Reconstruction Methods in Diffuse Optical Tomography
S. Arridge (University College London) and M. Schweiger (University College London)
Several problems in medical imaging can be characterised as parameter identification problems, and can be solved for example by an output least squares method, where the inverse problem is non-linear and illposed, and the parameters are the coefficients of a numerical method such as the finite element method (FEM), typically represented in a local pixel basis Newton schemes are amongst the most popular, and often involve construction of large dense Jacobian matrices that can be prohibitive to store. In this talk we present an efficient method for Gauss-Newton and full-Newton methods that do not involve the storage of the Jacobian. The method is shown applied to the recovery of absorption and scattering cross-sections in optical tomography. Alternatively, shape based methods, either implicit (such as level sets) or explicit (via a parametric surface model) can be used to identify structures. I will present some recent results comparing these approaches.