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L Cayon - One of the best experts on this subject based on the ideXlab platform.
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detection of non gaussianity in the wilkinson microwave anisotropy probe first year data using spherical wavelets
The Astrophysical Journal, 2004Co-Authors: P Vielva, R B Barreiro, J.l. Sanz, E Martinezgonzalez, L CayonAbstract:A Non-Gaussian detection in the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data is reported. The detection has been found in the combined Q - V - W map proposed by the WMAP team after applying a wavelet technique based on the spherical Mexican hat wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales (ranging from a few arcminutes to tens of degrees). A Non-Gaussian Signal is detected at scales of the SMHW around 4° (size in the sky of around 10°). The right-tail probability of the detection is ≈0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right-tail probability of ≈0.1%. Systematics, foregrounds, and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of Non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: (1) Each one of the Q, V, and W receivers shows the same Non-Gaussianity pattern. (2) Several combinations of the different receivers at each frequency band—which highly reduce the cosmic microwave background (CMB) and the foreground emissions—do not show this Non-Gaussian pattern. Similarly, Galactic foregrounds show a negligible contribution to the Non-Gaussian detection: Non-Gaussianity is detected in all the WMAP maps (from 23 to 94 GHz), and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behavior compatible with the Gaussian model. The influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (such as secondary anisotropies and primordial features) cannot be rejected as the source of this Non-Gaussian detection. We remark that our result implies not only asymmetries north/south—like other previous WMAP analyses—but also a direct Non-Gaussian detection.
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detection of non gaussianity in the wmap 1 year data using spherical wavelets
arXiv: Astrophysics, 2003Co-Authors: P Vielva, R B Barreiro, J.l. Sanz, E Martinezgonzalez, L CayonAbstract:A Non-Gaussian detection in the WMAP 1-year data is reported. The detection has been found in the combined Q-V-W map proposed by the WMAP team (Komatsu et al. 2003) after applying a wavelet technique based on the Spherical Mexican Hat Wavelet (SMHW). The skewness and the kurtosis of the SMHW coefficients are calculated at different scales. A Non-Gaussian Signal is detected at scales of the SMHW around 4 deg (size in the sky of around 10 deg). The right tail probability of the detection is approx. 0.4%. In addition, a study of Gaussianity is performed in each hemisphere. The northern hemisphere is compatible with Gaussianity, whereas the southern one deviates from Gaussianity with a right tail probability of approx. 0.1%. Systematics, foregrounds and uncertainties in the estimation of the cosmological parameters are carefully studied in order to identify the possible source of Non-Gaussianity. The detected deviation from Gaussianity is not found to be caused by systematic effects: 1) each one of the Q, V and W receivers shows the same Non-Gaussianity pattern, and 2) several combinations of the different receivers at each frequency band do not show this Non-Gaussian pattern. Similarly, galactic foregrounds show a negligible contribution to the Non-Gaussian detection: Non-Gaussianity is detected in all the WMAP maps and no frequency dependence is observed. Moreover, the expected foreground contribution to the combined WMAP map was added to CMB Gaussian simulations showing a behaviour compatible with the Gaussian model. Influence of uncertainties in the CMB power spectrum estimation are also quantified. Hence, possible intrinsic temperature fluctuations (like secondary anisotropies and primordial features) can not be rejected as the source of this Non-Gaussian detection.
M Liguori - One of the best experts on this subject based on the ideXlab platform.
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optimal bispectrum estimator and simulations of the cmb lensing integrated sachs wolfe non gaussian Signal
Astronomy and Astrophysics, 2013Co-Authors: A Mangilli, Benjamin D Wandelt, Franz Elsner, M LiguoriAbstract:We present the tools to optimally extract the lensing-integrated Sachs Wolfe (L-ISW) bispectrum Signal from future cosmic microwave background (CMB) data. We implemented two different methods to simulate the Non-Gaussian CMB maps with the L-ISW Signal: a non-perturbative method based on the FLINTS lensing code and the separable mode-expansion method. We implemented the Komatsu, Spergel, and Wandelt (KSW) optimal estimator analysis for the L-ISW bispectrum and tested it on the Non-Gaussian simulations for realistic CMB experimental settings with an inhomogeneous sky coverage. We show that the estimator approaches the Cramer-Rao bound and that Wiener filtering the L-ISW simulations slightly improves the estimate of f L-ISW NL by ≤10%. For a realistic CMB experimental setting that accounts for anisotropic noise and masked sky, we show that the linear term of the estimator is highly correlated to the cubic term and it is necessary to recover the Signal and the optimal error bars. We also show that the L-ISW bispectrum, if not correctly accounted for, yields an underestimation of the f local NL error bars of 4%. A joint analysis of the Non-Gaussian shapes and/or L-ISW template subtraction is needed to recover unbiased results of the primordial Non-Gaussian Signal from ongoing and future CMB experiments.
