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Monosynaptic connectivity mapping is crucial for building circuit-level models of neural computation. Two-photon optogenetic stimulation, when combined with whole-cell recording, enables large-scale mapping of physiological circuit parameters. In this experimental setup, recorded postsynaptic currents are used to infer the presence and strength of connections. For many cell types, nearby connections are those we expect to be strongest. However, when the postsynaptic cell expresses opsin, optical excitation of nearby cells can induce direct photocurrents in the postsynaptic cell. These photocurrent artifacts contaminate synaptic currents, making it difficult or impossible to probe connectivity for nearby cells. To overcome this problem, we developed a computational tool, Photocurrent Removal with Constraints (PhoRC). Our method is based on a constrained matrix factorization model which leverages the fact that photocurrent kinetics are less variable than those of synaptic currents. We demonstrate on real and simulated data that PhoRC consistently removes photocurrents while preserving synaptic currents, despite variations in photocurrent kinetics across datasets. Our method allows the discovery of synaptic connections which would have been otherwise obscured by photocurrent artifacts, and may thus reveal a more complete picture of synaptic connectivity. PhoRC runs faster than real time and is available as open source software.