A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient

Abstract

We compare, through simulations, the performance of four linear algorithms for diffuse optical tomographic reconstruction of the three-dimensional distribution of absorption coefficient within a highly scattering medium using the diffuse photon density wave approximation. The simulation geometry consisted of a coplanar array of sources and detectors at the boundary of a half-space medium. The forward solution matrix is both underdetermined, because we estimate many more absorption coefficient voxels than we have measurements, and ill-conditioned, due to the ill-posedness of the inverse problem. We compare two algebraic techniques, ART and SIRT, and two subspace techniques, the truncated SVD and CG algorithms. We compare three-dimensional reconstructions with two-dimensional reconstructions which assume all inhomogeneities are confined to a known horizontal slab, and we consider two 'object-based' error metrics in addition to mean square reconstruction error. We include a comparison using simulated data generated using a different FDFD method with the same inversion algorithms to indicate how our conclusions are affected in a somewhat more realistic scenario. Our results show that the subspace techniques are superior to the algebraic techniques in localization of inhomogeneities and estimation of their amplitude, that two-dimensional reconstructions are sensitive to underestimation of the object depth, and that an error measure based on a location parameter can be a useful complement to mean squared error.

An Efficient Numerical Method for General $L_{p}$ Regularization in Fluorescence Molecular Tomography

“…By rearranging these equations in matrix form we obtain (6) where is an matrix, and is the vector of fluorophore concentrations at each voxel. In general, this linear system of equations is solved using ART, SVD, regularized SVD, or Tikhonov regularization [22]- [24]. Note that there are several numerical methods to determine Green's functions (finite differences, finite elements, finite volumes).…”

“…Numerically, the regularization integral in (7) is computed using the Gauss quadrature formula [39] ( 22) where is the set of elements, for are fixed quadrature points and for are quadrature weights. Let be the matrix formed by concatenating the column vectors , , such that we have .…”

“…This results in a linear forward model [21], which is the context of the present paper. A number of methods that include regularization have been studied for linear reconstruction in optical tomography; the Kaczmarz method (ART) with an appropriate stopping criterion, the filtered singular value decomposition and Tikhonov regularization [22]- [25]. In this contribution, we propose general regularization as a new regularization technique for the reconstruction of fluorescence data, together with an optimization method developed specifically for regularization.…”

Information theoretic regularization in diffuse optical tomography

“…3.62 in conjunction with some adopted regularization technique, can be approached by direct or iterative methods such as the ones discussed in Chapter 2. DDOT example studies include Gaudette et al, 2000;Gibson et al, 2005b].…”

A comprehensive study of the use of temporal moments in time-resolved diffuse optical tomography: part I. Theoretical material

“…The algebraic reconstruction technique has been used in a large number of instances (Gaudette et al, 2000;Lam et al, 2005;Gao et al, 2002Gao et al, , 2006Nielsen et al, 2009) as well as other classical optimization approaches as Landweber algorithm, steepest descent or conjugate gradient descent (Gaudette et al, 2000). Then, the regularization strategy consists in stopping the retained algorithm before convergence to the minimum of (4).…”