Title :
Wavelet soft-threshold method for determining an unknown source in a diffusion equation
Author_Institution :
Dept. of Appl. Math., Beijing Univ. of Technol., Beijing, China
Abstract :
We consider the problem of determining an unknown source, which depends only on the spatial variable, in a diffusion equation. This is an ill-posed problem. For a reconstruction of the solution from indirect data, the dual least squares method generated by the family of Shannon wavelet subspaces is applied. Moreover, a certain simple nonlinear modification of the method based on local refinements of the wavelet expansion of the noisy data is investigated.
Keywords :
diffusion; least squares approximations; wavelet transforms; Shannon wavelet subspaces; diffusion equation; dual least squares method; local refinement; nonlinear modification; solution reconstruction; spatial variable; wavelet expansion; wavelet soft-threshold method; Equations; Pattern analysis; Pattern recognition; Wavelet analysis; Ill-posed problem; Shannon wavelets; dual least squares method; soft-threshold;
Conference_Titel :
Wavelet Analysis and Pattern Recognition, 2009. ICWAPR 2009. International Conference on
Conference_Location :
Baoding
Print_ISBN :
978-1-4244-3728-3
Electronic_ISBN :
978-1-4244-3729-0
DOI :
10.1109/ICWAPR.2009.5207496
