String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images

Author(s)

de Oliveira, Rafael Massambone ; Helou, Elias Salomao ; Costa, Eduardo Fontoura

• Document type: Journal article
• Source: INVERSE PROBLEMS; v. 32, n. 11 NOV 2016.
• Web of Science Citations: 3

Abstract

We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method. (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM. (AU)

• FAPESP's process: 13/19380-8 - Control and filtering of stochastic systems
• Grantee: Eduardo Fontoura Costa
• Support type: Regular Research Grants
• FAPESP's process: 15/10171-2 - Incremental methods and String-Averaging for non-differentiable convex optimization with inaccurate Subgradients
• Grantee: Rafael Massambone de Oliveira
• Support type: Scholarships in Brazil - Doctorate
• FAPESP's process: 13/16508-3 - Fast computation of the generalized Backprojection operator with applications in tomographic image reconstruction
• Grantee: Elias Salomão Helou Neto
• Support type: Regular Research Grants
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: José Alberto Cuminato
• Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC