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A numerical procedure for filtering and efficient high-order signal differentiation

Salim Ibrir, Sette Diop (2004)

International Journal of Applied Mathematics and Computer Science

In this paper, we propose a numerical algorithm for filtering and robust signal differentiation. The numerical procedure is based on the solution of a simplified linear optimization problem. A compromise between smoothing and fidelity with respect to the measurable data is achieved by the computation of an optimal regularization parameter that minimizes the Generalized Cross Validation criterion (GCV). Simulation results are given to highlight the effectiveness of the proposed procedure.

Adaptive tests for periodic signal detection with applications to laser vibrometry

Magalie Fromont, Céline Lévy-leduc (2006)

ESAIM: Probability and Statistics

Initially motivated by a practical issue in target detection via laser vibrometry, we are interested in the problem of periodic signal detection in a Gaussian fixed design regression framework. Assuming that the signal belongs to some periodic Sobolev ball and that the variance of the noise is known, we first consider the problem from a minimax point of view: we evaluate the so-called minimax separation rate which corresponds to the minimal l2-distance between the signal and zero so that the detection...

Application of the random field theory in PET imaging - injection dose optimization

Jiří Dvořák, Jiří Boldyš, Magdaléna Skopalová, Otakar Bělohlávek (2013)

Kybernetika

This work presents new application of the random field theory in medical imaging. Results from both integral geometry and random field theory can be used to detect locations with significantly increased radiotracer uptake in images from positron emission tomography (PET). The assumptions needed to use these results are verified on a set of real and simulated phantom images. The proposed method of detecting activation (locations with increased radiotracer concentration) is used to quantify the quality...

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