Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction...

Area of Science:

• Optics
• Image Reconstruction
• Tomography

Background:

• Optical refraction tomography (ORT) reconstructs refractive-index distributions (RID) from optical path-length difference (OPD) data.
• Accurate RID reconstruction is crucial for analyzing transparent objects.

Purpose of the Study:

• To develop and validate adaptive Extended Kalman Filter (EKF) based methods for RID reconstruction in ORT.
• To compare the performance of single-resolution and multi-resolution EKF approaches with existing deterministic methods.

Main Methods:

• Implemented a single-resolution EKF (SR-EKF) on a state variable model for RID estimation from noisy OPD data.
• Developed a multi-resolution EKF (MR-EKF) using wavelet transforms (Haar, Daubechies-4) of the state variable model.
• Adaptively estimated state and measurement noise biases and covariances for improved EKF performance.

Main Results:

• Both SR-EKF and MR-EKF approaches successfully reconstructed the RID from simulated noisy OPD data.
• Reconstruction results from EKF methods showed comparable accuracy to the algebraic reconstruction technique (ART).
• Demonstrated the capability of adaptive noise covariance estimation within the EKF framework for ORT.

Conclusions:

• Adaptive EKF methods offer a viable and effective approach for refractive-index distribution reconstruction in optical refraction tomography.
• The multi-resolution EKF, particularly with wavelet transforms, provides a powerful tool for ORT.
• This work presents novel applications of EKF and adaptive estimation in the field of ORT.