Under-sampling reconstruction with total variational optimization for Fourier ptychographic microscopy

Abstract Fourier ptychographic microscopy has recently attracted attention because of its ability to expand the space-bandwidth products of an imaging system. To improve the efficiency of information acquisition, large numerical apertures and low-overlapping rates should be employed. However, the pixel aliasing problem occurs in phase recovery in the under-sampling condition. An algorithm was developed to solve the pixel aliasing problem with low overlapping requirements. Combined with total variational optimization procedures, the overlapping requirements were reduced, and the noise was suppressed. Compared with the upsampled method, the proposed algorithm achieved evident overlapping rate reduction. With a spatial-sampling ratio of 0.72, satisfactory effects were achieved at the minimum overlapping rate of 24% in simulation, which meant a significant reduction in the amount of data. A limitation for the objective lens aperture was identified, and a theoretical explanation is proposed.

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