The deconvolution process allows to extract the impulse response of a sample by collecting the input/output response. In the blind deconvolution estimation (BDE), this process is implemented without the input signal information. In particular, this work is focused on fluorescence lifetime imaging microscopy (FLIM) datasets, where the fluorescence impulse responses are extracted by assuming an exponential library model and a common instrument response (input signal) to all the measurements. Due to the nonlinear interaction of the free variables, an alternated least-squares methodology is adopted, which is based on constrained quadratic optimizations. The new BDE algorithm is validated with synthetic FLIM datasets by comparing the standard deconvolution methodology with an exponential library under different model orders, and types and levels of noise, which shows the applicability and robustness of the proposal.