Parameter-free restoration of piecewise smooth images

We propose a novel strategy for the automatic estimation of the two regularization parameters arising in the image decomposition variational model employed for the restoration task when the underlying corrupting noise is known to be additive white Gaussian. In the model of interest, the target image is decomposed in its piecewise constant and smooth components, with a total variation term penalizing the former and a Tikhonov term acting on the latter. The proposed criterion, which relies on the whiteness property of the noise, extends the residual whiteness principle, originally introduced in the case of a single regularization parameter. The structure of the considered decomposition model allows for an efficient estimation of the pair of unknown parameters, that can be automatically adjusted along the iterations with the alternating direction method of multipliers employed for the numerical solution. The proposed multi-parameter residual whiteness principle is tested on different images with different levels of corruption. The performed tests highlight that the whiteness criterion is particularly effective and robust when moving from a single-parameter to a multi-parameter scenario.