Abstract

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF’s noise covariances.

© 2010 Optical Society of America

Non-stationary reconstruction for dynamic fluorescence molecular tomography with extended kalman filter

Xin Liu, Hongkai Wang, and Zhuangzhi Yan
Biomed. Opt. Express 7(11) 4527-4542 (2016)

Indirect and direct estimation of pharmacokinetic parameters in dynamic diffuse fluorescence tomography by adaptive extended Kalman filtering

Limin Zhang, Yingxue Pan, Zhichao Zhao, Nan Cheng, Xin Wang, Yiwen Ma, Mengyu Jia, and Feng Gao
Appl. Opt. 61(22) G48-G56 (2022)

Factorized extended Kalman filter for optical processing

James L. Fisher, David P. Casasent, and Charles P. Neuman
Appl. Opt. 25(10) 1615-1621 (1986)

Performance enhancement of diffuse fluorescence tomography based on an extended Kalman filtering-long short term memory neural network correction model

Lingxiu Xing, Limin Zhang, Wenjing Sun, Zhuanxia He, Yanqi Zhang, and Feng Gao
Biomed. Opt. Express 15(4) 2078-2093 (2024)

Fringe pattern demodulation using Zernike polynomials and a l1-norm regularized extended Kalman filter

Shikha Sharma and Rishikesh Kulkarni
Appl. Opt. 61(18) 5517-5523 (2022)