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V F Kravchenko - One of the best experts on this subject based on the ideXlab platform.

  • Truncation Error Bound for the Kravchenko–Kotelnikov Series
    Journal of Communications Technology and Electronics, 2018
    Co-Authors: K. A. Budunova, V F Kravchenko, V. I. Pustovoit
    Abstract:

    The truncation error of the Kravchenko–Kotelnikov series, which is a generalization of the Whittaker–Kotelnikov–Shannon series, is studied. The basis Functions of the Kravchenko–Kotelnikov series are the spectra Fa(t) of the Atomic Function ha(x), linearly transformed with respect to the argument. In this case, the Function Fa(t) is defined by an infinite product. Two theorems on the truncation error bound for the Kravchenko–Kotelnikov series are proven. A practically important case in which the infinite product Fa(t) is replaced by a partial one is considered. A comparative analysis of the obtained formulae is carried out.

  • truncation error bound for the kravchenko kotelnikov series
    Journal of Communications Technology and Electronics, 2018
    Co-Authors: K. A. Budunova, V F Kravchenko, V. I. Pustovoit
    Abstract:

    The truncation error of the Kravchenko–Kotelnikov series, which is a generalization of the Whittaker–Kotelnikov–Shannon series, is studied. The basis Functions of the Kravchenko–Kotelnikov series are the spectra Fa(t) of the Atomic Function ha(x), linearly transformed with respect to the argument. In this case, the Function Fa(t) is defined by an infinite product. Two theorems on the truncation error bound for the Kravchenko–Kotelnikov series are proven. A practically important case in which the infinite product Fa(t) is replaced by a partial one is considered. A comparative analysis of the obtained formulae is carried out.

  • New constructions of 1D and 2D generalized Kravchenko-Kotel’nikov theorems on the basis of Atomic Function up ( t )
    Journal of Communications Technology and Electronics, 2013
    Co-Authors: V F Kravchenko, A. V. Yurin
    Abstract:

    New constructions of 1D and 2D generalized Kravchenko-Kotel’nikov sampling theorems based on Atomic Function up(t) are proposed and justified. The theorems are rigorously proved for both 2D and 1D cases. A simulation performed to analyze the construction and improvement of new series estimates shows their advantage over the classical Whittaker-Kotel’nikov-Shannon series.

  • some estimates for the spectral density of a time series on the basis of the Atomic Function family
    Doklady Physics, 2007
    Co-Authors: V F Kravchenko, V I Pustovoĭt
    Abstract:

    INTRODUCTIONAnalysis of time series is closely related to a widescope of problems. Among them we can indicate thestatistical theory of communication, regulation theory,and the statistical analysis of time series. In the condi-tions when we deal with a large number of observationsand data analysis is required in prognostic and regula-tion goals, spectral methods turn out to be preferable. Inestimates of the spectral density of a time series, smooth-ing Functions (windows) play a specific role [1–6].When using an arbitrary method to estimate thepower spectral density, we have to make a lot of com-promise decisions in order to obtain statistically stablespectral estimates with the maximum possible resolu-tion, which are based on a finite number of data read-ings. These compromise decisions include the choice ofsmoothing Functions (windows) and physical parame-ters in both time and frequency regions. In practice, thismakes it possible to balance requirements to loweringthe side-lobe level, to perform effective averaging overan ensemble, and to provide acceptable spectral resolu-tion.SPECTRAL-DENSITY ESTIMATESFOR A TIME SERIES ON THE BASISOF Atomic FunctionSWe consider spectral-density estimates constructedwith the use of the Atomic-Function (AF) formalismof [5, 6]. Let ϕ(x) be a certain Atomic Function. Ifϕ(x) ≠ 0 for |x| > 1, then we introduce a certain multi-plier in such a manner that the AF carrier is within therange [–1, 1]. Thus, in this case, the Function k(x) hasthe form(1)where the AF carrier is , . Then, according tothe definition, we arrive at(2)where F(λ) is the AF Fourier transform.With the development of methods of the rapid Fou-rier transform, the methods of [1–4] came to play abasic role in the simplest estimates of the spectral den-sity f(ω). They were based on the periodogram deter-mined in accordance with the formula(3)In equality (3), the Function x (

