MIXING REGULARIZATION TOOLS FOR ENHANCING REGULARITY IN OPTICAL TOMOGRAPHY APPLICATIONS

In optical tomography, the optical properties of the medium under investigation are obtained through the solution of an inverse problem where some light is injected on some boundaries and the measurement is performed elsewhere on the boundary in terms of light intensity. The properties of interest are the diffusion and the absorption coefficients, denoted as s(x) and k(x) where in this paper x is in a two dimensional bounded region. Such an inverse problem is solved through optimization with the help of gradient-typemethods. Since it is well known that such inverse problem is ill-posed, regularizationis to be used. This communicationcompares three distinct regularization strategies for two very different kinds of optimization algorithms, namely the Gauss-Newton and the L-BFGS algorithms on the diffuse approximation model. The conclusion is that the use of Tikhonov-type regularization is absolutely compulsary when considering optimization algorithms that rely on matrix inversion. Moreover, combining this regularization with appropriate parameterization enhances quality reconstructions. However, the Tikhonov regularization does not bring much improvements when considering optimizers that do not rely on matrix inversion, while the combination of an appropriate parameterization of the control space and the use of Sobolev gradients brings much improvements.