Fourier ptychographic reconstruction using mixed Gaussian–Poisson likelihood with total variation regularisation

Abstract

In recent years, Fourier ptychography (FP) has become an attractive area of research in microscopy because it can be used to produce wide-field, high-resolution images, and makes it possible to realise resolutions beyond the optical limit of the numerical aperture of the objective. However, the reconstruction of FP is sensitive to noise. To accommodate the typical mixed Gaussian–Poisson noise in microscopy, the author proposes to reconstruct the images by solving an optimisation problem based on a mixed Gaussian–Poisson likelihood and total variation regularisation. An augmented Lagrangian method with Wirtinger derivatives is used for optimisation. Both synthetic examples and real captured data are used to test the efficiency of the method. Based on the experimental results, the author concludes that the proposed method outperforms other methods, especially in high noise level situations.