Fluorescence lifetime microscopy imaging (FLIM) is an optic technique that allows a quantitative characterization of the fluorescent components of a sample. However, for an accurate interpretation of FLIM, an initial processing step is required to deconvolve the instrument response of the system from the measured fluorescence decays. In this paper, we present a novel strategy for the deconvolution of FLIM data based on a library of exponentials. Our approach searches for the scaling coefficients of the library by non-negative least squares approximations plus Thikonov/l2 or l1 regularization terms. The parameters of the library are given by the lower and upper bounds in the characteristic lifetimes of the exponential functions and the size of the library, where we observe that this last variable is not a limiting factor in the resulting fitting accuracy. We compare our proposal to nonlinear least squares and global non-linear least squares estimations with a multi-exponential model, and also to constrained Laguerre-base expansions, where we visualize an advantage of our proposal based on Thikonov/l2 regularization in terms of estimation accuracy, computational time, and tuning strategy. Our validation strategy considers synthetic datasets subject to both shot and Gaussian noise and samples with different lifetime maps, and experimental FLIM data of ex-vivo atherosclerotic plaques and human breast cancer cells.