We consider the problem of restorating images from blur and noise. We find the minimum of the primal energy function, which has two terms, related to faithfulness to the data, and smoothness constraints, respectively. In general, we do not know and we have to estimate the discontinuities of the ideal image. We require that the obtained images are piecewise continuous and with thin edges. We associate with the primal energy function a dual energy function, which treats discontinuities implicitly. We determine a dual energy function, which is convex and takes into account non-parallelism constraints, in order to have thin edges. The proposed dual energy can be used as initial function in a GNC (Graduated Non-Convexity)-type algorithm, to obtain reconstructed images with Boolean discontinuities. In the experimental results, we show that the formation of parallel lines is inhibited.