On the extension of level-set curve evolution methods for low-sensitivity imaging problems

We address inverse medium problems characterized by low-sensitivity observation data. A new level-set based method to recover the structure of piecewise homogeneous media is proposed. We make two contributions to this area of research. First, we capitalize on the flexibility in specifying the level-set velocity function in a way which counteracts the low sensitivity characteristic of the problem. The new approach speeds convergence while keeping the level set function smooth. Second, extending the current state of the art in the use of level sets for known binary media, we describe a simple and efficient implementation for N-ary media problems. We restrict our application examples to the electrical resistance tomography (ERT) problem, however, the proposed approaches are applicable to a variety of inverse problems involving shape reconstruction. We demonstrate the utility of our approach through a series of simulations using synthetic ERT data. Despite the ill-posed nature of the ERT problem, the simulation results show quite accurate estimations of the locations, sizes and shapes of multiple spatial inhomogeneities.