES , TRANSFORMERS , PROTOTYPES , WAVE PROPAGATION , DEFICIENCIES , PARTIAL DIFFERENTIAL EQUATIONS , DIFFERENTIAL EQUATIONS , CONSERVATION , DECOMPOSITION


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE