  Information about microscopic objects with features smaller than the
diffraction limit is almost entirely lost in a far-field diffraction image but
could be partly recovered with data completition techniques. Any such approach
critically depends on the level of noise. This new path to superresolution has
been recently investigated with the use of compressed sensing and machine
learning. We demonstrate a two-stage technique based on deconvolution and
genetic optimization which enables the recovery of objects with features of
1/10 of the wavelength. We indicate that l1-norm based optimization in the
Fourier domain unrelated to sparsity is more robust to noise than its l2-based
counterpart. We also introduce an extremely fast general-purpose restricted
domain calculation method for Fourier transform based iterative algorithms
operating on sparse data.
