Accession Number : ADA330530

Title :   Estimation with Best Bases

Descriptive Note : Final rept. 30 Sep 96-29 Sep 97

Corporate Author : NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s) : Mallat, Stephane ; Geiger, Davi

PDF Url : ADA330530

Report Date : 15 SEP 1997

Pagination or Media Count : 9

Abstract : New models of non-stationary processes have been introduced. We showed that the covariance of locally stationary processes can be modeled as pseudodifferential operators. The spectrum of such processes is estimated by approximating the Karhunen-Loeve basis with a local cosine basis, that is optimized with a best basis search algorithm. Applications to geophysics have been studied. Locally dilated processes are a different kind of non-stationary processes that appear in image processing and in physical phenomena that involve Doppler effects. It was shown that the dilation parameters of such processes can be estimated with a wavelet transform, through the solution of a partial differential equation in the scale-space plane. An application concerns the reconstruction of three dimensional surfaces from texture gradient in images. The last part of this project was devoted to the analysis of the distortion-rate function of wavelet image transform codes. By modeling images as element of Besov spaces, we calculated precise analytical formula of distortion-rates, which are verified by numerical experiments.

Descriptors :   *MATHEMATICAL MODELS, *WAVELET TRANSFORMS, ALGORITHMS, IMAGE PROCESSING, APPROXIMATION(MATHEMATICS), COVARIANCE, STATISTICAL PROCESSES, APPLIED MATHEMATICS.

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE