This website is maintained by Jem Hebden.

Last update of this page: October 26, 2002.

Image reconstruction

Interest in the problem of optical imaging of large thicknesses of tissues has led to considerable effort devoted to the development of suitable algorithms for reconstructing images from diffuse radiation [1]. Because light does not travel through human soft tissues in straight lines, imaging techniques used for x-ray computed tomography are not strictly applicable. Optical tomography is based on the general principle that a finite set of measurements of transmitted light between pairs of points on the surface of an object is sufficient to reconstruct a transverse slice or 3D volume representing the distribution of internal scatterers and absorbers. The appropriate geometries for these tomographic measurements are illustrated in figure 1. Unfortunately the image reconstruction problem is both ill-posed (the solution may not be unique or cannot be achieved through stable convergence) and highly underdetermined (the number of unknowns, i.e. pixels in the image, far exceeds the amount of data). Nevertheless various mathematical techniques have been devised, invariably involving some simplifying assumptions about the light propagation in tissue, which have enabled images of a variety of tissues and tissue-equivalent phantoms to be successfully reconstructed.

Figure 1: Potential arrangements of sources and detectors for a) transverse slice imaging, and b) full three-dimensional imaging of the infant brain..

The approach we have pursued at UCL is to determine the parameters which describe an appropriate model of photon transport within the investigated medium by comparing its predictions with measured data [2]. The model is then adjusted iteratively until acceptable correspondence is achieved, and convergence towards the correct solution is assisted by the use of appropriate regularization methods. This technique requires three distinct components: a forward model which can generate a set of reliable measurements from a given three-dimensional (3D) distribution of scattering and absorbing parameters; the definition of an objective function to be minimised, based on the error between model predictions and experimental data; and a scheme for adjusting the parameters of the forward model to achieve the minimisation. This method is the basis of the algorithm known as TOAST (Temporal Optical Absorption and Scattering Tomography) which has been developed at UCL by Simon Arridge and Martin Schweiger [3]. TOAST employs a finite element method (FEM) forward model, and uses an iterative model-fitting routine wherein the FEM model parameters are repeatedly updated to optimise the match of the model to the data. For more information about this image reconstruction package, please click here to visit the TOAST website.

3D Mesh Generation

One of the major challenges involved in optical tomography is the generation of adequate 3D forward models with realistic geometries and optical properties. For our recent neonatal imaging studies [4], we have employed meshes based on a head of a child's doll.

Figure 2: A CT-scan of a realistic doll's head and the optical fibre helmet.	Figure 3: A surface mesh generated from the CT-scan.	Figure 4: A 3D mesh revealing the internal meshing structure.

We first acquired a 3D x-ray CT-scan (figure 2) of the doll's head, from which we generated a surface mesh (figure 3). The surface mesh was processed using the Visualization Toolkit (Kitware, Inc, USA) and a volume finite element mesh produced using Netgen [5], which is based on an advancing front algorithm. Appropriate software was then used to apply a non-linear warp to the surface mesh in order to fit it to the measured locations of the sources and detectors on the helmet. Finally, the resulting surface was used to construct a volume mesh (figure 4), containing 17559 second-order tetrahedral elements having a total of 26814 nodes. This is described in more detail by Gibson et al. [6,7].

1. Arridge, SR, and Hebden, JC (1997): Optical imaging in medicine II: Modelling and reconstruction. Physics in Medicine and Biology 42(5), 841-853. Download PDF file.
2. Arridge, SR (1999): Optical tomography in medical imaging. Inverse Problems 15(2), 41-93.
3. Arridge, SR, and Schweiger, M (1997): Image reconstruction in optical tomography. Philosophical Transactions of the Royal Society of London Series B-Biological Sciences 352(1354), 717-726.
4. Hebden, JC, Gibson, A, Yusof, R, Everdell, N, Hillman, EMC, Delpy, DT, Arridge, SR, Austin, T, Meek, JH, and Wyatt, JS (2002): Three-dimensional optical tomography of the premature infant brain, Physics in Medicine and Biology 47, 4155-4166. Download PDF file.
5. Schöberl, J. (1997): NETGEN - An Advancing front 2D/3D Mesh Generator based on Abstract Rules. Comput. Visual Sci. 1, 41-52.
6. Gibson, A, Yusof, R, Dehghani, H, Riley, J, Everdell, N, Richards, R, Hebden, JC, Schweiger, M, Arridge, SR, and Delpy, DT (2003): Optical tomography of a realistic neonatal head phantom. Applied Optics 42, 3109-3116. Download PDF file.
7. Gibson, AP, Riley, J, Schweiger, M, Hebden, JC, Arridge, SR, and Delpy, DT (2003): A method for generating patient-specific finite element meshes for head modelling. Physics in Medicine and Biology 48, 481-495. Download PDF file.