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Demonstrates solving the inverse problem in two-dimensional diffusion equations, implying a novel approach to image deblurring.
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.
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Wen et al. (2026) studied this question.
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