报告题目：Multi-parameter Image Approximation based on Framelet and Total Variation Regularization
报告摘要：Image restoration based on variational method is one of the hot topics in digital image processing. The best-known ROF model preserves shape edges but causes stair case in the flatten part. For the remedy of this defect, Several works proposing high order regularization method have been done in the literature, but which suffered numerical inefficiency due to high nonlinearity and non-smoothness of the Euler-Lagrange equation. Considering this we propose a new multi-parameter regularization model based on framlet and total variation to restore image from blurry and noisy or corrupted observations, which utilizes edge preserving property and the adaptivity of the framlet transform to the underlying regularity of image. We discussed the solution of the proposed model by alternative direction minimization algorithm which equivalent to split Bregman iteration with an efficient and automatical multi-regularization parameter choosing strategy based on balancing principle which overcome the difficulty of toning the regularization parameter manually in numerical simulation. Complexity of the algorithm was analyzed and convergence of the algorithm was proved and the performance of this new model was shown by several benchmark numerical results.