The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
G J Milburn - One of the best experts on this subject based on the ideXlab platform.
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the quantum Mellin Transform
arXiv: Quantum Physics, 2007Co-Authors: J Twamley, G J MilburnAbstract:We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a Transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, Transforms the wavefunction via a Mellin Transform on to the critial line $s=1/2-ip_\eta$. We utilise this new Transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.
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the quantum Mellin Transform
New Journal of Physics, 2006Co-Authors: J Twamley, G J MilburnAbstract:We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a Transformation to 'hyperbolic phase space' (η, pη). We show that this new unitary change of basis from the position x on the half line to the hyperbolic momentum pη, Transforms the wavefunction via a Mellin Transform on to the critical line s = 1/2−ipη. We utilize this new Transform to find quantum wavefunctions whose hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann–Zeta function. We finally give possible physical realizations to perform an indirect measurement of the hyperbolic momentum of a quantum system on the half-line.
Torbjoern Eltoft - One of the best experts on this subject based on the ideXlab platform.
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application of the matrix variate Mellin Transform to analysis of polarimetric radar images
IEEE Transactions on Geoscience and Remote Sensing, 2011Co-Authors: Stian Normann Anfinsen, Torbjoern EltoftAbstract:In this paper, we propose to use a matrix-variate Mellin Transform in the statistical analysis of multilook polarimetric radar data. The domain of the Transform integral is the cone of complex positive definite matrices, which allows for Transformation of the distributions used to model the polarimetric covariance and coherency matrix. Based on the matrix-variate Mellin Transform, an alternative characteristic function is defined, from which we can retrieve a new kind of matrix log-moments and log-cumulants. It is demonstrated that the matrix log-cumulants are of great value to analysis of polarimetric radar data, and that they can be used to derive estimators for the distribution parameters with low bias and variance.
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analysis of multilook polarimetric radar data with the matrix variate Mellin Transform
Synthetic Aperture Radar (EUSAR) 2010 8th European Conference on, 2010Co-Authors: Stian Normann Anfinsen, Torbjoern EltoftAbstract:In this paper we propose to use a matrix-variate Mellin Transform in the statistical analysis of multilook polarimetric radar data. The domain of the Transform integral is the cone of complex positive definite matrices, which allows for Transformation of the sample covariance matrix distributions used to model multilook polarimetric radar data. Based on the matrix-variate Mellin Transform, an alternative characteristic function is defined, from which we can retrieve a new kind of matrix log-moments and log-cumulants. We show that the matrix log-cumulants are of great value to the analysis of polarimetric radar data, and can be used to derive low bias and variance estimators for the distribution parameters.
M. Iqbal - One of the best experts on this subject based on the ideXlab platform.
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Spline regularization of numerical inversion of Mellin Transform
Approximation Theory and its Applications, 2000Co-Authors: M. IqbalAbstract:A method is described for inverting the Mellin Transform which uses an expansion in Laguerre polynomials and converts the Mellin Transform to the Laplace Transform, then the Laplace Transform is converted to the first kind convolution integral equation by a suitable substitution. The integral equation so obtained is an ill-posed problem and we use the spline regularization to solve it. The performance of the method is illustrated by the inversion of the test functions available in the literature [J. Inst. Math. & Appl. 20 (1977), p. 73], [J. Math. Comp. 53 (1989), p. 589], [J. Sci. Stat. Comp. 4 (1983), p. 164]. The effectiveness of the method is shown by results obtained demonstrated by means of tables and diagrams.
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SPLINE REGULARIZATION OF NUMERICAL INVERSION OF Mellin Transform
Foundations of Computing and Decision Sciences, 2000Co-Authors: M. IqbalAbstract:A method is described for inverting the Mellin Transform which uses an expansion in Laguerre polynomials and converts the Mellin Transform to the Laplace Transform, then the Laplace Transform is converted to the first kind convolution integral equation by a suitable substitution.
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On regularized numerical inversion of Mellin Transform
Computer Physics Communications, 1995Co-Authors: M. IqbalAbstract:A method is described for inverting the Mellin Transform which uses an expansion in Laguerre polynomials and converts Mellin Transform to Laplace Transform, then a regularization method is used to recover the original function of the Mellin Transform. The performance of the method is illustrated by the inversion of the test functions available in the literature [J. Inst. Math. & Appl. 20 (1977) 73; SIAM J. Sci. & Stat. Comput 2 (1983) 164]. Results are shown in the tables and diagrams.
Seyed Mahmoud Anisheh - One of the best experts on this subject based on the ideXlab platform.
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Mellin Transform, Hidden Markov Model and Support Vector Machine
2013Co-Authors: Abbas Yaseri, Seyed Mahmoud AnishehAbstract:A paper currency recognition system has a wide range of applications such as self receiver machines for automated teller machines and automatic good-selling machines. In this paper a new paper currency recognition system based on Fourier-Mellin Transform, Markovian characteristics and Support Vector Machine (SVM) is presented. In the first, a pre-processing algorithm by Fourier-Mellin Transform is performed. The key feature of Fourier-Mellin Transform is that it is invariant in rotation, translation and scale of the input image. Then, obtained image is segmented and markovian characteristics of each segment have been utilized to construct a feature vectors. These vectors are then fed into SVM classifier for paper currency recognition. In order to evaluate the effectiveness of the system several experiments are carried out. Experimental result indicates that the proposed method achieved high accuracy rate in paper currency recognition
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a novel paper currency recognition using fourier Mellin Transform hidden markov model and support vector machine
International Journal of Computer Applications, 2013Co-Authors: Abbas Yaseri, Seyed Mahmoud AnishehAbstract:A paper currency recognition system has a wide range of applications such as self receiver machines for automated teller machines and automatic good-selling machines. In this paper a new paper currency recognition system based on Fourier-Mellin Transform, Markovian characteristics and Support Vector Machine (SVM) is presented. In the first, a pre-processing algorithm by Fourier-Mellin Transform is performed. The key feature of Fourier-Mellin Transform is that it is invariant in rotation, translation and scale of the input image. Then, obtained image is segmented and markovian characteristics of each segment have been utilized to construct a feature vectors. These vectors are then fed into SVM classifier for paper currency recognition. In order to evaluate the effectiveness of the system several experiments are carried out. Experimental result indicates that the proposed method achieved high accuracy rate in paper currency recognition.
Wang Jun - One of the best experts on this subject based on the ideXlab platform.
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Application of Mellin Transform in Wideband Underwater Acoustic Signal Processing
2007Co-Authors: Wang JunAbstract:According to the features of the wideband underwater acoustic signals, an algorithm for the wideband ambiguity function is put forward based on Mellin Transform. The wideband acoustic signal processing using the fast Mellin Transform is also explored. The theoretical analysis and simulation results show that the algorithm has not only high computation efficiency but also good concentration in wideband ambiguity domain. It suits for the wideband underwater acoustic signal processing.
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A Research on Wideband Underwater Acoustic Signal Processing Based on Mellin Transform
2007Co-Authors: Wang JunAbstract:According to the features of wideband underwater acoustic signal,a solving method of wideband ambiguity fuction based on Mellin Transform was put forward and the wideband signal processing based on fast Mellin Transform algorithm was studied.Theoretical analysis and simulation indicate that this algorithm not only implememts efficiently but also has good concentration in wideband ambiguity domain,so it is very suited for online processing of wideband underwater acoustic signal.
