Sparsity-based approach for 3D super-resolution microscopy from correlation information of high emitter-density frames

Breakthroughs in the field of chemistry have enabled surpassing the classical optical diffraction limit by utilizing photo-activated fluorescent molecules. In the single-molecule localization microscopy (SMLM) approach, a sequence of diffraction-limited images, produced by a sparse set of emitting fluorophores with minimally overlapping point-spread functions is acquired, allowing the emitters to be localized with high precision by simple post-processing. However, the low emitter density concept requires lengthy imaging times to achieve full coverage of the imaged specimen on the one hand, and minimal overlap on the other. Thus, this concept in its classical form has low temporal resolution, limiting its application to slow-changing specimens. In recent years, a variety of approaches have been suggested to reduce imaging times by allowing the use of higher emitter densities. One of these methods is the sparsity-based approach for super-resolution microscopy from correlation information of high emitter-density frames, dubbed SPARCOM, which utilizes sparsity in the correlation domain while assuming that the blinking emitters are uncorrelated over time and space, yielding both high temporal and spatial resolution. However, SPARCOM has only been formulated for the two-dimensional setting, where the sample is assumed to be an infinitely thin single-layer, and thus is unsuitable to most biological specimens. In this work, we present an extension of SPARCOM to the more challenging three-dimensional scenario, where we recover a volume from a set of recorded frames, rather than an image.