The problem of observation-based characterization of operators, closely related to the well-studied problem of blind source separation, remains nonetheless considerably less studied. Inspired by the recent success of non-negative and sparse blind source separation, we aim at extending constrained blind source separation models to the data-driven characterization of operators. We introduce a novel non-negative decomposition model for linear operators and investigate different parameter estimation algorithms. We study and compare the proposed algorithms in terms of identification and reconstruction performance in a variety of experimental settings, in order to gain insight into the robustness and limitations of the proposed algorithms. We further discuss the main contribution of our approach compared with state-of-the-art methods for the analysis and decomposition of operators.