告题目：Multigrid iterative regularization with framelet denoising for image deblurring

报告人：Marco Donatelli（意大利因苏布里亚大学副教授）

报告时间：2018年4月19日下午15:30

报告地点：清水河校区 主楼A1 – 512

报告摘要：Recent numerical methods for image deblurring decompose nonlinear problems into simpler subproblems and usually require an inner step of linear regularization. For instance, the classical iterative shrinkage thresholding algorithm combines one step of Landweber method with one step of soft-thresholding. Assuming that an estimation of the noise level is available, we combine a recently proposed iterative regularization method with linear framelet denoising. This combination allows a fast frequency filtering and produces a sparse reconstruction in the wavelet domain. Moreover, its employment in a multigrid scheme ensures a stable convergence and a reduced noise amplification. The coarsening strategy used in our multigrid method is defined by the low-pass filter used for the framelet denoising and is able to achieve fast computations at each coarser level independently of the imposed boundary conditions. Finally, the iterations are projected in a closed and convex set that is known to contain the exact solution of the problem, e.g., the nonnegative cone. We study the convergence of the proposed algorithm and prove that, if supplied with the suitable stopping criterion, it is a regularization method. The comparison with other methods from the literature proves that it is able to provide highly accurate reconstruction without requiring the setting of any parameter.

报告人简介： Prof. Marco Donatelli是意大利因苏布里亚大学科学与高科技系-数值分析组的副教授。目前担任SIAM J. Sci. Comput., SIAM J. Imaging Sci., SIAM J. Matrix Anal. Appl., IMA J. Numer. Anal., Inverse Problems, Appl. Math. Comput., Linear Algebra Appl., BIT, J. Comput. Appl. Math., Appl. Numer. Math.等著名国际杂志编委。他还是National Group for Scientific Calcolus (GNCS)，Italian Society of Applied and Industrial Mathematics (SIMAI)，Society for Industrial and Applied Mathematics  (SIAM) 的成员。