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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 6 — Feb. 20, 2010
  • pp: 986–1000

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

Naren Naik, R. M. Vasu, and M. R. Ananthasayanam  »View Author Affiliations

Applied Optics, Vol. 49, Issue 6, pp. 986-1000 (2010)

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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

OCIS Codes
(110.3175) Imaging systems : Interferometric imaging
(110.6955) Imaging systems : Tomographic imaging
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Imaging Systems

Original Manuscript: August 3, 2009
Manuscript Accepted: October 16, 2009
Published: February 17, 2010

Virtual Issues
Vol. 5, Iss. 5 Virtual Journal for Biomedical Optics

Naren Naik, R. M. Vasu, and M. R. Ananthasayanam, "Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography," Appl. Opt. 49, 986-1000 (2010)

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