String-Averaging Incremental Subgradients for Constrained Convex Optimization with Applications to Reconstruction of Tomographic Images
| Autor: | Rafael Massambone de Oliveira, Elias S. Helou, Eduardo F. Costa |
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| Rok vydání: | 2016 |
| Předmět: |
PROCESSOS ESTOCÁSTICOS
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION 02 engineering and technology 030218 nuclear medicine & medical imaging Theoretical Computer Science Set (abstract data type) 03 medical and health sciences 0302 clinical medicine Tomographic image reconstruction Convergence (routing) 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Numerical tests Mathematics - Optimization and Control Subgradient method Mathematical Physics Mathematics Tomographic reconstruction Applied Mathematics String (computer science) Computer Science Applications Optimization and Control (math.OC) Signal Processing Convex optimization 020201 artificial intelligence & image processing Algorithm |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| DOI: | 10.48550/arxiv.1610.05823 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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