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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)

- Nilson Costa Roberty, Rogerio Chaffin Nunes
- J. Applied Mathematics
- 2011

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)

The method of Generalized Maximum Entropy, this based on the minimization of the distance of Bregman subject to the function error. This Bregman distance [1] depends on the parameters B and q. The objective of this work is to determine of optimum values of B and q for which the minimization of the distance of Bregman tends to zero. The method of Generalized… (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)

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