A Regularized Affine-Scaling Trust-Region Method for Parametric Imaging of Dynamic PET Data

Parametric imaging of nuclear medicine data exploits dynamic functional images in order to reconstruct maps of kinetic parameters related to the metabolism of a specific tracer injected in the biological tissue. Classical approaches to parametric imaging rely on linearized schemes that, on the one hand, are computationally effective but, on the other hand, provide information just on a very limited number of parameters (typically two). Possible nonlinearized approaches require the pixelwise numerical solution of compartmental nonlinear ill-posed inverse problems and therefore typically imply a notable computational burden. In the present paper we introduce a fast numerical optimization scheme for parametric imaging relying on a regularized version of the standard affine-scaling trust-region method. The main advantages of this approach are both that it is a regularization method (and therefore it reduces the numerical instabilities in the reconstructed images) and that it is significantly faster than other algorithms in the optimization market (and therefore it may be utilized for clinical applications). The validation of this approach is realized in a simulation framework for brain imaging and also in the case of an experimental set of nuclear medicine data acquired from a murine model. Comparison of performances is made with respect to a regularized Gauss--Newton scheme and a standard nonlinear bound-constrained least-squares algorithm.