Ultimate resolution limits of speckle-based compressive imaging

Compressive imaging using sparsity constraints is a very promising field of microscopy that provides dramatic enhancement the spatial resolution beyond Abbe diffraction limit. Moreover, it simultaneously overcomes Nyquist limit by reconstructing an N -pixel image from less than single-point measurements. Here we present fundamental limits noiseless compressive via constraints, speckle illumination and single-pixel detection. We addressed experimental setup uses randomly generated patterns (in scattering media or multimode fiber). The optimal number measurements, ultimate surprisingly important role discretization are demonstrated theoretical analysis numerical simulations. show that, in contrast to conventional microscopy, oversampling may decrease reconstruction quality imaging.