Unsupervised solution for in-line holography phase retrieval using Bayesian inference.

Area of Science:

• X-ray imaging
• Phase contrast imaging
• Computational imaging

Background:

• Phase retrieval in in-line holography is crucial for reconstructing object properties from recorded intensity patterns.
• Classical Tikhonov regularization is commonly used but presents challenges, particularly in selecting the regularization parameter.
• The ill-posed nature of phase retrieval necessitates effective regularization techniques.

Purpose of the Study:

• To develop an alternative phase retrieval method for in-line holography using Bayesian inference principles.
• To introduce an iterative optimization algorithm that simultaneously retrieves phase information and determines regularization parameters.
• To address limitations of existing methods, such as the unsupervised selection of regularization parameters.

Main Methods:

• Application of Bayesian inference principles to construct an iterative optimization algorithm.
• Development of a multi-dimensional regularization parameter determination within the iterative process.
• Testing the algorithm on both simulated and experimental in-line holography data.

Main Results:

• The proposed Bayesian inference algorithm successfully retrieves phase information.
• The method demonstrates unsupervised determination of multi-dimensional regularization parameters.
• Robust solutions were obtained, showing improved handling of low-frequency noise and the twin-image problem.

Conclusions:

• Bayesian inference offers a powerful alternative to Tikhonov regularization for phase retrieval in in-line holography.
• The developed algorithm provides robust and accurate phase reconstruction with unsupervised parameter selection.
• This approach enhances the reliability and applicability of propagation-based phase contrast imaging.