Image deblurring and denoising are formulated as the minimization of an energy function in which a line process is implicitly referred through a novel discontinuity-adaptive stabilizer. This stabilizer depends on a parameter, called temperature, which is related to the threshold for the creation of intensity discontinuities (edges). The solution is computed using a GNC-like algorithm that minimizes in sequence the energy function at decreasing values of the temperature. We show that this allows for a coarse-to-fine recovery of edges of decreasing width, while smoothing off the noise. Furthermore, the need for a fine tuning of the regularization and threshold parameters is significantly relaxed. As a further advantage with respect to the most edge-preserving stabilizers, the method is also flexible for the introduction of self-interactions between lines, in order to express various constraints on the configurations of edge field, without any increase in the computational cost.
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