Using classical smoothers in restoration processes, such as total variation regularisation, while capturing well discontinuities, is known to induce an estimation bias in the final result, materialised by a loss of contrast. If the literature is prolific when dealing with standard modalities of images (grayscale or RGB images), it is more tenuous when the involved modality encodes some intrinsic geometrical properties, requiring the design of specific purpose-built algorithms. In this work, focused on such a specific modality, namely polarimetric imaging, we address the joint restoration and contrast re-enhancement (equivalently referred to as debiasing or refitting) question within an extension of the CLEAR framework (Covariant LEAst-square Refitting, [5]), emphasising the importance of preserving the Jacobian (with respect to the observed signal) of the original estimator.