Accelerated bregman operator splitting with backtracking
Yunmei Chen Xianqi Li Yuyuan Ouyang Eduardo Pasiliao
Inverse Problems & Imaging 2017, 11(6): 1047-1070 doi: 10.3934/ipi.2017048

This paper develops two accelerated Bregman Operator Splitting (BOS) algorithms with backtracking for solving regularized large-scale linear inverse problems, where the regularization term may not be smooth. The first algorithm improves the rate of convergence for BOSVS [5] in terms of the smooth component in the objective function by incorporating Nesterov's multi-step acceleration scheme under the assumption that the feasible set is bounded. The second algorithm is capable of dealing with the case where the feasible set is unbounded. Moreover, it allows more aggressive stepsize than that in the first scheme by properly selecting the penalty parameter and jointly updating the acceleration parameter and stepsize. Both algorithms exhibit better practical performance than BOSVS and AADMM [21], while preserve the same accelerated rate of convergence as that for AADMM. The numerical results on total-variation based image reconstruction problems indicate the effectiveness of the proposed algorithms.

keywords: Bregman operator splitting accelerated ADMM convex optimization Barzilai-Borwein stepsize backtracking total variation image reconstruction
Total variation and wavelet regularization of orientation distribution functions in diffusion MRI
Yuyuan Ouyang Yunmei Chen Ying Wu
Inverse Problems & Imaging 2013, 7(2): 565-583 doi: 10.3934/ipi.2013.7.565
We introduce a variational model and a numerical method for simultaneous ODF smoothing and reconstruction. The model uses the sparsity of MR images in finite difference domain and wavelet domain as the spatial regularization means in ODF's reconstruction. The model also incorporates angular regularization using Laplace-Beltrami operator on the unit sphere. A primal-dual scheme is applied to solve the model efficiently. The experimental results indicate that with spatial and angular regularization in the process of reconstruction, we can get better directional structures of reconstructed ODFs.
keywords: orientation distribution function primal dual hybrid gradient method. Diffusion magnetic resonance image

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