A common problem in medical imaging is the reconstruction of one or more anomalous hot spots distinct from the background. Many such problems are severely data limited and highly noise sensitive. Thus, a voxel-based reconstruction could be both overkill and an overreach. Shape-based methods can be used as an alternative; a recent such proposal is to use a parametric level set (PaLS) approach, whereby the image is described using the level-set of a linear combination of a relatively small number of basis functions of compact support. Remaining concerns are the nonlinear least squares problem for the image model parameters and, in the case of a nonlinear forward model, the solution of the large-scale linear systems at each step of the optimization process. We report on recent advances on both fronts, notably a trust-region regularized Gauss-Newton process for the optimization, and a reduced-order modeling approach tailored to the PaLS formulation.
Misha E. Kilmer
Dept. of Mathematics, Tufts University, US