Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient

Abstract

Fourier ptychographic microscopy (FPM) is a novel computational coherent imaging technique for high space-bandwidth product imaging. Mathematically, Fourier ptychographic (FP) reconstruction can be implemented as a phase retrieval optimization process, in which we only obtain low resolution intensity images corresponding to the sub-bands of the sample’s high resolution (HR) spatial spectrum, and aim to retrieve the complex HR spectrum. In real setups, the measurements always suffer from various degenerations such as Gaussian noise, Poisson noise, speckle noise and pupil location error, which would largely degrade the reconstruction. To efficiently address these degenerations, we propose a novel FP reconstruction method under a gradient descent optimization framework in this paper. The technique utilizes Poisson maximum likelihood for better signal modeling, and truncated Wirtinger gradient for effective error removal. Results on both simulated data and real data captured using our laser-illuminated FPM setup show that the proposed method outperforms other state-of-the-art algorithms. Also, we have released our source code for non-commercial use.

Model-independent noise-robust extension of ptychography

“…Previous proposals for noise robust ptychographic algorithms mainly revolved around assuming a known noise model, and using a maximum-likelihood optimization scheme [10,11] or a variance-stabilizing scheme [12][13][14] to construct a cost function which, when minimized, yields a superior reconstruction, because prior knowledge of the noise model has been incorporated. In this section, we discuss the methods in more detail to see where there is room for improvement in these reconstruction schemes, which is what motivated the development of the algorithm that is proposed in this article.…”

“…For both regular [1] and Fourier ptychography [5], the effects of noise in the intensity measurements on the object reconstruction have been studied, and to make the reconstruction algorithm more noise robust several methods have been proposed, most of which rely on choosing the right cost function to minimize [9], sometimes combined with a regularization scheme [10]. One choice for the cost-function is the log-likelihood cost function which can be derived from a maximum-likelihood principle [10,11].…”

“…One choice for the cost-function is the log-likelihood cost function which can be derived from a maximum-likelihood principle [10,11]. In this scheme, one needs to assume a certain noise model and maximize the likelihood of obtaining the measured intensity patterns by minimizing the negative logarithm of the likelihood function.…”

“…In this scheme, one needs to assume a certain noise model and maximize the likelihood of obtaining the measured intensity patterns by minimizing the negative logarithm of the likelihood function. A very good initial guess is required, or some regularization to prevent divergence is necessary [10,11].…”

“…We propose an extension to the ptychographic algorithm that can be applied to any of the aforementioned algorithms [10][11][12][13][14], does not require an assumed noise model, and works by adapting the intensity constraints. We test the algorithm with a proof-of-principle experiment in the visible light regime where we use a phase-only Spatial Light Modulator (SLM) to create and shift the object.…”