Optimized Denoising Method for Fourier Ptychographic Microscopy Based on Wirtinger Flow

Fourier ptychographic microscopy (FPM) is a recently developed technique for high-resolution complex imaging with a wide field-of-view. FPM combines captured low-resolution images corresponding to angle-varying illuminations in the Fourier domain with phase retrieval and synthetic aperture algorithms; consequently, it can surpass the space-bandwidth product limit of an objective lens. In typical FPM systems, the reconstructed result is sensitive to various types of system and environmental noise; thus, the quality can be significantly degraded. In this paper, based on the Wirtinger flow gradient descent framework, we propose an optimized phase retrieval method, which searches for the optimization results with iteratively changing weights and suppresses noise by utilizing captured noise and its corresponding constrained item. A correction term is further introduced into the new algorithm. This method cannot only adapt to varying sampling conditions but also provide an accurate optimum solution. We validate our method with both simulated and experimental images. The reconstructed results all illustrate the effectiveness and robustness of our method and demonstrate that the proposed method can significantly depress noise and improve the reconstruction performance of high-resolution complex images.