This work is part of a continuous effort to achieve characterization of tissue from auto-fluorescence measurements. One particular problem is the estimation of the number of components in a sample from multi-spectral Fluorescence Lifetime Imaging Data (m-FLIM). The proposed method is based on a two-step iterative procedure, where first a blind end-member and abundance extraction algorithm is employed, followed by an evaluation of the resulting end-members by solving an optimal approximation problem. A threshold method is employed to evaluate if the extracted end-members are nonredundant. The validation of the proposal is performed by 3 m-FLIM data sets from post-mortem human coronary artery samples, where the results obtained matched the qualitative description provided by histopathology slides.