Browsing by Subject "Discretization"

Now showing 1 - 6 of 6

Open Access
A aurvey of signal processing problems and tools in holographic three-dimensional television
(Institute of Electrical and Electronics Engineers, 2007) Onural, L.; Gotchev, A.; Özaktaş, Haldun M.; Stoykova, E.
Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory.
Open Access
A discretization method based on maximizing the area under receiver operating characteristic curve
(World Scientific Publishing Co. Pte. Ltd., 2013) Kurtcephe, M.; Güvenir H. A.
Many machine learning algorithms require the features to be categorical. Hence, they require all numeric-valued data to be discretized into intervals. In this paper, we present a new discretization method based on the receiver operating characteristics (ROC) Curve (AUC) measure. Maximum area under ROC curve-based discretization (MAD) is a global, static and supervised discretization method. MAD uses the sorted order of the continuous values of a feature and discretizes the feature in such a way that the AUC based on that feature is to be maximized. The proposed method is compared with alternative discretization methods such as ChiMerge, Entropy-Minimum Description Length Principle (MDLP), Fixed Frequency Discretization (FFD), and Proportional Discretization (PD). FFD and PD have been recently proposed and are designed for Naïve Bayes learning. ChiMerge is a merging discretization method as the MAD method. Evaluations are performed in terms of M-Measure, an AUC-based metric for multi-class classification, and accuracy values obtained from Naïve Bayes and Aggregating One-Dependence Estimators (AODE) algorithms by using real-world datasets. Empirical results show that MAD is a strong candidate to be a good alternative to other discretization methods. © 2013 World Scientific Publishing Company.
Open Access
EFIE and MFIE, why the difference?
(IEEE, 2008-07) Chew W.C.; Davis, C. P.; Warnick, K. F.; Nie, Z. P.; Hu, J.; Yan, S.; Gürel, Levent
EFIE (electric field integral equation) suffers from internal resonance, and the remedy is to use MFIE (magnetic field integral equation) to come up with a CFIE (combined field integral equation) to remove the internal resonance problem. However, MFIE is fundamentally a very different integral equation from EFIE. Many questions have been raised about the differences.
Open Access
On the discretization of Darboux integrable systems admitting the second-order integrals
(Rossiiskaya Akademiya Nauk Ufimskii Nauchnyi Tsentr, Institut Matematiki s Vychislitel'nym Tsentrom, 2021) Zheltukhin, Kostyantyn; Zheltukhina, Natalya
We consider a discretization problem for hyperbolic Darboux integrable systems. In particular, we discretize continuous systems admitting 𝑥- and 𝑦-integrals of the first and second order. Such continuous systems were classified by Zhyber and Kostrigina. In the present paper, continuous systems are discretized with respect to one of continuous variables and the resulting semi-discrete system is required to be also Darboux integrable. To obtain such a discretization, we take 𝑥- or 𝑦-integrals of a given continuous system and look for a semi-discrete systems admitting the chosen integrals as 𝑛-integrals. This method was proposed by Habibullin. For all considered systems and corresponding sets of integrals we were able to find such semi-discrete systems. In general, the obtained semi discrete systems are given in terms of solutions of some first order quasilinear differential systems. For all such first order quasilinear differential systems we find implicit solutions. New examples of semi-discrete Darboux integrable systems are obtained. Also for each of considered continuous systems we determine a corresponding semi-discrete system that gives the original system in the continuum limit.
Open Access
On the discretization of Laine equations
(Taylor and Francis, 2018) Zheltukhin, K.; Zheltukhina, Natalya
We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semi-discrete equation which has that integral as an n-integral, or we proved that such an equation does not exist. It is also shown that all constructed semi-discrete equations are Darboux integrable.
Open Access
Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations
(SPIE - International Society for Optical Engineering, 2004) Onural, L.
The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily, periodic masks at some specific distances. © 2004 Society of Photo-Optical Instrumentation Engineers.