Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm.

Area of Science:

• Computational imaging
• Applied mathematics
• Image reconstruction

Background:

• Phase retrieval is crucial for reconstructing images from intensity measurements in various applications.
• Current gradient descent methods are computationally intensive and difficult to optimize for higher-order derivatives.
• Existing second-order methods face memory limitations with large datasets.

Purpose of the Study:

• To develop an efficient and generalizable phase retrieval algorithm using automatic differentiation.
• To adapt the Levenberg-Marquardt algorithm for constrained optimization problems in phase retrieval.
• To overcome the computational and memory challenges of traditional second-order methods.

Main Methods:

• Implemented a matrix-free Levenberg-Marquardt algorithm using reverse-mode automatic differentiation.
• Extended the algorithm for general constrained optimization beyond least-squares problems.
• Required only the forward model specification, with derivatives computed automatically.

Main Results:

• Successfully solved unconstrained and constrained ptychographic retrieval problems.
• Demonstrated effectiveness under both Gaussian and Poisson noise models.
• Outperformed state-of-the-art first-order methods in convergence speed and accuracy.

Conclusions:

• The proposed automatic differentiation-based Levenberg-Marquardt method offers a powerful and efficient solution for phase retrieval.
• This approach provides excellent convergence guarantees and superlinear rates.
• It presents a computationally viable alternative to existing methods for data-rich imaging modalities.