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optimal bispectrum estimator and simulations of the the cmb lensing isw non gaussian Signal
arXiv: Cosmology and Nongalactic Astrophysics, 2013Co-Authors: A Mangilli, Benjamin D Wandelt, Franz Elsner, M LiguoriAbstract:In this paper we present the tools to optimally extract the Lensing-Integrated Sachs Wolfe (L-ISW) bispectrum Signal from future CMB data. We implement two different methods to simulate the Non-Gaussian CMB maps with the L-ISW Signal: a non-perturbative method based on the FLINTS lensing code and the separable mode expansion method. We implement the Komatsu, Spergel and Wandelt (KSW) optimal estimator analysis for the Lensing-ISW bispectrum and we test it on the Non-Gaussian simulations in the case of a realistic CMB experimental settings with an inhomogeneous sky coverage. We show that the estimator approaches the Cramer-Rao bound and that Wiener filtering the L-ISW simulations gives a slight improvement on the estimate of $f_{NL}^{L-ISW}$ of $\leq 10%$. For a realistic CMB experimental setting accounting for anisotropic noise and masked sky, we show that the linear term of the estimator is highly correlated to the cubic term and it is necessary to recover the Signal and the optimal error bars. We also show that the L-ISW bispectrum, if not correctly accounted for, yields an underestimation of the $f_{NL}^{local}$ error bars of $\simeq 4%$. A joint analysis of the Non-Gaussian shapes and/or L-ISW template subtraction is needed in order to recover unbiased results of the primordial Non-Gaussian Signal from ongoing and future CMB experiments.
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constraining running non gaussianity
Journal of Cosmology and Astroparticle Physics, 2009Co-Authors: M Liguori, Emiliano Sefusatti, Amit Yadav, Mark G Jackson, Enrico PajerAbstract:The primordial Non-Gaussian parameter fNL has been shown to be scale-dependent in several models of inflation with a variable speed of sound, such as Dirac-Born-Infeld (DBI) models. We perform a Fisher matrix analysis of the bispectra of the temperature and polarization of the Cosmic Microwave Background (CMB) radiation and derive the expected constraints on the parameter nNG that quantifies the running of fNL(k) for current and future CMB missions. We find that CMB information alone, in the event of a significant detection of the Non-Gaussian component, corresponding to fNL = 50 for the local model and fNL = 100 for the equilateral model of Non-Gaussianity, is able to determine nNG with a 1-σ uncertainty of nNG 0.1 and ΔnNG 0.3, respectively, for the Planck mission and a factor of two better for CMBPol. In addition, we show how future large-scale structure observations should achieve results comparable to or even better than those from the CMB, while showing some complementarity due to the different distribution of the Non-Gaussian Signal over the relevant range of scales. Finally, we compare our findings to the predictions on the amplitude and running of Non-Gaussianity of DBI inflation, showing how the constraints on a scale-dependent fNL(k) translate into constraints on the parameter space of the theory.
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constraining running non gaussianity
arXiv: Cosmology and Nongalactic Astrophysics, 2009Co-Authors: M Liguori, Emiliano Sefusatti, Amit Yadav, Mark G Jackson, Enrico PajerAbstract:The primordial Non-Gaussian parameter fNL has been shown to be scale-dependent in several models of inflation with a variable speed of sound. Starting from a simple ansatz for a scale-dependent amplitude of the primordial curvature bispectrum for two common phenomenological models of primordial Non-Gaussianity, we perform a Fisher matrix analysis of the bispectra of the temperature and polarization of the Cosmic Microwave Background (CMB) radiation and derive the expected constraints on the parameter nNG that quantifies the running of fNL(k) for current and future CMB missions such as WMAP, Planck and CMBPol. We find that CMB information alone, in the event of a significant detection of the Non-Gaussian component, corresponding to fNL = 50 for the local model and fNL = 100 for the equilateral model of Non-Gaussianity, is able to determine nNG with a 1-sigma uncertainty of Delta nNG = 0.1 and Delta nNG = 0.3, respectively, for the Planck mission. In addition, we consider a Fisher matrix analysis of the galaxy power spectrum to determine the expected constraints on the running parameter nNG for the local model and of the galaxy bispectrum for the equilateral model from future photometric and spectroscopic surveys. We find that, in both cases, large-scale structure observations should achieve results comparable to or even better than those from the CMB, while showing some complementarity due to the different distribution of the Non-Gaussian Signal over the relevant range of scales. Finally, we compare our findings to the predictions on the amplitude and running of Non-Gaussianity of DBI inflation, showing how the constraints on a scale-dependent fNL(k) translate into constraints on the parameter space of the theory.
Jose C Principe - One of the best experts on this subject based on the ideXlab platform.
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kernel risk sensitive loss definition properties and application to robust adaptive filtering
IEEE Transactions on Signal Processing, 2017Co-Authors: Badong Chen, Nanning Zheng, Lei Xing, Haiquan Zhao, Jose C PrincipeAbstract:Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian Signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation.
