Non-convex optimization for image reconstruction with implicitly referred discontinuities

Edge-preserving image reconstruction can be performed by minimizing appropriate cost functionals in which image intensity and discontinuities are explicitly referred. Equivalent and less expensive reconstructions can be obtained by using a class of functionals that only depend on the image intensity and have been shown to implicitly refer to an underlying discontinuity process. We analyze the performances of two of these functionals and show that Graduated Non-Convexity (GNC) algorithms permit a further reduction of the computational costs if compared with Simulated Annealing algorithms, commonly used in non-convex optimization.