Structure-dependent amplification for denoising and background correction in Fourier ptychographic microscopy

Fourier Ptychographic Microscopy (FPM) allows high resolution imaging using iterative phase retrieval to recover an estimate of the complex object from a series of images captured under oblique illumination. FPM is particularly sensitive to noise and uncorrected background signals as it relies on combining information from brightfield and noisy darkfield (DF) images. In this article we consider the impact of different noise sources in FPM and show that inadequate removal of the DF background signal and associated noise are the predominant cause of artefacts in reconstructed images. We propose a simple solution to FPM background correction and denoising that outperforms existing methods in terms of image quality, speed and simplicity, whilst maintaining high spatial resolution and sharpness of the reconstructed image. Our method takes advantage of the data redundancy in real space within the acquired dataset to boost the signal-to-background ratio in the captured DF images, before optimally suppressing background signal. By incorporating differentially denoised images within the classic FPM iterative phase retrieval algorithm, we show that it is possible to achieve efficient removal of background artefacts without suppression of high frequency information. The method is tested using simulated data and experimental images of thin blood films, bone marrow and liver tissue sections. Our approach is non-parametric, requires no prior knowledge of the noise distribution and can be directly applied to other hardware platforms and reconstruction algorithms making it widely applicable in FPM.