Regularized Newton methods for x-ray phase contrast and general imaging problems

Area of Science:

• Physics
• Materials Science
• Computational Imaging

Background:

• Advanced imaging techniques like X-ray phase contrast imaging and tomography rely on mathematical inversion to reconstruct real-space information.
• Accurate forward models are available, but explicit inversion formulas are often unknown, and data may be insufficient for stable reconstruction.
• A priori information is frequently required to overcome ill-posedness in imaging problems.

Purpose of the Study:

• To present regularized Newton methods as a general framework for solving ill-posed nonlinear imaging problems.
• To apply these methods to X-ray phase contrast imaging in the near-field propagation regime.
• To demonstrate simultaneous phase retrieval and tomographic inversion for 3D imaging.

Main Methods:

• Development and application of regularized Newton methods for nonlinear inverse problems in imaging.
• Utilizing a single near-field diffraction pattern for simultaneous phase and amplitude recovery.
• Implementing all-at-once phase contrast tomography for simultaneous phase retrieval and tomographic inversion.

Main Results:

• First-time demonstration of simultaneous phase and amplitude recovery from a single near-field diffraction pattern without homogeneity constraints.
• Successful application of regularized Newton methods to X-ray phase contrast imaging.
• Achieved 3D imaging of a colloidal crystal with 95nm isotropic resolution.

Conclusions:

• Regularized Newton methods provide a versatile framework for solving ill-posed nonlinear imaging problems.
• The developed approach enables novel capabilities in X-ray phase contrast imaging and tomography.
• High-resolution 3D imaging of complex structures is achievable with this advanced computational imaging technique.