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Simplified digital holographic reconstruction using statistical methods

For reconstructing a complex object wavefront from digital holograms, we propose a new penalized-likelihood approach based on the measurement statistics and edge-preserving regularization. The log-likelihood is complicated since the measurements are related to the magnitude of the complex beam. We use optimization transfer to derive a new simplified iterative algorithm that monotonically decreases the cost function. Unlike the conventional FFT-based holographic reconstruction method, the new approach uses all of the measured data and can be applied to holograms with any (known) reference beam pattern. Simulation results demonstrate the potential for improved image quality.