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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, where the entropy functional was derived. Our method is applied to true Atomic Force Microscopy (AFM)(More)
A source-detector methodology is presented for the construction of an inverse transport equation that once solved provides estimates for radiative properties and/or internally distributed sources in participating media. From the proper combination of source and detector pairs, a system of non-linear equations is assembled, taking also in consideration(More)
The domain partition for the construction of a natural base is presented in order to solve the inverse problem of absorption coefficient estimation from the available measurements (experimental noisy data) of transmitted radiation. Within the framework of Lebesgue measure, a family of reconstruction algorithms is constructed based on Bregman distances using(More)
the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We introduce algorithms marching over a polygonal mesh with elements consistent with the propagation directions of the particle radiation flux. The decision for adopting this kind of mesh to(More)
We consider the problem of reconstruction of an unknown characteristic transient thermal source inside a domain. By introducing the definition of an extended dirichlet-to-Neumann map in the time-space cylinder and the adoption of the anisotropic Sobolev-Hilbert spaces, we can treat the problemwith methods similar to those used in the analysis of the(More)
We consider the problem of reconstruction of an unknown characteristic interval and block transient thermal source inside a domain. By exploring the definition of an Extended Dirichlet to Neumann map in the time space cylinder that has been introduced in Roberty and Rainha 2010a , we can treat the problemwithmethods similar to that used in the analysis of(More)
This work presents different applications in progress with the aid of the atomic force microscopy (AFM) technique for biomedical and biotechnological applications, comprising both the acquisition of three-dimensional images and spectroscopic force measurements, in the following systems: first, low-density lipoprotein (LDL)-glycosaminoglycans; second,(More)
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