Quantitative magnetic resonance imaging (qMRI) allows images to be compared across sites and time points, which is particularly important for assessing long-term conditions or for longitudinal studies. The multiparametric mapping (MPM) protocol is used to acquire images with conventional clinical contrasts, namely PD-, T1-, and MT-weighted volumes. Through multi-echo acquisition for each contrast and variations in flip angles between PD- and T1-weighted contrasts, parameter maps, such as proton density (PD), longitudinal relaxation rate (R1), apparent transverse relaxation rate (R2$^*$), and magnetization transfer saturation (MT$_{sat}$), can be estimated. Various algorithms have been employed to estimate these parameters from the acquired volumes. This paper extends an existing maximum a posteriori approach, which uses joint total variation regularization, by transitioning from a Gaussian noise approximation to a more physically plausible model that assumes noncentral chi-distributed noise.