  • Optimization of the profile of the electrodynamic system of a powerful gyro-traveling-wave-tube (gyro-TWT)
    Third International Kharkov Symposium 'Physics and Engineering of Millimeter and Submillimeter Waves'. MSMW'98. Symposium Proceedings (Cat. No.98EX119, 1998
    Co-Authors: V F Kravchenko, A. A. Kuraev, Stanislav V. Kolosov
    Abstract:

    The three-dimensional self-consistent mathematical model of a relativistic gyro-TWT with an irregular electrodynamic system (EDS) was described in Kuraev (1979) and Kuraev et al. (1988). The problem of the efficient optimization of gyro-TWTs over the frequency band is discussed. The optimized waveguide profile and magnetostatic field distribution are determined and the Atomic Function is defined to solve equations. The application of Atomic Functions in the approximation of the waveguide profile and the magnetostatic field distribution makes it possible to predict new effective mechanisms of interaction in a gyro-TWT with an irregular electrodynamic system and inhomogeneous magnetostatic fields

V. I. Pustovoit - One of the best experts on this subject based on the ideXlab platform.

  • Truncation Error Bound for the Kravchenko–Kotelnikov Series
    Journal of Communications Technology and Electronics, 2018
    Co-Authors: K. A. Budunova, V F Kravchenko, V. I. Pustovoit
    Abstract:

    The truncation error of the Kravchenko–Kotelnikov series, which is a generalization of the Whittaker–Kotelnikov–Shannon series, is studied. The basis Functions of the Kravchenko–Kotelnikov series are the spectra Fa(t) of the Atomic Function ha(x), linearly transformed with respect to the argument. In this case, the Function Fa(t) is defined by an infinite product. Two theorems on the truncation error bound for the Kravchenko–Kotelnikov series are proven. A practically important case in which the infinite product Fa(t) is replaced by a partial one is considered. A comparative analysis of the obtained formulae is carried out.

  • truncation error bound for the kravchenko kotelnikov series
    Journal of Communications Technology and Electronics, 2018
    Co-Authors: K. A. Budunova, V F Kravchenko, V. I. Pustovoit
    Abstract:

    The truncation error of the Kravchenko–Kotelnikov series, which is a generalization of the Whittaker–Kotelnikov–Shannon series, is studied. The basis Functions of the Kravchenko–Kotelnikov series are the spectra Fa(t) of the Atomic Function ha(x), linearly transformed with respect to the argument. In this case, the Function Fa(t) is defined by an infinite product. Two theorems on the truncation error bound for the Kravchenko–Kotelnikov series are proven. A practically important case in which the infinite product Fa(t) is replaced by a partial one is considered. A comparative analysis of the obtained formulae is carried out.

Eduardo Bayro-corrochano - One of the best experts on this subject based on the ideXlab platform.

  • Hilbert and Riesz Transforms Using Atomic Function for Quaternionic Phase Computation
    Advances in Applied Clifford Algebras, 2013
    Co-Authors: E. U. Moya-sánchez, Eduardo Bayro-corrochano
    Abstract:

    Complex and hyper-complex valued filtering play a substantial role in signal processing, especially to obtain local features in the frequency and phase domain. In the case of 1D signals, the analytic signal is typically computed using the Hilbert transform. Such complex representation allows us to compute the phase and magnitude of the signal. For high-dimension signals, the Riesz transform and partial Hilbert transforms have been used as extensions of the analytic signal to compute the local phase and local orientation. A major goal of this work is to highlight the role of an Atomic Function (AF) up(x) as a kernel for the Hilbert and Riesz transforms. It is well known that the use of phase information has a big potential because it is invariant to illumination and rotations. In this regard, we show the advantages to carry out computations of local Riesz phase using the Atomic Function instead of the classical global-phase approach. In addition, we explain how the Atomic Function up(x), formulated in the quaternionic algebra framework, can be used as a building block to perform multiple analytical operations commonly used in image processing, such as low-pass filter, derivatives, local phase processing, steering quaternionic filters, multi-resolution analysis and symmetries detection.

  • Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions
    Quaternion and Clifford Fourier Transforms and Wavelets, 2013
    Co-Authors: Eduardo Moya-sanchez, Eduardo Bayro-corrochano
    Abstract:

    In this work we address the topic of image processing using an Atomic Function (AF) in a representation of quaternionic algebra. Our approach is based on the most important AF, the up(??) Function. The main reason to use the Atomic Function up(??) is that this Function can express analytically multiple operations commonly used in image processing such as low-pass filtering, derivatives, local phase, and multiscale and steering filters. Therefore, the modelling process in low level-processing becomes easy using this Function. The quaternionic algebra can be used in image analysis because lines (even), edges (odd) and the symmetry of some geometric objects in R2 are enhanced. The applications show an example of how up(??) can be applied in some basic operations in image processing and for quaternionic phase computation.

  • CIARP - Quaternionic Analytic Signal Using Atomic Functions
    Progress in Pattern Recognition Image Analysis Computer Vision and Applications, 2012
    Co-Authors: Eduardo Moya-sanchez, Eduardo Bayro-corrochano
    Abstract:

    Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. In 1D signals, is usual to compute the phase and the magnitude of a signal using the analytic signal (the signal and its Hilbert transform using complex numbers). However, for high dimensional signals the monogenic signal (the signal and its Riesz transform) has been used to obtain the local phase and orientation with good results. The main aim of this work is to present a new way to make the computation of the Hilbert transform using the Atomic Function. The computation of the Hilbert transform take relevance when the phase computation is required.

  • Guide to Geometric Algebra in Practice - Quaternion Atomic Function for Image Processing
    Guide to Geometric Algebra in Practice, 2011
    Co-Authors: Eduardo Bayro-corrochano, Eduardo Moya-sanchez
    Abstract:

    In this work we introduce a new kernel for image processing called the Atomic Function. This kernel is compact in the spatial domain, and it can be adapted to the behavior of the input signal by broadening or narrowing its band ensuring a maximum signal-to-noise ratio. It can be used for smooth differentiation of images in the quaternion algebra framework. We discuss the role of the quaternion Atomic Function with respect to monogenic signals. We then propose a steerable quaternion wavelet scheme for image structure and contour detection. Making use of the generalized Radon transform and images processed with the quaternion wavelet Atomic Function transform, we detect shape contours in color images. We believe that the Atomic Function is a promising kernel for image processing and scene analysis.

  • CIARP - Quaternion Atomic Function wavelet for applications in image processing
    Progress in Pattern Recognition Image Analysis Computer Vision and Applications, 2010
    Co-Authors: Eduardo Moya-sanchez, Eduardo Bayro-corrochano
    Abstract:

    Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. The main contribution of this work is to develop a Quaternionic Atomic Function Wavelet as a new quaternionic image wavelet transform. This filter have a real part and three imaginary parts (i, j, k) of the Quaternion Atomic Function, as a result we can extract more information from the image by the three phases (Φ, θ, ϕ) of the quaternion representation. The experimental part shows clearly that the phase information of the image is not afected by illumination changes.

Noriyuki Fujimoto - One of the best experts on this subject based on the ideXlab platform.

