Genetically encoded calcium indicators cause neurons to fluoresce when they fire. Combined with optical imaging techniques, they have become a key tool for modern neuroscience, enabling in vivo tracking of neural activity in model organisms from zebrafish to mice. Diffuser-based fluorescence microscopes are a great choice for calcium imaging because they enable single-shot (fast) 3D imaging, by encoding 3D information into a 2D measurement that can then be computationally extracted. But solving that 3D sparsity-constrained deconvolution problem frame-by-frame is difficult and slow, and tends to fail when the sample is not sparse enough. Spatiotemporal algorithms process all the frames at once, leveraging information about the temporal behavior of the emissions. Jointly solving for the spatial and temporal domains is very powerful because they share so much information; for example, pixels that are part of the same neuron probably flash at the same times, and neurons overlapping in space can be separated if they have different temporal signals. However, spatiotemporal algorithms are challenging to apply because they are tackling a large and non-convex optimization problem. In this project, we use prior and domain knowledge to guide the optimization towards a meaningful solution, by testing and improving the robustness of initialization procedures. We also precisely interrogate what features of experimental data (e.g. noise, background, or sparsity) cause the algorithms to fail, along with how and why. With this knowledge, we achieve promising results extracting neural activity traces from both simulated and experimental diffuser-based calcium imaging data.