Gaussian Detection Research Articles

A hierarchical signal detection model with unequal variance for binary responses.

Gaussian signal detection models with equal variance are commonly used in simple yes-no detection and discrimination tasks whereas more flexible models with unequal variance require additional information. Here, a hierarchical Bayesian model with equal variance is extended to an unequal-variance model by exploiting variability of hit and false-alarm rates in a random sample of participants. This hierarchical model is investigated analytically, in simulations and in applications to existing data sets. The results suggest that signal variance and other parameters can be accurately estimated if plausible assumptions are met. It is concluded that the model provides a promising alternative to the ubiquitous equal-variance model for binary data.

Generalized Gaussian signal detection theory: A unified signal detection framework for confidence data analysis.

Human decision behavior entails a graded awareness of its certainty, known as a feeling of confidence. Until now, considerable interest has been paid to behavioral and computational dissociations of decision and confidence, which has raised an urgent need for measurement frameworks that can quantify the efficiency of confidence rating relative to decision accuracy (metacognitive efficiency). As a unique addition to such frameworks, we have developed a new signal detection theory paradigm utilizing the generalized Gaussian distribution (GGSDT). This framework evaluates the observer's metacognitive efficiency and internal standard deviation ratio through shape and scale parameters, respectively. The shape parameter quantifies the kurtosis of internal distributions and can practically be understood in reference to the proportion of the Gaussian ideal observer's confidence being disrupted with random guessing (metacognitive lapse rate). This interpretation holds largely irrespective of the contaminating effects of decision accuracy or operating characteristic asymmetry. Thus, the GGSDT enables hitherto unexplored research protocols (e.g., direct comparison of yes/no vs. forced-choice metacognitive efficiency), expected to find applications in various fields of behavioral science. This article provides a detailed walkthrough of the GGSDT analysis with an accompanying R package (ggsdt). (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Supplemental Material for Generalized Gaussian Signal Detection Theory: A Unified Signal Detection Framework for Confidence Data Analysis

Supplemental Material for Generalized Gaussian Signal Detection Theory: A Unified Signal Detection Framework for Confidence Data Analysis

An Active Detection Strategy Based on Dimensionality Reduction for False Data Injection Attacks in Cyber-Physical Systems

In recent years, different intelligent and undetectable cyber-attacks against networked control systems (e.g., replay and covert attacks) have been investigated. In this paper, we design a novel control architecture that prevents their existence. In particular, first, we propose to encode the sensor outputs into a randomly changing lower-dimensional space obtained by means of principal component analysis. Such a transformation ensures optimal information reconstruction on the controller's side, and it prevents the attacker from accessing the original sensor measurements, nullifying the possibility of perfect stealthy attacks. Then, on the controller's side, we design a passive Gaussian anomaly detector that leverages the output of an unknown input observer ad-hoc designed to estimate the system's states and unknown inputs simultaneously. It is formally shown that the proposed detection strategy is able to discover the presence of replay and covert attacks. Simulation results obtained considering a quadruple water tank system confirm the capability of the developed architecture.

Objective Bayesian Approach for Binary Hypothesis Testing of Multivariate Gaussian Observations

This paper proposes an objective Bayesian detector for the binary hypothesis testing problem in which the observation vectors are IID and follow multivariate Gaussian distribution under both the null and alternative hypotheses. The mean vector and covariance matrix under each hypothesis are not known, they also do not have special structure other than the covariance matrices are partially ordered in the positive definite cone with their difference positive semi-definite. An example of such a problem is the detection of Gaussian random signal in Gaussian noise. Non-informative priors are imposed on the unknown parameters for computing the marginals and evaluating the Bayes factor test statistic, where the prior for the covariance matrix is applied to the Cholesky factorization of the precision matrix. For the null hypothesis, we propose conjugate priors for the unknowns. For the alternative hypothesis, we propose uniform prior on the mean vector, and a class of objective priors that encompasses the Jeffreys, Independence Jeffreys, Geisser and Cornfield, Haar Measure and Reference priors for the precision matrix. The proposed priors enable closed-form expressions for the marginals and lead to an objective Bayes factor having the posteriors mainly governed by the data. The proposed detector is analyzed for justifying the priors used, deriving the theoretical moments, and approximating the false alarm and detection probability densities by the shifted Gamma distributions. The developed detector exhibits improvement in detection performance over the energy detector (ED) and the generalized likelihood ratio test (GLRT).

Adaptive Detection of Gaussian Rank-One Signals Using Adaptively Whitened Data and Rao, Gradient and Durbin Tests

We address the problem of detecting a Gaussian rank-one signal using training samples to learn the covariance matrix of the noise present in the samples under test. Towards this end, we propose to use the latter after they have been whitened by the sample covariance matrix of the training samples. As an alternative to the generalized likelihood ratio test, we investigate three simpler alternatives, namely the Rao, gradient and Durbin tests. Closed-form expressions of the corresponding test statistics are derived and the detectors are shown to have a constant false alarm rate. Their performance is assessed via numerical simulations.

Maximum Likelihood Detection in Single-Input Double-Output Non-Gaussian Barrage-Jammed Systems

We derive the likelihood functions and the maximum likelihood (ML) detectors for four classes of single-input double-output (SIDO) communication systems, i.e., systems with one transmit and two receive antennas. For all classes, the received signals are contaminated by a Gaussian noise component and a non-Gaussian component induced by the Gaussian transmissions of a proactive continuous single-antenna jammer over an unknown complex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\times 1$</tex-math></inline-formula> Gaussian vector channel. The considered classes correspond to whether full channel distribution information (CDI), or partial CDI about the transmitter channel and the jammer channel is available at the receiver. Unlike their scalar counterparts, the vector channels considered herein interweave the components of the received signal, rendering the derivation of the likelihood function a daunting task for more than two receive antennas. Furthermore, the interweaving of the received signal components in the vector channel case prevents the optimal ML detector for unit-norm constellations from reducing to the corresponding Gaussian approximation-based detector. This is in sharp contrast with the scalar case, wherein the two detectors are equivalent for unit-norm constellations. Confirming our analytical findings, experimental results show that the difference between the two detectors can be significant, especially when the transmitter-receiver and jammer-receiver channels have substantial line-of-sight components. Although the computational cost of performing optimal ML detection in the presence of non-Gaussian jamming is higher in the case of two receive antennas, the performance advantage over the single antenna case justifies it.

Hunt for light primordial black hole dark matter with ultrahigh-frequency gravitational waves

Light primordial black holes may comprise a dominant fraction of the dark matter in our Universe. This paper critically assesses whether planned and future gravitational wave detectors in the ultra-high-frequency band could constrain the fraction of dark matter composed of sub-solar primordial black holes. Adopting the state-of-the-art description of primordial black hole merger rates, we compare various signals with currently operating and planned detectors. As already noted in the literature, our findings confirm that detecting individual primordial black hole mergers with currently existing and operating proposals remains difficult. Current proposals involving gravitational wave to electromagnetic wave conversion in a static magnetic field and microwave cavities feature a technology gap with respect to the loudest gravitational wave signals from primordial black holes of various orders of magnitude. However, we point out that one recent proposal involving resonant LC circuits represents the best option in terms of individual merger detection prospects in the range $(1\div 100) \, \text{MHz}$. In the same frequency range, we note that alternative setups involving resonant cavities, whose concept is currently under development, might represent a promising technology to detect individual merger events. We also show that a detection of the stochastic gravitational wave background produced by unresolved binaries is possible only if the theoretical sensitivity of the proposed Gaussian beam detector is achieved. Such a detector, whose feasibility is subject to various caveats, may be able to rule-out some scenarios for asteroidal mass primordial black hole dark matter. We conclude that pursuing dedicated studies and developments of gravitational wave detectors in the ultra-high-frequency band remains motivated and may lead to novel probes on the existence of light primordial black holes.

On the assumptions behind metacognitive measurements: Implications for theory and practice.

Theories of visual confidence have largely been grounded in the gaussian signal detection framework. This framework is so dominant that idiosyncratic consequences from this distributional assumption have remained unappreciated. This article reports systematic comparisons of the gaussian signal detection framework to its logistic counterpart in the measurement of metacognitive accuracy. Because of the difference in their distribution kurtosis, these frameworks are found to provide different perspectives regarding the efficiency of confidence rating relative to objective decision (the logistic model intrinsically gives greater meta-dʹ/dʹ ratio than the gaussian model). These frameworks can also provide opposing conclusions regarding the metacognitive inefficiency along the internal evidence continuum (whether meta-dʹ is larger or smaller for higher levels of confidence). Previous theories developed on these lines of analysis may need to be revisited as the gaussian and logistic metacognitive models received somewhat equivalent support in our quantitative model comparisons. Despite these discrepancies, however, we found that across-condition or across-participant comparisons of metacognitive measures are relatively robust against the distributional assumptions, which provides much assurance to conventional research practice. We hope this article promotes the awareness for the significance of hidden modeling assumptions, contributing to the cumulative development of the relevant field.

Accurate modeling and mitigation of overlapping signals and glitches in gravitational-wave data

The increasing sensitivity of gravitational-wave detectors has brought about an increase in the rate of astrophysical signal detections as well as the rate of ``glitches''; transient and non-Gaussian detector noise. Temporal overlap of signals and glitches in the detector presents a challenge for inference analyses that typically assume the presence of only Gaussian detector noise. In this study we perform an extensive exploration of the efficacy of a recently proposed method that models the glitch with sine-Gaussian wavelets while simultaneously modeling the signal with compact-binary waveform templates. We explore a wide range of glitch families and signal morphologies and demonstrate that the joint modeling of glitches and signals (with wavelets and templates respectively) can reliably separate the two. We find that the glitches that most affect parameter estimation are also the glitches that are well modeled by such wavelets due to their compact time-frequency signature. As a further test, we investigate the robustness of this analysis against waveform systematics like those arising from the exclusion of higher-order modes and spin-precession effects. Our analysis provides an estimate of the signal parameters; the glitch waveform to be subtracted from the data and an assessment of whether some detected excess power consists of a glitch, signal, or both. We analyze the low-significance triggers (191225_215715 and 200114_020818) and find that they are both consistent with glitches overlapping high-mass signals.

Investigation of the effects of non-Gaussian noise transients and their mitigation in parameterized gravitational-wave tests of general relativity

The detection of gravitational waves from compact binary coalescence by Advanced LIGO and Advanced Virgo provides an opportunity to study the strong-field, highly relativistic regime of gravity. Gravitational-wave tests of general relativity (GR) typically assume Gaussian and stationary detector noise and, thus, do not account for non-Gaussian, transient noise features (glitches). We present the results obtained by performing parametrized gravitational-wave tests on simulated signals from binary-black-hole coalescence overlapped with three classes of frequently occurring instrumental glitches with distinctly different morphologies. We then review and apply three glitch mitigation methods and evaluate their effects on reducing false deviations from GR. By considering nine cases of glitches overlapping with simulated signals, we show that the short-duration, broadband blip and tomte glitches under consideration introduce false violations of GR, and using an inpainting filter and glitch model subtraction can consistently eliminate such false violations without introducing additional effects.

Markerless Image Alignment Method for Pressure-Sensitive Paint Image.

We propose a markerless image alignment method for pressure-sensitive paint measurement data replacing the time-consuming conventional alignment method in which the black markers are placed on the model and are detected manually. In the proposed method, feature points are detected by a boundary detection method, in which the PSP boundary is detected using the Moore-Neighbor tracing algorithm. The performance of the proposed method is compared with the conventional method based on black markers, the difference of Gaussian (DoG) detector, and the Hessian corner detector. The results by the proposed method and the DoG detector are equivalent to each other. On the other hand, the performances of the image alignment using the black marker and the Hessian corner detector are slightly worse compared with the DoG and the proposed method. The computational cost of the proposed method is half of that of the DoG method. The proposed method is a promising for the image alignment in the PSP application in the viewpoint of the alignment precision and computational cost.

Polarimetric Target Detection in Compound Gaussian Sea Clutter With Inverse Gaussian Texture

This letter addresses the polarimetric target detection problem in compound Gaussian sea clutter. In view of the heavy-tailed characteristic of sea clutter, we model the sea clutter as compound Gaussian distribution with inverse Gaussian texture (IGCG). We propose three polarimetric compound Gaussian detectors based on the two-step Rao test, the Wald test, and the generalized likelihood ratio test (GLRT). Specifically, we assume that the polarimetric clutter covariance matrix (PCCM) and the inverse Gaussian textures are known in the first step, and the test statistics of the proposed polarimetric detectors are derived. In the second step, we use the training data to estimate PCCM and maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) to estimate the inverse Gaussian textures, and we obtain the fully adaptive detectors. Then, we give proof of the constant false alarm rate (CFAR) properties of the proposed detectors. We validate the performance of the proposed polarimetric detectors by conducting experiments based on simulated and real sea clutter data. Finally, the numerical results indicate that the proposed detectors exhibit better detection performance than their competitors and are robust when the mismatched signal occurs.

Persymmetric Range-Spread Targets Detection in Compound Gaussian Sea Clutter With Inverse Gaussian Texture

This letter addresses the persymmetric adaptive detection problem of range-spread targets in compound Gaussian sea clutter. Based on the generalized likelihood ratio test (GLRT), Rao test, and Wald test, three novel compound Gaussian detectors are developed. Specifically, the sea clutter is modeled as compound Gaussian with inverse Gaussian distribution, and the detectors are derived by the two-step maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posterior</i> (MAP) procedures. In the first step, we assume the clutter covariance matrix (CCM) and the inverse Gaussian texture are known and derive the proposed detectors’ test statistics. In the second step, we use the persymmetric property and MAP criterion to estimate the CCM and inverse Gaussian texture parameters. Then the proposed detectors are proved to be constant false alarm rate (CFAR) detectors with respect to the real CCM. The simulation experiments are conducted by comparing the proposed detectors with their counterparts on both synthetic data and real sea clutter data. The numerical results indicate that the novel detectors exhibit better detection performance than their competitors.

How will our knowledge of short gamma-ray bursts affect the distance measurement of binary neutron stars?

Gravitational waves from binary neutron stars associated with short gamma-ray bursts have drawn considerable attention due to their prospect in cosmology. For such events, the sky locations of sources can be pinpointed with techniques such as identifying the host galaxies. However, the cosmological applications of these events still suffer from the problem of degeneracy between luminosity distance and inclination angle. To address this issue, a technique was proposed in previous study, i.e., using the collimation property of short gamma-ray bursts. Based on the observations, we assume that the cosine of inclination follows a Gaussian distribution, which may act as a prior in the Bayes analysis to break the degeneracy. This paper investigates the effects of different Gaussian priors and detector configurations on distance measurement and cosmological research. We first derive a simplified Fisher information matrix for demonstration, and then conduct quantitative analyses via simulation. By varying the number of third-generation detectors and the scale of prior, we generate four catalogs of 1000 events. It is shown that, in the same detecting period, a network of detectors can recognize more and farther events than a single detector. Besides, adopting tighter prior and employing multiple detectors both decrease the error of luminosity distance. Also considered is the performance of a widely adopted formula in the error budget, which turns out to be a conservative choice in each case. As for cosmological applications, for the ΛCDM model, 500, 200, 600, and 300 events are required for the four configurations to achieve 1% H0 accuracy. With all 1000 events in each catalog, H0 and Ωm can be constrained to (0.66%, 0.37%, 0.76%, 0.49%), and (0.010, 0.006, 0.013, 0.010), respectively. The results of the Gaussian process also show that the gravitational wave standard siren can serve as a probe of cosmology at high redshifts.

Extraction of binary black hole gravitational wave signals from detector data using deep learning

Accurate extractions of the detected gravitational wave (GW) signal waveforms are essential to validate a detection and to probe the astrophysics behind the sources producing the GWs. This however could be difficult in realistic scenarios where the signals detected by existing GW detectors could be contaminated with non-stationary and non-Gaussian noise. While the performance of existing waveform extraction methods are optimal, they are not fast enough for online application, which is important for multi-messenger astronomy. In this paper, we demonstrate that a deep learning architecture consisting of Convolutional Neural Network and bidirectional Long Short-Term Memory components can be used to extract binary black hole (BBH) GW waveforms from realistic noise in a few milli-seconds. We have tested our network systematically on injected GW signals, with component masses uniformly distributed in the range of 10 to 80 solar masses, on Gaussian noise and LIGO detector noise. We find that our model can extract GW waveforms with overlaps of more than 0.95 with pure Numerical Relativity templates for signals with signal-to-noise ratio (SNR) greater than six, and is also robust against interfering glitches. We then apply our model to all ten detected BBH events from the first (O1) and second (O2) observation runs, obtaining greater than 0.97 overlaps for all ten extracted BBH waveforms with the corresponding pure templates. We discuss the implication of our result and its future applications to GW localization and mass estimation.

On Minimax Detection of Gaussian Stochastic Sequences and Gaussian Stationary Signals

We consider the detection problem for Gaussian stochastic sequences (signals) with unknown covariance matrices in white Gaussian noise. For a given false alarm probability (1st-kind error probability), the quality of minimax detection is given by the best miss probability (2nd-kind error probability) exponent over a growing observation interval. The goal is finding the largest set of covariance matrices (composite hypothesis) such that its minimax testing can be replaced with testing a single particular covariance matrix (simple hypothesis) with no degradation of the detection exponent. We completely describe this maximal set of covariance matrices. We also consider some consequences concerning minimax detection of Gaussian stochastic signals against Gaussian white noise and detection of Gaussian stationary signals.

Secure data transmission in IoTs based on CLoG edge detection

Cyber–physical Systems (CPS) have revolutionized the industry by utilizing the Internet of Things (IoT) for interconnecting various system components. IoT plays a significant role in the development of the smart system paradigm by building a link between physical components with the virtual world for improving smart services and quality of life. It significantly improves people’s activities, be it their personalized health care, living, or the way they monitor control, and organize the businesses. However, data streaming/communication over an open IoT environment creates several security issues that need to be taken care of, for transferring data securely. This paper presents an efficient information embedding solution for ensuring data security in a cyber–physicalnetwork. In this work, a new efficient edge detector called CLoG, (based on Canny and Laplacian of Gaussian detectors) has been developed and is used for the detection of edge areas in digital images. The secret information has been embedded in detected edges. The proposed detector finds finer edge details compared to state-of-art, making it possible to hide more information in a cover image. This, in turn, reduces the number of cover images required to transmit secret data and as such fulfills the requirements of resource-constrained platforms like IoT. Experimental results show that the proposed scheme is capable of providing high-quality stego-images with an average peak signal-to-noise ratio (PSNR) of 48.12 dB for a payload of 2 bits per pixel (bpp) payload. Further, the scheme has been analyzed for its efficacy in terms of histogram analysis, normalized cross-correlation (NCC), and other objective parameters. Besides, we show that the proposed scheme supports blind extraction, has less computational complexity, and is suitable for IoT based systems.

Inference of protoneutron star properties from gravitational-wave data in core-collapse supernovae

The eventual detection of gravitational waves from core-collapse supernovae (CCSN) will help improve our current understanding of the explosion mechanism of massive stars. The stochastic nature of the late post-bounce gravitational wave signal due to the non-linear dynamics of the matter involved and the large number of degrees of freedom of the phenomenon make the source parameter inference problem very challenging. In this paper we take a step towards that goal and present a parameter estimation approach which is based on the gravitational waves associated with oscillations of proto-neutron stars (PNS). Numerical simulations of CCSN have shown that buoyancy-driven g-modes are responsible for a significant fraction of the gravitational wave signal and their time-frequency evolution is linked to the physical properties of the compact remnant through universal relations, as demonstrated in [1]. We use a set of 1D CCSN simulations to build a model that relates the evolution of the PNS properties with the frequency of the dominant g-mode, which is extracted from the gravitational-wave data using a new algorithm we have developed for our study. The model is used to infer the time evolution of a combination of the mass and the radius of the PNS. The performance of the method is estimated employing simulations of 2D CCSN waveforms covering a progenitor mass range between 11 and 40 solar masses and different equations of state. Considering signals embedded in Gaussian gravitational wave detector noise, we show that it is possible to infer PNS properties for a galactic source using Advanced LIGO and Advanced Virgo data at design sensitivities. Third generation detectors such as Einstein Telescope and Cosmic Explorer will allow to test distances of ${\cal O}(100\, {\rm kpc})$.

Adaptive CFAR Detectors for Mismatched Signal in Compound Gaussian Sea Clutter With Inverse Gaussian Texture

This letter deals with the adaptive detection problem in compound Gaussian sea clutter with inverse Gaussian texture when the mismatched signal occurs. In order to reject the mismatched signal, we introduce a fictitious signal to the null hypothesis based on the adaptive beamformer orthogonal rejection test (ABORT). We adopt the two-step generalized likelihood ratio test (GLRT) criterion and develop two selective detectors, i.e., the ABORT-like compound Gaussian with inverse Gaussian (A-IGCG) detector and ABORT-like maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) compound Gaussian with inverse Gaussian (AM-IGCG) detector. Both the proposed detectors are proved to be constant false alarm rate (CFAR) detectors. The several experiments that compare the proposed detectors with other selective detectors and compound Gaussian detectors are conducted by using two types of real sea data, i.e., IPIX 1998 and 2019 real sea data. The numerical results indicate that the novel detectors exhibit significant tradeoffs between performances of detection and selectivity property.