  • CEC - Parallel Multi-Objective Particle Swarm Optimization for Large Swarm and High Dimensional Problems
    2018 IEEE Congress on Evolutionary Computation (CEC), 2018
    Co-Authors: Maruf Hussain, Noriyuki Fujimoto
    Abstract:

    In last couple of years, parallel two or many objective MOPSO (Multi-objective Particle Swarm Optimization) have been proposed in literature. Denumerable implementations were published, however they had not achieved faster execution time and good Pareto fronts. They have alluded some limitation of archive handling, picked up nondominated solutions, high dimensional problems and so on for large swarm population. Moreover, none of the researchers have implemented MOPSO and tested the performance for large swarm population and high dimensional problem simultaneously. In particular, they skipped high dimensional problems. This paper presents a faster implementation of parallel MOPSO on a GPU based on the CUDA architecture, which uses coalescing memory access, pseudorandom number generator (PRNG), Thrust library, Atomic Function, parallel archiving and so on. In addition, our implementation has a positive impact on the performance to solve high dimensional optimization problems with large swarm population. Therefore, our proposed algorithm can be widely used in real optimizing problems. The proposed parallel implementation of MOPSO using a master-slave model provides up to 182 times speedup compared to the corresponding CPU MOPSO.

Eduardo Moya-sanchez - One of the best experts on this subject based on the ideXlab platform.

  • Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions
    Quaternion and Clifford Fourier Transforms and Wavelets, 2013
    Co-Authors: Eduardo Moya-sanchez, Eduardo Bayro-corrochano
    Abstract:

    In this work we address the topic of image processing using an Atomic Function (AF) in a representation of quaternionic algebra. Our approach is based on the most important AF, the up(??) Function. The main reason to use the Atomic Function up(??) is that this Function can express analytically multiple operations commonly used in image processing such as low-pass filtering, derivatives, local phase, and multiscale and steering filters. Therefore, the modelling process in low level-processing becomes easy using this Function. The quaternionic algebra can be used in image analysis because lines (even), edges (odd) and the symmetry of some geometric objects in R2 are enhanced. The applications show an example of how up(??) can be applied in some basic operations in image processing and for quaternionic phase computation.

  • CIARP - Quaternionic Analytic Signal Using Atomic Functions
    Progress in Pattern Recognition Image Analysis Computer Vision and Applications, 2012
    Co-Authors: Eduardo Moya-sanchez, Eduardo Bayro-corrochano
    Abstract:

    Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. In 1D signals, is usual to compute the phase and the magnitude of a signal using the analytic signal (the signal and its Hilbert transform using complex numbers). However, for high dimensional signals the monogenic signal (the signal and its Riesz transform) has been used to obtain the local phase and orientation with good results. The main aim of this work is to present a new way to make the computation of the Hilbert transform using the Atomic Function. The computation of the Hilbert transform take relevance when the phase computation is required.

  • Guide to Geometric Algebra in Practice - Quaternion Atomic Function for Image Processing
    Guide to Geometric Algebra in Practice, 2011
    Co-Authors: Eduardo Bayro-corrochano, Eduardo Moya-sanchez
    Abstract:

    In this work we introduce a new kernel for image processing called the Atomic Function. This kernel is compact in the spatial domain, and it can be adapted to the behavior of the input signal by broadening or narrowing its band ensuring a maximum signal-to-noise ratio. It can be used for smooth differentiation of images in the quaternion algebra framework. We discuss the role of the quaternion Atomic Function with respect to monogenic signals. We then propose a steerable quaternion wavelet scheme for image structure and contour detection. Making use of the generalized Radon transform and images processed with the quaternion wavelet Atomic Function transform, we detect shape contours in color images. We believe that the Atomic Function is a promising kernel for image processing and scene analysis.

  • CIARP - Quaternion Atomic Function wavelet for applications in image processing
    Progress in Pattern Recognition Image Analysis Computer Vision and Applications, 2010
    Co-Authors: Eduardo Moya-sanchez, Eduardo Bayro-corrochano
    Abstract:

    Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. The main contribution of this work is to develop a Quaternionic Atomic Function Wavelet as a new quaternionic image wavelet transform. This filter have a real part and three imaginary parts (i, j, k) of the Quaternion Atomic Function, as a result we can extract more information from the image by the three phases (Φ, θ, ϕ) of the quaternion representation. The experimental part shows clearly that the phase information of the image is not afected by illumination changes.