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

Autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: INVERSE PROBLEMS; v. 32, n. 11 NOV 2016.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 13/16508-3 - Cálculo rápido do operador generalizado de retroprojeção com aplicações em reconstrução tomográfica de imagens
• Beneficiário: Elias Salomão Helou Neto
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 15/10171-2 - Métodos incrementais e de média das sequências para otimização convexa não-diferenciável com Subgradientes Inexatos
• Beneficiário: Rafael Massambone de Oliveira
• Linha de fomento: Bolsas no Brasil - Doutorado
• Processo FAPESP: 13/19380-8 - Controle e filtragem de sistemas estocásticos
• Beneficiário: Eduardo Fontoura Costa
• Linha de fomento: Auxílio à Pesquisa - Regular