Fourier ptychographic reconstruction using Poisson maximum likelihood and truncated Wirtinger gradient

Area of Science:

• Computational Imaging
• Optics and Photonics
• Image Reconstruction

Background:

• Fourier ptychographic microscopy (FPM) is a computational imaging technique enabling high space-bandwidth product imaging.
• FPM reconstruction involves phase retrieval from low-resolution intensity images to recover a high-resolution spectrum.
• Real-world FPM measurements are degraded by noise (Gaussian, Poisson, speckle) and pupil location errors, impacting reconstruction quality.

Purpose of the Study:

• To develop a novel Fourier ptychographic (FP) reconstruction method robust to common measurement degenerations.
• To enhance the accuracy and quality of reconstructed images in FPM systems.
• To provide an efficient and effective solution for overcoming noise and errors in FP reconstruction.

Main Methods:

• A gradient descent optimization framework is employed for FP reconstruction.
• Poisson maximum likelihood is utilized for improved signal modeling.
• Truncated Wirtinger gradient is applied for effective error removal and noise reduction.

Main Results:

• The proposed FP reconstruction method demonstrates superior performance compared to existing state-of-the-art algorithms.
• Simulated and real experimental data validate the effectiveness of the new method in handling noise and errors.
• Significant improvements in image reconstruction quality were observed using the developed technique.

Conclusions:

• The novel FP reconstruction method offers a robust solution for addressing degenerations in FPM.
• The technique enhances the reliability and accuracy of computational imaging reconstructions.
• The source code is available for non-commercial use, promoting further research and application.