Piecewise constant reconstruction using a stochastic continuation approach

We address the problem of reconstructing a piecewise constant 3-D signal from a few noisy 2-D line-integral projections. More generally, the theory developed here readily applies to the recovery of an ideal n-D signal (n >= 1) from indirect measurements corrupted by noise. Stabilization of this class of ill-conditioned inverse problems is achieved with the Potts prior model, which leads to the minimization of a discontinuous, highly multimodal cost function. To carry out this challenging optimization task, we introduce a new class of annealing-type algorithms we call stochastic continuation (SC). We show that SC inherits the desirable finite-time convergence properties of generalized simulated annealing (under mild assumptions) and that it can be successfully applied to signal reconstruction. Our numerical experiments indicate that SC outperforms standard simulated annealing.