6,278 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
Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm
We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system
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