High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude.

We apply a nonlocal adaptive spectral transform for sparse modeling of phase and amplitude of a coherent wave field. The reconstruction of this wave field from complex-valued Gaussian noisy observations is considered. The problem is formulated as a multiobjective constrained optimization. The developed iterative algorithm decouples the inversion of the forward propagation operator and the filtering of phase and amplitude of the wave field. It is demonstrated by simulations that the performance of the algorithm, both visually and numerically, is the current state of the art.