Solving ptychography with a convex relaxation.

Area of Science:

• Computational imaging
• Optimization algorithms
• Image reconstruction

Background:

• Ptychography is a computational imaging technique for high-resolution sample reconstruction.
• Current ptychography algorithms lack stability, robustness, and theoretical guarantees.
• Convex optimization shows promise for improving related reconstruction tasks.

Purpose of the Study:

• To propose a novel convex formulation for the ptychography problem.
• To develop a more stable and robust ptychography reconstruction algorithm.
• To improve the accuracy and reliability of ptychographic reconstructions.

Main Methods:

• Developed a convex optimization formulation for ptychography.
• Utilized a low-rank factorization-based algorithm for reconstruction.
• Incorporated noise models and a priori constraints into the formulation.

Main Results:

• The proposed convex formulation has no local minima and is broadly solvable.
• The low-rank factorization algorithm achieves near-linear runtime and memory complexity.
• Experimental results show a 25% lower average background variance compared to alternating projections.

Conclusions:

• The convex formulation offers a stable and robust approach to ptychography.
• This method enhances the reliability and accuracy of high-resolution sample reconstruction.
• The new algorithm provides a significant improvement over existing ptychographic reconstruction techniques.