Soft constraints in nonlinear spectral fitting with regularized lineshape deconvolution.

This article presents a novel method for incorporating a priori knowledge into regularized nonlinear spectral fitting as soft constraints. Regularization was recently introduced to lineshape deconvolution as a method for correcting spectral distortions. Here, the deconvoluted lineshape was described by a new type of lineshape model and applied to spectral fitting. The nonlinear spectral fitting was carried out in two steps that were subject to hard constraints and soft constraints, respectively. The hard constraints step provided a starting point and, therefore, only the changes of the relevant variables were constrained in the soft constraints step and incorporated into the linear substeps of the Levenberg-Marquardt algorithm. The method was demonstrated using localized averaged echo time point resolved spectroscopy proton spectroscopy of human brains.