Quantitative mapping of myelin water fractions (MWF) can substantially improve our understanding of the progression of several demyelination white matter diseases such as multiple sclerosis. While MWF can be determined from both T2-weighted and T2*-weighted imaging data, it is much faster to collect T2*-weighted imaging data. However, estimation of MWF from T2*-weighted imaging data using a multi-exponential component model is an ill-conditioned problem whose solutions are often very sensitive to noise and modeling errors. In this work, we address this problem using a new model-based method. This method is characterized by: a) absorbing the spectral priors using the Bayesian-based statistical framework, and b) absorbing the spatial priors using a reproducing kernel based model. Both simulation and experimental results show the proposed method significantly outperforms the conventional parameter estimation methods currently used for MWF estimation.