Compressive Holography From Poisson Noise Plagued Holograms Using Expectation-Maximization

Lensless in-line holography is a simple, portable, and cost-effective method of imaging especially for the biomedical microscopy applications. We propose a multiplicative gradient descent optimization based method to obtain multi-depth imaging from a single hologram acquired in this imaging system. We further extend the method to achieve phase imaging from a single hologram. Negative-log-likelihood functional with the assumption of Poisson noise has been used as the cost function to be minimized. The ill-posed nature of the problem has been handled by the sparse regularization and the upper-bound constraint in this expectation-maximization framework. In microscopy of non-fluorescent objects, the pixel-level upper bound is previously known from the reference illumination image. The gradient descent optimization requires calculation of the partial derivative of the cost function with respect to a given estimate of the object at every iteration. A method of obtaining this quantity for holography, for both the cases of real object and complex object has been shown. The reconstruction method has been validated using extensive simulation and experimental studies. The comparison with the previously established iterative shrinkage/thresholding algorithm based compressive in-line holography shows that the proposed method has following advantages: faster convergence rate, better reconstructed image quality and the ability to perform phase imaging.