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 nois y and incomplete data. This work proposes a variable norm discrepancy funct ion as the regularization term of a Tikhonov expression, where the cross-en tropy functional was derived. Our method was applied to true Atomic Force M icroscopy (AFM) images obtained from biological samples, producing satisfac tory results towards the most probable sample morphological aspect. These i mages represent a mapping of local interaction forces exerted between a red uced scaled AFM sensing tip and the biological sample surface, kept alive i n aqueous or air environment.