A wavelet multiscale iterative regularization method for the parameter estimation problems of partial differential equations

Authors:
Hongsun Fu;Bo Han;Hongbo Liu
Affiliations:
Department of Mathematics, Dalian Maritime University, Dalian 116026, China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;School of Information, Dalian Maritime University, Dalian 116026, China
Venue:
Neurocomputing
Year:
2013

Citing 9
Cited 0

On the representation of operators in bases of compactly supported wavelets

SIAM Journal on Numerical Analysis
A multiresolution method for distributed parameter estimation

SIAM Journal on Scientific Computing
An adaptive wavelet-vaguelette algorithm for the solution of PDEs

Journal of Computational Physics
A wavelet-based method for numerical solution of nonlinear evolution equations

Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Wavelet methods for PDEs — some recent developments

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Adaptive Wavelet Galerkin Methods for Linear Inverse Problems

SIAM Journal on Numerical Analysis
Comparison of generalization ability on solving differential equations using backpropagation and reformulated radial basis function networks

Neurocomputing
Adaptive wavelet-Galerkin methods for limited angle tomography

Image and Vision Computing
Shift and gray scale invariant features for palmprint identification using complex directional wavelet and local binary pattern

Neurocomputing

Quantified Score

Hi-index	0.01

Visualization

Abstract

A wavelet multiscale iterative regularization method is proposed for the parameter estimation problems of partial differential equations. The wavelet analysis is introduced and a wavelet multiscale method is constructed based on the idea of hierarchical approximation. The inverse problem is decomposed into a sequence of inverse problems which rely on the scale variables and are solved successively according to the size of scale from the longest to the shortest. By combining multiscale approximations, the problem of local minimization is overcomed, and the computational cost is reduced. At each scale, based on the wavelet approximation, the problem of inverting the parameter is transformed into the problem of estimating the finite wavelet coefficients in the scale space. A novel iterative regularization method is constructed. The efficiency of the method is illustrated by solving the coefficient inverse problems of one- and two-dimensional elliptical partial differential equations.