Wirtinger gradient descent optimization for reducing Gaussian noise in lensless microscopy

Lensless microscopy is an imaging technique that records diffraction measurements without using any lens and recovers the complex object profile via phase retrieval. The successful reconstruction of lensless imaging experiments often requires the captured images to have a high signal-to-noise ratio (SNR), but high SNR is hard to guarantee in practice. Here we report a novel iterative algorithm for reducing Gaussian noise in lensless microscopy. Our method incorporates the Gaussian noise model in the Wirtinger gradient descent optimization process to perform phase retrieval. The reported algorithm is tested on both the multi-angle illumination and multi-height detection schemes of lensless microscopy for diversity measurements. As demonstrated by simulations and experiments, the method is able to obtain better reconstructions under low SNR conditions, in comparison with the traditional Gerchberg Saxton method. We have provided open-source implementation code for non-commercial use.