Fast Proximal Gradient Methods for Nonsmooth Convex Optimization for Tomographic Image Reconstruction

Autor(es)

Helou, Elias S. ^[1] ; Zibetti, Marcelo V. W. ^[2] ; Herman, Gabor T. ^[3]

Afiliação do(s) autor(es)

^[1] Inst Ciencias Matemat & Comp, Sao Carlos - Brazil

^[2] NYU, Sch Med, Ctr Adv Imaging Innovat & Res CAI2R, New York, NY - USA

^[3] CUNY, PhD Program Comp Sci, New York, NY 10021 - USA

• Tipo de documento: Artigo Científico
• Fonte: SENSING AND IMAGING; v. 21, n. 1 SEP 5 2020.
• Citações Web of Science: 0

Resumo

The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective function values are derived, including a O(1/k(2)) non-asymptotic bound. The presented theory broadens current knowledge and explains the convergence behavior of certain methods that are known to present good practical performance. Numerical experimentation involving computerized tomography image reconstruction shows the methods to be competitive in practical scenarios. Experimental comparison with Algebraic Reconstruction Techniques are performed uncovering certain behaviors of accelerated Proximal Gradient algorithms that apparently have not yet been noticed when these are applied to tomographic image reconstruction. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 16/24286-9 - Avanços teóricos e computacionais em problemas inversos com aplicações para reconstrução tomográfica de imagens
• Beneficiário: Elias Salomão Helou Neto
• Modalidade de apoio: Bolsas no Exterior - Pesquisa