Projection algorithms

Calculate 3D structures for each particle by use of an R-weighted back-projection algorithm (93). 

The loop, worm and directed loop algorithms can be used for the simulation of a wide class of quantum magnets. They are of interest not only to theoretical physicists, but also to experimentalists who want to fit experimental measurements to theoretical models. The wide applicability of these methods has led to the publication of open-source versions of these algorithms as part of the ALPS project (Algorithms and Libraries for Physics Simulations) [10] on the web page http //alps.comp-phys.org/. 

Fig. 4 Reconstructed spectra using the additive back-projection algorithm, showing the effect of increasing the number of projections, (a) n = 6, (b) n = 12, (c) n = 18. Six responses are detected as the signal-to-noise ratio increases and the artefacts become less obtrusive. Residual ridges are apparent in (a) but not in (c)...

Wu, D., H.X. Wu, J.B. Cao, Z.H. Huang, and Y. He. 2009. Classifying the species of exopalaemo by using visible and near infrared spectra with uninfomiative variable elimination and successive projections algorithm. Journal of Infrared and Millimeter Waves. 28(6) 423-427. 

The images are shown in Fig. 6 al to a3. The device weighs 110 g and hence is portable. The images obtained are reconstructed by filtered back projection algorithm. The device is such that it can be connected to a computer in which the image processing can be performed. This can also thus be extremely crucial in telemedicine [3]. 

While the Fourier slice theorem implies that given a sufficient number of projections, an estimate of the two-dimensional transform of the object could be assembled and by inversion an estimate of the object obtained, this simple conceptual model of tomography is not implemented in practice. The approach that is usually adopted for straight ray tomography is that known as the filtered back-projection algorithm. This method has the advantage that the reconstruction can be started as soon as the first projection has been taken. Also, if numerical interpolation is necessary to compute the contribution of each projection to an image point, it is usually more accinate to conduct this in physical space rather than in frequency space. 

Line Shape Profiling from 2-D Spectral-Spatial ESRI. Each 2-D image is reconstructed from a complete set of projections, collected as a function of the magnetic field gradient, using a convoluted back-projection algorithm (58). 

Katafygiotis, L.S. Lam, H.-F. 2002. Tangential-projection algorithm for manifold representation in unidentifiable model updating problems. Earthquake Engineering and Structural Dynamics, 31, 791-812. 

From the projection algorithm above note that the vectors wj, are coordinates of the latent variables on the original variable axes. The choice of these weightings defines the various methods. Principal components represent the special case of the general projection method defined above where wj, and normalized loadings p are identical. Principal components can thus be found by iterating steps 1-3 until = p. ... 

ALPS Project (Algorithms and Libraries for Physics Simulations). Available http //alps. 

Multiple Linear Regression-Successive Projections Algorithm,... 

FIGURE 28.3 Flow system for the simultaneous determination of MSG, GMP, and IMP. MSG, monosodium glutamate GMP, guanosine monophosphate, IMP, inosine monophosphate AC, acetate column BS, buffer solution D, detector PP, peristaltic pump qi, buffer solution flow rate (2.06 mL min 0 qi5 standard and sample solution flow rate (1.08 mL min 1) RC, reactor coil S, sample SS, standard solution SV, selection valve W, waste. (Reprinted from Talanta, 82, Acebal, C. C. et al.. Successive projections algorithm applied to spectral data for the simultaneous determination of flavor enhancers, 222-226, Copyright 2010, with permission from Elsevier.)... 

Acebal, C. C., M. Griinhut, A. G. Lista, and B. S. Fernandez Band. 2010. Successive projections algorithm applied to spectral data for the simultaneous determination of flavor enhancers. Talanta 82 222-226. 

Galvao, R. K. H., M. F. Pimentel, M. C. U. Araujo, T. Yoneyama, and V. Visani. 2001. Aspects of the successive projections algorithm for variable selection in multivariate calibration applied to plasma emission spectrometry. Anal, Chim. Acta 443 107-115. 

Rein, U. Implementation of a Recursive Projection Algorithm in a General Purpose Computer Program, Diplomarbeit am Institut A fiir Mechanik, Universitat Stuttgart, 1989. 

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