A GNC algorithm for constrained image reconstruction with continuous-valued line processes

Image reconstruction is formulated as the problem of minimizing a non-convex functional F(f) in which the smoothness stabilizer implicitly refers to a continuous-valued line process. Typical functionals proposed in the literature are considered. The minimum of F(f) is computed using a GNC algorithm that employs a sequence F?(p) (f) of approximating functionals for F(f), to be minimized in turn by gradient descent techniques. The results of a simulation evidence that GNC algorithms are computationally more efficient than simulated annealing algorithms, even when the latter are implemented in a simplified form. A comparison between the performance of these functionals and that of a functional that refers to an implicit binary line process is also carried out; this shows that assuming a continuous-valued line process gives a better reconstruction of the smooth, planar or quadratic regions ofthe image, even with first-order models.