Digital phase-shifting holography based on sparse approximation of phase and amplitude

Phase-shifting holography with a lens focussing the complex object on the sensor plane is considered. In this setup a scaled copy of the complex object is reconstructed at the sensor plane. In order to reconstruct the complex object from noisy data, we apply variational inverse imaging, where the amplitude and the absolute phase of the object are assumed to admit sparse representations in suitable sparsifying transforms. The developed technique is based on the sparse phase and amplitude reconstruction (SPAR) algorithm developed in [4]–[6]. Numerical experiments demonstrate effectiveness of SPAR for holographic reconstruction of 3D objects.