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Single-molecule localization based super-resolution microscopy, by localizing a sparse subset of stochastically activated emitters in each frame, achieves subdiffraction-limit spatial resolution. Its temporal resolution, however, is constrained by the maximal density of activated emitters that can be successfully reconstructed. The state-of-the-art three-dimensional (3-D) reconstruction algorithm...
Compressed sensing theory suggests that successful inversion of an image of the physical world from its modal parameters can be achieved at measurement dimensions far lower than the image dimension, provided that the image is sparse in an a priori known basis. The assumed basis for sparsity typically corresponds to a gridding of the parameter space, e.g., an DFT grid in spectrum analysis. However,...
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