On the iterative inversion of generalized attenuated Radon transforms

Autor(es)

Miqueles, Eduardo X. ^[1] ; De Pierro, Alvaro R. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Appl Math, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Inverse and Ill-Posed Problems; v. 21, n. 5, p. 695-712, OCT 2013.
• Citações Web of Science: 4

Resumo

We are concerned with an iterative inversion of the Generalized Attenuated Radon Transform (GART) first introduced by Kunyansky (1992). It is essentially based on approximating the inverse of GART by a scaled inverse Radon transform followed by an appropriate iterative refinement. This paper presents a convergence proof for this iterative method introducing tighter and computable estimates (compared to Kunyansky) for the iteration contraction constants. As expected, such constants depend on the attenuation parameter mu, i.e., the higher mu is, the closer the constant is to one yielding slow convergence to the solution. Such values are compared with those obtained using the infinite-dimensional version of the power method by Krein and Rutman (1950). (AU)

• Processo FAPESP: 09/15844-4 - Inversão da transformada generalizada de Radon: novos resultados em tomografia por fluorescência
• Beneficiário: Eduardo Xavier Miqueles
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado