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Feature selection is one of the commonly used technique in machine learning literature. It aims to reduce irrelevant, redundant, unneeded attributes from data that do not contribute to improve or even decrease the performance of analytical model. This paper proposes a new feature selection method that evaluate by back-propagated weighting the nongaussianity, Kurtosis, of the corresponding independent components. The nongaussianity scores are normalized using a suitable logistic function where the parameters of the logistic function are selected using an auto fitting curve technique. This proposed method is called the Logistic function of Kurtosis of Independent Component Analysis (KL-ICA). The results on various benchmarks show significant improvement of analytical model performance over existing technique.

Complex information contained in single-channel synthetic aperture radar (SAR) imagery is often discarded due to the conventional resolution theory. However, recent researches show that noncircularity and non-Gaussianity can be of significance for ocean monitoring. This paper presents a study into kurtosis of ships and sea clutter in complex-valued Sentinel-1 imagery. Kurtosis can measure the outlier-prone of a distribution. Thus, it can identify Gaussianity and non-Gaussianity. Interferometric Wide Swath (IW) Single Look Complex (SLC) data are taken into account in the kurtosis calculation. The statistical results show that the real and imaginary parts of sea clutter present Gaussianity while ships show sup-Gaussiantiy. The kurtosis of sea clutter is approximately constant and reaches 3 while the kurtosis of ships is much larger than 3. This also implies that ships can be detected and segmented by kurtosis test efficiently. Two preliminary experiments relevant to ship detection and segmentation are then presented. These results demonstrate that kurtosis can be a vital indicator for ocean monitoring in single-channel complex-valued SAR imagery.

Higher order spectra are very useful in problems where either non Gaussianity, noise and non linearities are important. These properties are proved to be present in natural images. This yield higher order spectra and especially the third order, namely the bispectrum, to be an interesting tool in image processing. This paper presents higher order spectra in signal processing and their extension and applications to image processing, where the images are proved to be non Gaussian and non linear.

In underwater signal processing, acoustic signals are used to transmit and receive information for communication. But the acoustic signals get affected due to spreading, reverberation, attenuation and absorption which produce ambient noise. Ambient noise is the background noise created due to natural sources as well as anthropogenic (man-made) sources. Ambient noise can be characterized as Gaussian, non-Gaussian, stationary and non-stationary because of what the sonar system get disturbed. So to improve sonar system performance, characterization of ambient noise is important. In this paper, non-Gaussianity in tropical waters of the western coast of India is compared using various hypothetical tests like Lilliefors test, Anderson-Darling test, and Shapiro-Wilk test. Non-stationarity is identified using Kolmogorov-Smirnov two-sample test.

In this paper, we propose a method to solve a compressed sensing problem in the multiple measurement vector model using a mixture of Gaussians prior, inspired by existing sparse Bayesian learning approaches. We show that in the multiple measurement vector model we can take advantage of having multiple samples to learn the properties of the distributions of the sources as part of the reconstruction process, and we show that this method can be applied to significantly improve the reconstruction quality of ultrasound images. We further show that we can also improve the quality of reconstruction by taking advantage of the block structure of ultrasound images, using an existing algorithm for block sparse Bayesian learning.

In Independent Component Analysis (ICA) and its diverse algorithms, uniqueness is the most essential requirement and rationality problem compared with performances of existence, stability and convergence. For ICA's maximum non-Gaussianity estimation (MNE), many achievements have been made in recent twenty years based on uniqueness assumption, which has been taken for granted all along except for some intuitive interpretation. From the perspective of constrained cost function optimization, the paper is to provide a mathematical proof for uniqueness principle in MNE. The research focuses on skewless assumption and kurtosis-based cost function with basic linear ICA model. Provided that the sources are skewless, the relationship between the Kuhn-Tucker (K-T) points of cost function and the local maxima of non-Gaussianity are derived with the help of constrained optimization theory, and then a conclusion is drawn that there is a one-to-one correspondence between independent components and the local maxima, i.e. maximum non-Gaussianity is the sufficient and necessary condition for independent sources recovery. Moreover, the result also leads to an alternative and straightforward approach to the proof of the Xu' one-bit-matching conjecture for the availability of multi-unit approaches.

In cognitive radio networks, secondary users (SUs) need to sense/detect the vacant spectrum holes in a wide frequency band for achieve the dynamic spectrum access. The combination of compressive sensing (CS) with wavelet edge detection makes the wideband spectrum reconstruction and detection to be feasible. The existence of small-scale primary users (SSPUs) such as wireless microphones and mobile devices, however, brings a difficulty for the wideband spectrum sensing of SUs mainly due to the SSPUs' weak signal strengths and low singal-noise-ratio (SNR) conditions. To solve this probelm, a novel robust compressive wideband spectrum sensing algorithm is proposed in this paper by exploiting the non-Gaussianity properties of the SSPUs' spectrum and utilizing the non-Gaussianity test. Since the spectrum of a SU's received signal theoretically follows different statistical distribution when the primary users (PUs) are present or not, the proposed algorithm uses the Pearson's Chi-squared test statistic to measure the non-Gaussianity properties of the compressive reconstructed wideband spectrum, then find out the vacant spectrum regions. Simulation results show that our algorithm can obtain a good wideband spectrum sensing performance even for the SSPUs under low SNRs in cognitive wireless networks.

In cognitive radio networks (CRNs), wideband spectrum sensing is an important task for secondary users (SUs) to achieve the dynamic spectrum access. Even though the wideband spectrum detection is feasible by combining the compressive sensing (CS) with wavelet transform, however, accurate detection of the small-scale primary users (SSPUs) such as wireless microphones and mobile devices is still difficult especially under low signal-noise-ratio (SNR) conditions due to the SSPU's weak signal strength. To cope with this challenge, we propose a novel robust compressive wideband spectrum sensing algorithm by exploiting the non-Gaussianity properties of the SSPU's spectrum. Since the spectrum of received signal at SUs more closely approximate the Gaussian distribution when the primary users (PUs) are absent than that of the PU's spectrum, it is possible to design a test statistic to measure the non-Gaussianity properties of the wideband spectrum reconstructed by CS method, then make a decision on whether there are vacant frequency bands. Simulation results show the effectiveness of the proposed algorithm even

Recently, there is a growing need for statistical learning of causal structures in data with many variables. A structural equation model called Linear Non-Gaussian Acyclic Model (LiNGAM) has been extensively studied to uniquely estimate causal structures in data. The key assumptions are that external influences are independent and follow non-Gaussian distributions. However, LiNGAM does not capture temporal structural changes in observed data. In this paper, we consider learning causal structures in longitudinal data that collects samples over a period of time. In previous studies of LiNGAM, there was no model specialized to handle longitudinal data with multiple samples. Therefore, we propose a new model called longitudinal LiNGAM and a new estimation method using the information on temporal structural changes and non-Gaussianity of data. The new approach requires less assumptions than previous methods.

In this paper, we proposed the approach which combines inverse filter criteria with non-Gaussianity to separate convolutive mixtures of speech in the time domain. In this case, the proposed method first extract innovation processes of speech sources by non-Gaussianity maximization and then artificially color them by re-coloration filters. Computer simulation experiments are presented to illustrate the proposed approach.

The purpose of this paper is to develop novel Blind Source Extraction (BSE) algorithms from linear mixtures of the statistically dependent source signals. we show that maximization of the non Gaussianity (NG) measure can not only separate the statistically independent but also dependent source signals. The NG measure is defined by statistical distances between distributions based on the cumulative density function instead of traditional probability density function which can be estimated by the order statistics efficiently. The NG distance provide new cost function whose maximization performs the extraction of one dependent component at each successive stage of a de1ation procedure using an iterative algorithm.

In this paper, we provide a systematic method to construct contrast functions through the use of sub- or super- additive functionals. The used sub- or super-additive functionals are applied to the distributions of the extracted sources to quantify the degree of non-Gaussianity or sparsity. In this work, we assume a completely blind scenario where one knows only the observations and the existence of at most one Gaussian independent component in the mixture. However, there is no a priori information about the mixing matrix nor about the source density. Some practical examples of useful contrast functions are introduced and discussed in order to illustrate the usefulness of the proposed approach.

In this contribution, we propose a Bayesian sampling solution to the problem of noisy blind separation of generalized hyperbolic (GH) signals. GH models, introduced by Barndorff-Nielsen in 1977, represent a parametric family able to cover a wide range of real signal distributions. The alternative construction of these distributions as a normal mean-variance (continuous) mixture leads to an efficient implementation of the MCMC method applied to source separation. The incomplete data structure of the GH distribution is indeed compatible with the hidden variable nature of the source separation problem. Our algorithm involves hyperparameters estimation as well. Therefore, it can be used, independently, to fit the parameters of the GH distribution to real data.

In estimation theory, the asymptotic efficiency of the maximum likelihood (ML) method for independent identically distributed observations and when the number of observations, T, tends to infinity is a well known result. In some scenarios, the number of snapshots may be small, making this result inapplicable. In the array processing framework, for Gaussian emitted signals, we fill this lack at high signal-to-noise ratio (SNR). In this situation, we show that the ML estimation is asymptotically (with respect to SNR) inefficient and non Gaussian.

A nonlinear analysis of musical lung sounds based on the bicoherence index is presented in this paper. The detection of quadratic phase coupling between any frequency components of musical lung sounds, by means of third-order statistics and spectra, provides a measure of their nonlinear interaction. This harmonic analysis was conducted on pre-classified signals (wheezes, ronchi, striders) selected from international teaching tapes. The derived results have shown a high degree of deviation from Gaussianity along with quadratic self-coupling within the distinct frequencies of the corresponding power spectrum of musical lung sounds. Differences in the degree of phase coupling, the nonlinearity and non Gaussianity of the processed signals, establish a new field in characterization and feature extraction of the pulmonary pathology associated with musical lung sounds.