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Absolute phase image reconstruction: a stochastic nonlinear filtering approach.

J N Leitão¹, M A Figueiredo

¹Instituto de Telecomunicações and Departamento de Engenharia Electrotécnica e de Computadores, Instituto Superior Técnico, 1096 Lisboa Codex, Portugal.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|February 16, 2008

Summary

This study introduces a novel Bayesian method for reconstructing absolute phase images from noisy real and imaginary data. The approach enhances phase estimation in critical imaging applications.

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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.