Detecção de descontinuidades e reconstrução de funções a partir de dados espectrais : filtros splines e metodos iterativos / Detection of discontinuities and reconstruction of functions from spectral data : splines filters and iterative methods

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

Detecting discontinuities from Fourier coefficients is a problem that arises in several areas of application. Important examples are Fourier methods in Computed Tomography, Nuclear Magnetic Resonance Inversion and Conservation Law Differential Equations. Also, the knowledge of the precise location of the discontinuity points is essential to obtain exponential convergence of the Fourier series for a piecewise continuous function, avoiding the well known Gibbs phenomenon. In the work of Wei et al. (1999, 2004), polynomial filters were developed to reconstruct functions from their Fourier coefficients. In the work of Wei et. al. (2005), these fillters were used to develop fast iterative methods for discontinuity detection. In this thesis we introduce more general spline based filters, that achieve higher accuracy than those works, and the corresponding iterative methods for the discontinuities. Estimates for the errors are presented as well as many numerical experiments validating the algorithms. Also, we show that a new and simple method, not using any nonlinear solver, performs better than those based on the conjugate Fourier series as in the work of Gelb and tadmor

ASSUNTO(S)

series de iterative methods (mathematics) metodos iterativos (matematica) fourier reconstrução de imagens fourier series image reconstruction

ACESSO AO ARTIGO

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