Image reconstruction with a non-parallelism constraint

We consider the problem of restoration of images corrupted by blur and noise. We find the minimum of the primal energy function, which has two terms. The former is related to faithfulness to the data and the latter is associated with smoothness constraints. In general, 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. In order to have thin edges, we determine a dual energy function, which is convex and takes into account non-parallelism constraints. 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 parallel lines are inhibited.