Two-photon (TP) calcium imaging is an important imaging modality in neuroscience, allowing for large-scale recording of neural activity in awake, behaving animals at behavior-relevant timescales. Interpretation of TP data requires the accurate extraction of temporal neural activity traces, which can be accomplished via manual or automated methods. In this work we seek to improve the accuracy of both manual and automated TP microscopy demixing methods by introducing a denoising algorithm based on a statistical model of TP data which includes spatial contiguity, sparse activity and Poisson observations. Our method leverages recent developments in stochastic filtering of structured signals based on Laplacian-scale mixture models (LSMs) to model the neural activity in TP data as a set of spatially correlated sparse variables. We apply our method on TP images taken from the visual cortex of an awake, behaving mouse, and demonstrate improved neural activity demixing over current pre-processing techniques.