7,508 research outputs found
Uniform Penalty inversion of two-dimensional NMR Relaxation data
The inversion of two-dimensional NMR data is an ill-posed problem related to
the numerical computation of the inverse Laplace transform. In this paper we
present the 2DUPEN algorithm that extends the Uniform Penalty (UPEN) algorithm
[Borgia, Brown, Fantazzini, {\em Journal of Magnetic Resonance}, 1998] to
two-dimensional data. The UPEN algorithm, defined for the inversion of
one-dimensional NMR relaxation data, uses Tikhonov-like regularization and
optionally non-negativity constraints in order to implement locally adapted
regularization. In this paper, we analyze the regularization properties of this
approach. Moreover, we extend the one-dimensional UPEN algorithm to the
two-dimensional case and present an efficient implementation based on the
Newton Projection method. Without any a-priori information on the noise norm,
2DUPEN automatically computes the locally adapted regularization parameters and
the distribution of the unknown NMR parameters by using variable smoothing.
Results of numerical experiments on simulated and real data are presented in
order to illustrate the potential of the proposed method in reconstructing
peaks and flat regions with the same accuracy
Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements
We present new method for the numerical reconstruction of the variable
refractive index of multi-layered circular weakly guiding dielectric waveguides
using the measurements of the propagation constants of their eigenwaves. Our
numerical examples show stable reconstruction of the dielectric permittivity
function for random noise level using these measurements
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