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The applications of present nanoscopy techniques for live cell imaging are limited by the long sampling time and low emitter density. Here we developed a new single frame wide-field nanoscopy based on ghost imaging via sparsity constraints (GISC Nanoscopy), in which a spatial random phase modulator is applied in a wide-field microscopy to achieve random measurement for fluorescence signals. This new method can effectively utilize the sparsity of fluorescence emitters to dramatically enhance the imaging resolution to 80 nm by compressive sensing (CS) reconstruction for one raw image. The ultra-high emitter density of 143 {\mu}m-2 has been achieved while the precision of single-molecule localization below 25 nm has been maintained. Thereby working with high-density of photo-switchable fluorophores GISC nanoscopy can reduce orders of magnitude sampling frames compared with previous single-molecule localization based super-resolution imaging methods.

Single-frame wide-field nanoscopy based on ghost imaging via sparsity constraints