A regularizing method for ill-posed problems: application to quantitative reconstruction in single photon emission computed tomography

The problem of the general 3D reconstruction of a volumic distributed function may be considered as the inversion of the operator modelling the actual detection procedure of the multiple projections. In the context of single photon emission computed tomography (SPECT), the operators, are Fredholm integrals of the first kind. This mean that the problem is the so-called Hadamard ''ill-posed'' problem, and that weak perturbations in the initial data could lead to large variations in the sought solution. A regularizing method of the SPECT reconstruction problem is proposed. The regularization shown on the simulated and clinical studies seems to be valuable for contrast enhancement, quantitative precision and noise minimization