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correntropy properties and applications in non gaussian Signal processing
IEEE Transactions on Signal Processing, 2007Co-Authors: Weifeng Liu, Puskal Prasad Pokharel, Jose C PrincipeAbstract:The optimality of second-order statistics depends heavily on the assumption of Gaussianity. In this paper, we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure. A close relationship between correntropy and M-estimation is established. Connections and differences between correntropy and kernel methods are presented. As such correntropy has vastly different properties compared with second-order statistics that can be very useful in Non-Gaussian Signal processing, especially in the impulsive noise environment. Examples are presented to illustrate the technique.
Badong Chen - One of the best experts on this subject based on the ideXlab platform.
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fixed point minimum error entropy with fiducial points
Sport Psychologist, 2020Co-Authors: Yingsong Li, Yuantao Gu, Badong ChenAbstract:Compared with traditional learning criteria, such as minimum mean square error (MMSE), the minimum error entropy (MEE) criterion has received increasing attention in the domains of nonlinear and Non-Gaussian Signal processing and machine learning. Since the MEE criterion is shift-invariant, one has to add a bias to achieve zero-mean error over training datasets. Thus, a modification of the MEE called minimization of error entropy with fiducial points (MEEF) was proposed, which controls the bias for MEE in a more elegant and efficient way. In the present paper, we propose a fixed-point minimization of error entropy with fiducial points (MEEF-FP) as an alternative to the gradient based MEEF for training a linear-in-parameters (LIP) model because of its fast convergence speed, robustness and step-size free. Also, we provide a sufficient condition that guarantees the convergence of the MEEF-FP algorithm. Moreover, we develop a recursive MEEF-FP (RMEEF-FP) for online adaptive learning with low-complexity. Finally, illustrative examples are presented to show the excellent performance of the new methods.
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kernel risk sensitive loss definition properties and application to robust adaptive filtering
IEEE Transactions on Signal Processing, 2017Co-Authors: Badong Chen, Nanning Zheng, Lei Xing, Haiquan Zhao, Jose C PrincipeAbstract:Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian Signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation.
Shengyang Luan - One of the best experts on this subject based on the ideXlab platform.
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generalized covariance for non gaussian Signal processing and gc music under alpha stable distributed noise
Digital Signal Processing, 2021Co-Authors: Shengyang Luan, Minglong Zhao, Yinrui Gao, Tianshuang Qiu, Zhaojun ZhangAbstract:Abstract Direction of arrival (DOA) estimation is one of the most important techniques applied in many practical engineering applications. Multiple Signal classification (MUSIC) has gained increasing attention due to its high resolution in space. Many methods have been studied to handle the noise of Alpha-stable distribution within the framework of Non-Gaussian Signal processing. Inspired by a state-of-the-art concept, bounded nonlinear covariance (BNC), a more generalized concept, named generalized covariance (GC), is proposed. A series of existing concepts based on the fractional lower-order moment (FLOM), the correntropy, and the BNC are unified in the name of GC. Then, the convergence of GC under Alpha-stable distributed random variables is addressed. Furthermore, four different types of nonlinear functions are introduced for GC and BNC to handle impulsive noise, including sigmoid functions, score functions, FLOM mapping, Gaussian-like functions. These curves with different parameters are also exhibited in detail to illustrate their capabilities to suppress outliers. Also, GC-MUSIC is proposed, and its performances are compared with other 6 MUSIC-like algorithms in the presence of heavy-tailed impulsive noise. Besides, Cramer-Rao bound (CRB) of root mean squared error is also deduced and exhibited. Through Monte-Carlo simulations, the superiority of GC-MUSIC and BNC-MUSIC under Alpha-stable distributed noise is demonstrated.
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hyperbolic tangent function based cyclic correlation definition and theory
Signal Processing, 2019Co-Authors: Shengyang LuanAbstract:Abstract Non-stationary, Non-Gaussian Signal processing is a challenging topic in Signal processing research. Over the past decade, due to effectively addressing co-channel interference, cyclostationarity-based methodologies have found a wide range of applications, such as wireless communication, cognitive radio, and mechanical vibration monitoring. Despite offering a feasible scheme, the second and higher-order cyclostationarity-based methodologies suffer under Non-Gaussian noise environments, particularly impulsive noise environments. In this paper, through studying the similarity measurement, nonlinear function, and mapping mode, we propose a novel methodology named hyperbolic-tangent-function-based cyclic correlation (HTCC) to address both Gaussian and Non-Gaussian noises with a uniform expression. The idea is inspired by the fact that hyperbolic tangent function is not only a bounded function but also achieves a differential compression. In addition, the theoretical foundations of this novel method are introduced step by step, including the definition, property, and spectrum. A number of numerical experiments are carried out to compare the algorithm performance with existing competitive methods. The proposed method generally shows good effectiveness and robustness and can be utilized for denoising problems in Signal processing.