Resolution enhancement in digital in-line holography with sparsity

In digital holography, the reconstructed resolution is generally limited by the size of the numerical aperture. For a lens-free imaging configuration, the high-frequency information is lost due to the finite size of the recorded area. It is challenging to obtain an enhanced-resolution recovery with the finite-recorded hologram. Here, we propose an algorithm to enhance the reconstructed resolution by utilizing sparse prior of the image. We combine the sparse regularization term with the extrapolation of the recorded area based on the inverse problem approach. For regularization, the tau(0)-norm is utilized to promote the sparsity of the solution during the iterative process. An iterative optimization algorithm is developed to solve the nonconvex resolution enhancement problem, which is implemented by substituting the primal-dual saddle-point problem for the primal problem. Our method can circumvent the limitation of the recorded area and produce enhanced-resolution recovery by employing the sparsity of the object distribution. Both the simulation and experiment indicate that the proposed algorithm can achieve the superior enhancement for reconstructed resolution with a single captured hologram in digital in-line holography .(C) 2018 Society of Photo-Optical Instrumentation Engineers (SPIE)