A generalized approach for atomic force microscopy image restoration with Bregman distances as Tikhonov regularization terms

Tikhonov's regularization approach applied to image restoration, stated in terms of ill-posed problems, has proved to be a powerful tool to solve noisy and incomplete data. This work proposes a variable norm discrepancy function as the regularization term of a Tikhonov expression, where the cross-entropy functional was derived. Our method was applied to true Atomic Force Microscopy (AFM) images obtained from biological samples, producing satisfactory results towards the most probable sample morphological aspect. These images represent a mapping of local interaction forces exerted between a reduced scaled AFM sensing tip and the biological sample surface, kept alive in aqueous or air environment.