There have been many attempts to separate mixed relaxation-time decays. Among them, some approaches do not assume the number of exponential decays a priori for the analysis of multiple-component decay signals. However, they are sensitive to ill conditions and have a poor resolving ability in terms of decay constants. In this study, a new method is proposed that can analyze multiple T2 decays with high resolution using the inverse Z-transform, which was demonstrated in simulation and in vivo human brain experiment. T2-selective images were also presented and used for myelin-water fraction mapping and deep brain-tissue segmentation.