Deep Gauss-Newton for phase retrieval.

Area of Science:

• Computational imaging
• Deep learning for scientific applications
• Image reconstruction algorithms

Background:

• Iterative reconstruction methods often require manual parameter tuning.
• Phase retrieval from diffraction patterns is a challenging inverse problem.
• Existing neural network approaches may lack interpretability or require specific training data.

Purpose of the Study:

• To develop a novel deep learning algorithm for image reconstruction that incorporates physical model knowledge.
• To enable simultaneous retrieval of phase and absorption from single-distance diffraction data.
• To improve reconstruction accuracy and resolution without manual regularization or step-size selection.

Main Methods:

• Unrolling a Gauss-Newton optimization method within a deep neural network architecture.
• Utilizing convolutional neural networks to learn regularization and step-size parameters automatically.
• Applying the deep Gauss-Newton (DGN) algorithm to simulated and experimental diffraction data.

Main Results:

• The DGN algorithm achieved significant improvements in reconstruction error compared to state-of-the-art methods.
• Enhanced resolution was observed in reconstructions obtained using the DGN approach.
• Simultaneous retrieval of phase and absorption was successfully demonstrated from single-distance diffraction patterns.

Conclusions:

• The deep Gauss-Newton algorithm offers a powerful, data-driven approach to image reconstruction.
• DGN effectively integrates physical model knowledge into deep learning for enhanced performance.
• This method shows great promise for advancing computational imaging and phase retrieval applications.