Optimal Fresnelet sparsification for compressive complex wave retrieval from an off-axis digital Fresnel hologram

Complex wave retrieval (CWR) from an off-axis digital Fresnel hologram proposed by Liebling et al. is a single-exposure scheme in which a non-linear holographic process is modeled using simultaneous linear equations. This linear model fits well into the compressive sensing (CS) framework. We propose a method in which the CS is applied to a CWR method with Fresnelet sparsification. This approach compensates for the noise in the retrieved Fresnel field that is aroused due to the linear modeling approximations involved in the reconstruction process. As a result, a superior intensity and phase reconstruction were obtained by this method. Four methods including the direct CWR (conventional) method, compressive CWR method without sparsification, compressive CWR method with Haar wavelet, and compressive CWR method were compared with Fresnelet sparsification. The simulation and the optical experimental results converge to the same conclusion: the Fresnelet sparsified case is the best choice for quantitative phase imaging using compressive off-axis digital Fresnel holography.