Complexity-guided Fourier phase retrieval from noisy data.

Area of Science:

• Optics
• Image Processing
• Computational Science

Background:

• Phase retrieval from single-shot Fourier intensity data is crucial but challenging, especially with noise.
• Existing algorithms like hybrid input-output (HIO) struggle with noisy datasets, leading to unstable solutions.

Purpose of the Study:

• To investigate the behavior of HIO algorithm solutions with noisy data.
• To develop and test a novel complexity guidance strategy for robust phase retrieval.
• To enhance the stability and quality of reconstructed solutions from noisy Fourier intensity data.

Main Methods:

• Examined HIO algorithm performance on noisy Fourier intensity data.
• Introduced and applied a complexity guidance methodology to control solution complexity.
• Actively tracked and managed the growth of solution complexity inside and outside the defined support region during HIO iterations.
• Tested the strategy with Poisson noise across a wide range of photon counts.

Main Results:

• Observed increasing solution complexity outside the support with HIO iterations for noisy data.
• Demonstrated that the proposed strategy effectively controls solution complexity, improving phase retrieval quality.
• The strategy showed noise robustness, with gradual quality degradation as noise increased.
• Main object features were retained even at higher noise levels, though textural details were lost.
• Successfully handled pure phase objects, mixed amplitude-phase objects, and data with blocked DC components.

Conclusions:

• The developed complexity guidance strategy offers a robust method for phase retrieval from noisy single-shot Fourier intensity data.
• This approach enhances the stability and quality of reconstructed solutions, outperforming standard HIO for noisy datasets.
• The findings have broad applicability in fields requiring critical single-shot Fourier phase retrieval.