Implementation of an optimal first-order method for strongly convex total variation regularization

被引:88
|
作者
Jensen, T. L. [2 ]
Jorgensen, J. H. [1 ]
Hansen, P. C. [1 ]
Jensen, S. H. [2 ]
机构
[1] Tech Univ Denmark, Dept Informat & Math Modelling, DK-2800 Lyngby, Denmark
[2] Aalborg Univ, Dept Elect Syst, DK-9220 Aalborg O, Denmark
关键词
Optimal first-order optimization methods; Strong convexity; Total variation regularization; Tomography; TOTAL VARIATION MINIMIZATION; CONSTRAINED TOTAL VARIATION; ALGORITHM; BARZILAI;
D O I
10.1007/s10543-011-0359-8
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to mu-strongly convex objective functions with L-Lipschitz continuous gradient. In the framework of Nesterov both mu and L are assumed known-an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient mu and L during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss the convergence rate and iteration complexity of several first-order methods, including the proposed algorithm, and we use a 3D tomography problem to compare the performance of these methods. In numerical simulations we demonstrate the advantage in terms of faster convergence when estimating the strong convexity parameter mu for solving ill-conditioned problems to high accuracy, in comparison with an optimal method for non-strongly convex problems and a first-order method with Barzilai-Borwein step size selection.
引用
收藏
页码:329 / 356
页数:28
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