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Regularization Methods for Linear Inverse Problems with Sparse Constraint
发布时间:2018-03-28     点击次数:
报告题目: Regularization Methods for Linear Inverse Problems with Sparse Constraint
报 告 人: 吕锡亮 教授(武大数学与统计学院)
报告时间: 2018年03月29日 12:15--12:50
报告地点: 理学院东北楼一楼报告厅(110)
报告摘要:

In this talk, we consider the linear inverse problems of recovering a sparse vector from noisy measurement data. Two different class of regularization methods are proposed: iterative regularization method and variational regularization method.  For iterative regularization method, we showed that ADMM method is a regularization method, which explained why ADMM works well for the image debluring problem. For the variational regularization method, we provided an algorithm of primal-ual active set type for a class of convexnconvex sparsity-promoting penalties. A novel necessary optimality condition for the global minimizer using the associated thresholding operator is derived. Upon introducing the dual variable, the active set can be determined from the primal and dual variables. This relation lends itself to an iterative algorithm of active set type which at each step involves updating the primal variable only on the active set and then updating the dual variable explicitly. This approach can also extend to the group sparse model. Numerical examples are given to validate the theoretical results.

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