The advancement of improved photoactive materials, such as those proposed for next-generation solar cells, low-power lighting, and lasing applications, requires a deep understanding of their correlated spatial, spectral, and temporal properties. In principle, correlated time-resolved microscopy techniques are capable of capturing such information. However, the large data sets that encapsulate temporal, spectral, and spatial information create the prodigious challenge of analyzing gigabytes of correlated data, which typically takes enormous computational resources. These challenges motivate the development of robust and efficient data analysis tools to realize fast spatial and spectral decomposition and to gain physical insights that arise from statistical analysis. Herein, we propose a reliable and fast global analysis method based on variable projection and subsampling methods, which exhibits exceptionally high sensitivity to buried spatial and spectral information in large and multidimensional microscopy data sets as compared to traditional methods. The reliability and robustness of this new method is tested on transient absorption and impulsive vibrational microscopy data sets acquired on polycrystalline CH3NH3PbI3 perovskite films.