Artículo de revista
Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data
Fecha
2015Registro en:
Inverse Problems Volumen: 31 Número: 9 Sep 2015
0266-5611
DOI: 10.1088/0266-5611/31/9/095002
Autor
Courdurier Bettancourt, Matías
Monard, F.
Osses Alvarado, Axel
Romero, F.
Institución
Resumen
In medical single-photon emission computed tomography (SPECT) imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first-order scattering measurements and assuming a very specific scattering regime. The problem is modeled using the radiative transfer equation by means of an explicit non-linear operator that gives the ballistic and scattering measurements as a function of the radioactive source and attenuation distributions. First, by differentiating this non-linear operator we obtain a linearized inverse problem. Then, under regularity hypothesis for the source distribution and attenuation map and considering small attenuations, we rigorously prove that the linear operator is invertible and we compute its inverse explicitly. This allows proof of local uniqueness for the non-linear inverse problem. Finally, using the previous inversion result for the linear operator, we propose a new type of iterative algorithm for simultaneous source and attenuation recovery for SPECT based on the Neumann series and a Newton-Raphson algorithm.