Stochastic and deterministic algorithms for image reconstruction with implicitly referred discontinuities

The MRF-based approach to the solution of visuai reconstruction problems, even if extremely flexible in describing the Iocal behaviour of the image intensity and its discontinuities, generally needs stochastic reIaxation algorithms to compute the MAP estimate. These algorithms, despite their asymptotic convergence properties, often present insurmountable computational costs. Different methods, which consider the discontinuities implicitly rather than explicitIy, have been recently proposed. In these methods, a generaI image reconstruction problem is formulated as the minimization of a regularized energy F(f) of the onIy intensity process f. Geman and Reynolds showed that, if the stabilizer employed has the attributes of concavity and finite asymptotic behaviour, the solution to this problem permits the recovery of discontinuities without introducing auxiliary variables. While this probIem is equivalent to one involving an explicit line process, its complexity is greatly reduced. They minimized the non-convex energy F by using an optimization method based on simulated annealing. In this paper, we investigate the possibility of solving the same problem through the Graduated Non-Convexity algorithm, that is by constructing a sequence of approximating energies and using gradient descent techniques to minimize them. This deterministic method is compared with the direct minimization of the energy through stochastic relaxation, in terms of quality of the reconstructed images and of computational costs.