Implementation of an optimal first-order method for strongly convex total variation regularization
The paper presents a practical implementation of an optimal first-order optimization algorithm for large-scale problems. This algorithm is suited for smooth and strongly convex functions. While the underlying algorithm by \textit{Y. Nesterov} [Math. Program. 103, No. 1 (A), 127--152 (2005; Zbl 1079.90102)] requires the knowledge of two parameters that characterize the smoothness and the strong convexity, the proposed algorithm estimates these parameters during the iteration. This makes the algorithm of practical use. The mechanisms are also allowed for the application to non-strongly convex functions. The authors test the performance of the algorithm and compare it with two variants of the gradient projection algorithm and a variant of the FISTA-algorithm. They apply the method to total variation regularized tomographic reconstruction of a generic three-dimensional test problem. The software is available as a C-implementation with an interface to MATLAB.
scientific article; zbMATH DE number 6062477
scientific article