Absolute phase image reconstruction: a stochastic nonlinear filtering approach.

Area of Science:

• Signal Processing
• Image Reconstruction
• Computational Imaging

Background:

• Estimating absolute phase from noisy real and imaginary data is crucial for advanced imaging techniques.
• Existing methods often struggle with noise and the inherent complexities of phase reconstruction.
• Applications include interferometric synthetic aperture radar, optical interferometry, MRI, and diffraction tomography.

Purpose of the Study:

• To develop and propose solutions for reconstructing the absolute phase of a complex random field.
• To address the limitations of existing phase estimation techniques in noisy environments.
• To improve the accuracy and robustness of phase reconstruction in various imaging modalities.

Main Methods:

• A Bayesian approach incorporating a probabilistic observation model and prior knowledge.
• Utilizing a nonsymmetrical half-plane autoregressive (NSHP AR) Gauss-Markov random field (GMRF) as the prior.
• Deriving a recursive stochastic nonlinear filter based on state-space formulation and nonlinear observation mechanism.

Main Results:

• The proposed recursive stochastic nonlinear filter effectively estimates absolute phase.
• Demonstrated superior performance compared to the classical extended Kalman-Bucy filter.
• Illustrative examples confirm the effectiveness and accuracy of the developed approach.

Conclusions:

• The proposed Bayesian method offers a robust solution for absolute phase estimation.
• The recursive nonlinear filter significantly improves phase reconstruction accuracy.
• This work advances phase estimation techniques for key scientific and engineering imaging applications.