Nilson Costa Roberty

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In the present work the inverse problem of identification of radiative properties, the total extinction and scattering coefficients, is analyzed and explicitly formulated based in an elementary semi-group theory. The Chandrasekhar discrete ordinates finite dimensional approximation of the angular variables is used for the direct problem representation with(More)
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 purpose of this paper is to explore the Hilbert space functional structure of the Helmholtz equation inverse source problem. An integral equation for the sources reconstruction based on the composition of the trace and Green’s function operators is introduced and compared with the reciprocity source reconstruction methodologies. An equivalence theorem(More)
ABSTRACT 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(More)
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 solve the one-speed Boltzmann transport equation is due to characteristics of the domain of the transport operator which controls derivatives only in the direction of(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)
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)
Abstract The problem of simultaneous spatial determination of the absorption and scattering coefficients in the stationary linear one velocity Boltzmann transport equation via boundary measurements is investigated. The original first-order problem is shown to be equivalent to a second order self-adjoint problem. Then, I introduce an a priori operator K that(More)
ABSTRACT: This work presents a methodology for reconstruction of constants by parts functions. The paper focus in one application of this methodology for identify the phases of the stratified multi-phase flow (oil-watergas) in a duct. The principle physics is based in attenuation of X rays and Gamma rays. Each element of the composed have a specific(More)