Sparsity based super-resolution in optical measurements

We propose and experimentally demonstrate a method of exploiting prior knowledge of a signal's sparsity to perform super-resolution in various optical measurements, including: single-shot sub-wavelength Coherent Diffractive Imaging (CDI), i.e. algorithmic object reconstruction from Fourier amplitude measurements, and ultra-fast pulse measurement, i.e. exceeding the temporal resolution imposed by the rise time of the photodiode. The prior knowledge of the signal's sparsity compensates for the loss of phase information and the loss of high spatial frequencies in the case of CDI, and for the loss of temporal frequencies accompanying the photodiode measurement process.