The effect of the nonlinearity on GCV applied to conjugate gradients in computerized tomography

Autor(es)

Reginaldo J. Santos ^[1] ; Álvaro R. de Pierro ^[2]

Afiliação do(s) autor(es)

^[1] Universidade Federal de Minas Gerais. ICEx. Departamento de Matemática - Brasil

^[2] State University of Campinas. IMECC. Department of Applied Mathematics - Brasil

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL & APPLIED MATHEMATICS; v. 25, n. 1, p. 111-128, 2006-00-00.

Resumo

We study the effect of the nonlinear dependence of the iterate x k of Conjugate Gradients method (CG) from the data b in the GCV procedure to stop the iterations. We compare two versions of using GCV to stop CG. In one version we compute the GCV function with the iterate x k depending linearly from the data b and the other one depending nonlinearly. We have tested the two versions in a large scale problem: positron emission tomography (PET). Our results suggest the necessity of considering the nonlinearity for the GCV function to obtain a reasonable stopping criterion. (AU)

• Processo FAPESP: 02/07153-2 - Algoritmos para a reconstrução tomográfica: otimização, restauração, quantificação e aplicação
• Beneficiário: Sergio Shiguemi Furuie
• Modalidade de apoio: Auxílio à Pesquisa - Temático