Institute of Mathematics for Industry

Seminar



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ON IMAGE RESTORATION FROM RANDOM SAMPLING NOISY FREQUENCY DATA WITH MULTI-REGULARIZATION


Hold Date 2019-02-05 15:30~2019-02-05 16:00

Place Seminar Room W1-D-710, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Xiaoman Liu (Southeast University)

Abstract.
Consider the image restoration using random sampling noisy frequency data by total variation regularization. By exploring image sparsity property under wavelet expansion, we establish an optimization model with two regularizing terms specifying image sparsity and edge preservation on the restored image. The choice strategy for the regularizing parameters are rigorously set up together with corresponding error estimate on the restored image. The cost functional with data-fitting in frequency domain is mini-mized using the Bregman iteration scheme. By deriving the gradient of the cost functional explicitly, the minimizer of the cost functional at each Bregman step is also generated by an inner iteration process with Tikhonov regularization, which is implemented stably and efficiently due to the special structure of the regularizing iterative matrix. Numerical tests are given to show the validity of the proposed scheme.
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