POD Method for the Inverse Initial Value Problem of Two‐Dimensional Time‐Fractional Diffusion Equation and Application to Image Deblurring
Abstract
ABSTRACT In this paper, we mainly investigate the backward problem for the two‐dimensional time‐fractional diffusion equation by the proper orthogonal decomposition (POD) method, and also apply this method to solve the image deblurring problem. The approach constructs a low‐dimensional basis by solution snapshots to accelerate the reconstruction of the initial field from noisy terminal time measurements. Besides, we give the Tikhonov regularization method and obtain the convergence analysis about the regularization solutions. Finally, we propose several numerical experiments to show the efficiency and accuracy of our method.
Fields of Study & Subjects
Numerical methods in inverse problems
Model Reduction and Neural Networks
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Volume
- 49
- Issue
- 10
- Pages
- 10173–10189
- Publication date
- 13 February 2026
- Language
- EN