Computationally efficient optical tomographic reconstructions through waveletizing the normalized quadratic perturbation equation

B. Kanmani; Puneet Bansal; R. M. Vasu

doi:10.1117/12.696394

7 July 2006 Computationally efficient optical tomographic reconstructions through waveletizing the normalized quadratic perturbation equation

B. Kanmani, Puneet Bansal, R. M. Vasu

Author Affiliations +

Proceedings Volume 6164, Saratov Fall Meeting 2005: Coherent Optics of Ordered and Random Media VI; 61640R (2006) https://doi.org/10.1117/12.696394
Event: Saratov Fall Meeting 2005, 2005, Saratov, Russian Federation

Abstract

In this paper, we present a wavelet-based approach to solve the non-linear perturbation equation encountered in optical tomography. A particularly suitable data gathering geometry is used to gather a data set consisting of differential changes in intensity owing to the presence of the inhomogeneous regions. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding the representation of the original non-linear perturbation equation in the wavelet domain. The advantage in use of the non-linear perturbation equation is that there is no need to recompute the derivatives during the entire reconstruction process. Once the derivatives are computed, they are transformed into the wavelet domain. The purpose of going to the wavelet domain, is that, it has an inherent localization and de-noising property. The use of approximation coefficients, without the detail coefficients, is ideally suited for diffuse optical tomographic reconstructions, as the diffusion equation removes most of the high frequency information and the reconstruction appears low-pass filtered. We demonstrate through numerical simulations, that through solving merely the approximation coefficients one can reconstruct an image which has the same information content as the reconstruction from a nonwaveletized procedure. In addition we demonstrate a better noise tolerance and much reduced computation time for reconstructions from this approach.

Citation Download Citation

B. Kanmani, Puneet Bansal, and R. M. Vasu "Computationally efficient optical tomographic reconstructions through waveletizing the normalized quadratic perturbation equation", Proc. SPIE 6164, Saratov Fall Meeting 2005: Coherent Optics of Ordered and Random Media VI, 61640R (7 July 2006); https://doi.org/10.1117/12.696394

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