Three-dimensional reconstruction of shape and piecewise constant region values for optical tomography using spherical harmonic parametrization and a boundary element method

Abstract

We consider the recovery of smooth 3D region boundaries with piecewise constant coefficients in optical tomography. The method is based on a parametrization of the closed boundaries of the regions by spherical harmonic coefficients, and a Newton type optimization process. A boundary integral formulation is used for the forward modelling. The calculation of the Jacobian is based on an adjoint scheme for calculating the corresponding shape derivatives. We show reconstructions for 3D situations. In addition we show the extension of the method for cases where the constant optical coefficients are also unknown. An advantage of the proposed method is the implicit regularization effect arising from the reduced dimensionality of the inverse problem. M This article features online multimedia enhancements

Shape reconstruction of irregular bodies with multiple complementary data sources

“…A popular approach is the usual spherical harmonics representation in which each coordinate function is represented independently as a spherical harmonics series (see, e.g., Zacharopoulos et al 2006). However, while this parametrization is powerful enough to represent any shape that can be Article published by EDP Sciences A97, page 1 of 9 A&A 543, A97 (2012) parametrized on the unit sphere S 2 (with sufficient continuity properties), it requires excessive smoothness regularization during the inversion process.…”

Numerical modelling and image reconstruction in diffuse optical tomography

“…But, perhaps the most promising reason for adoption of numerical approaches is to facilitate the combination of NIR tomography with standard clinical imaging systems, using predefined tissue geometries as the input domain. A number of different numerical models have been developed and used with specific application in DOT, including finite elements (Arridge et al 1993;Jiang & Paulsen 1995;Schweiger et al 1995;Gao et al 1998;Jiang 1998;Dehghani et al 2003b), finite difference (Hielscher et al 1998;, finite volume (Ren et al 2004) and boundary elements (Zacharopoulos et al 2006;Srinivasan et al 2007). …”

3D shape based reconstruction of experimental data in Diffuse Optical Tomography

“…Based on the assumption that the unknowns in such cases could be defined by the subdomain boundaries, a field of shape based reconstruction techniques has emerged in recent years. There have been many results in literature of either level-set techniques [18,19,20,21,22,23,24], where the boundaries of the subdomains are implicitly modeled by the zero level of level-set functions, or parametric methods [25,26,27,28] where an explicit parameterisation of the boundaries is used. In the case of the shape based reconstructions that use an explicit parameterisation of the boundaries, many different ways to describe the shapes have been used such as spherical harmonics, ellipsoids and spheres in 3D or Fourier curves, and Hermite polynomials, in 2D.…”

“…To develop the FEM based forward mapping from the spherical harmonics coefficients to the DOT data, we generalize the 2D element division technique presented in [26] into a 3D element subdivision technique for the mapping of the spherical harmonics coefficients to the absorption and scattering distributions inside an unstructured volumetric FEM mesh. In our previous work [25] we have evaluated a boundary element method (BEM) based 3D shape estimation method for reconstructing simulated DOT data. In this work we evaluate the shape based method by reconstructing experimental data and recover the location and shape of absorption and scattering targets inside a cylindrical phantom.…”