Anisotropic regularization for sparsely sampled and noise-robust Fourier ptychography

Area of Science:

• Computational imaging
• Microscopy
• Image reconstruction

Background:

• Fourier ptychography (FP) offers super-resolution and quantitative phase imaging.
• FP reconstruction is ill-posed with noisy or insufficient data.
• High-throughput imaging demands robust FP reconstruction.

Purpose of the Study:

• To develop a regularized FP reconstruction algorithm for improved performance under challenging conditions.
• To enhance image quality and data recovery in sparse and noisy FP measurements.

Main Methods:

• Proposed a regularized FP reconstruction algorithm.
• Utilized anisotropic total variation (TV) for object function regularization.
• Employed Tikhonov regularization for pupil function.
• Formulated reconstruction using the alternating direction method of multipliers (ADMM).

Main Results:

• Successfully recovered high-quality images from sparsely sampled and noisy measurements.
• Demonstrated effective noise suppression and edge preservation with TV regularization.
• Retrieved accurate amplitude and phase images under insufficient sampling.
• Outperformed other FP reconstruction algorithms under harsh conditions.

Conclusions:

• The proposed regularized FP algorithm significantly improves reconstruction quality.
• Anisotropic TV and Tikhonov regularizations are effective for noisy and sparse FP data.
• The method is validated on real experimental FP microscopy images, showing practical utility.