Complexity-guided Fourier phase retrieval from noisy data

Area of Science:

• Optics
• Image Processing
• Computational Science

Background:

• Phase retrieval from noisy single-shot Fourier intensity data is challenging.
• Existing algorithms like Hybrid Input-Output (HIO) struggle with noise robustness.

Purpose of the Study:

• To develop a noise-robust phase retrieval strategy using complexity guidance.
• To improve the quality and stability of solutions from noisy Fourier data.

Main Methods:

• Examined HIO algorithm behavior with noisy data using complexity guidance.
• Proposed and tested a strategy to control solution complexity within and outside the support region during HIO iterations.
• Tracked and controlled the growth of solution complexity outside the support to guide adjustments within the support.

Main Results:

• The proposed strategy demonstrates noise robustness, with gradual quality degradation as noise increases.
• Object features are retained even at higher noise levels, though textural details may be lost.
• The strategy successfully handles pure phase objects, mixed amplitude-phase objects, and dc-blocked data.

Conclusions:

• Complexity guidance offers an effective method for stable phase retrieval from noisy single-shot Fourier data.
• The developed strategy enhances the reliability of phase retrieval in various imaging applications.
• This work provides a significant advancement for applications critically dependent on single-shot Fourier phase retrieval.