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When a single molecule is detected in a wide-field microscope, the imageapproximates the point spread function of the system. However, as thedistribution of molecules becomes denser and their images begin to coincide,existing solutions to determine the number of molecules present and theirprecise three-dimensional locations can tolerate little to no overlap. Asolution to this problem involving matched optical and digital techniques, ashere proposed, is critical to increase the allowable labeling density and toaccelerate single-molecule localization microscopy.

Sparse reconstructions of overlapping three-dimensional point spread functions using overcomplete dictionaries