Subspace Detector Research Articles

A weighted detector for mismatched subspace signals

This paper investigates the problem of detecting a multichannel signal when subspace signal mismatch occurs. A new detector is proposed, which is obtained by weighting two existing detectors, namely, the subspace-based adaptive matched filter and adaptive subspace detector. The proposed weighted detector has flexibility in controlling its capability of rejection mismatched subspace signals. Specifically, its robustness (or selectivity) for mismatched subspace signals improves as the weight value increases (or decreases). Closed-form expressions for the probabilities of detection and false alarm are derived. The theoretical results are confirmed by Monte Carlo simulations.

Tensor Matched Subspace Detector for Hyperspectral Target Detection

In this paper, a new framework for tensor hyperspectral target detection is proposed. In this new framework, tensor is well integrated into the conventional target detection algorithm. As a result, a tensor matched subspace detector (MSD) for hyperspectral target detection is proposed. The proposed method is mainly applied to detect multipixel targets rather than subpixel targets. In this new method, the hyperspectral data are considered as a form of third-order tensor in order to jointly utilize the information of multidimensional data. In conventional detection methods, the spatial–spectral information has not been taken into account, even some algorithms have been presented for improving the utilization efficiency of the spatial–spectral structural feature, but the overall structural characteristic of the extracted feature is still ignored. In our algorithm, the tensor subspace projection is defined for the first time, which is easily calculated by three predetermined orthogonal direction mapping matrices without any iteration. Then, the test tensor blocks are projected into the tensor subspace and finally measured by the ratio of residual energy, just like the general likelihood ratio test. The proposed method can be regarded as an extension of conventional MSD. The reliability and superiority are demonstrated by the experiments on real hyperspectral imaging data sets. The experimental results indicate that our approach compares favorably to some classical and novel methods by jointly processing multidimensional data with tensorial form.

Hyperspectral data acquisition and analysis in imaging and real-time active MIR backscattering spectroscopy

Abstract In this work we present data analysis algorithms for detection of hazardous substances in hyperspectral observations acquired using active mid-infrared (MIR) backscattering spectroscopy. We present a novel background extraction algorithm based on the adaptive target generation process proposed by Ren and Chang called the adaptive background generation process (ABGP) that generates a robust and physically meaningful set of background spectra for operation of the well-known adaptive matched subspace detection (AMSD) algorithm. It is shown that the resulting AMSD-ABGP detection algorithm competes well with other widely used detection algorithms. The method is demonstrated in measurement data obtained by two fundamentally different active MIR hyperspectral data acquisition devices. A hyperspectral image sensor applicable in static scenes takes a wavelength sequential approach to hyperspectral data acquisition, whereas a rapid wavelength-scanning single-element detector variant of the same principle uses spatial scanning to generate the hyperspectral observation. It is shown that the measurement timescale of the latter is sufficient for the application of the data analysis algorithms even in dynamic scenarios.

High Order Multi-User MIMO Subspace Detection

An efficient high order multi-user multiple-input multiple-output (MU-MIMO) subspace detector is proposed. The detector employs joint modulation classification (MC) and subspace detection (SD), by ...

The matched subspace detector with interaction effects

This paper aims to propose a new hyperspectral target-detection method termed the matched subspace detector with interaction effects (MSDinter). The MSDinter introduces “interaction effects” terms into the popular matched subspace detector (MSD), from regression analysis in multivariate statistics and the bilinear mixing model in hyperspectral unmixing. In this way, the interaction between the target and the surrounding background, which should have but not yet been considered by the MSD, is modelled and estimated, such that superior performance of target detection can be achieved. Besides deriving the MSDinter methodologically, we also demonstrate its superiority empirically using two hyperspectral imaging datasets.

Analyses of the performance of adaptive subspace detector on fluctuating target detection in system‐dependent clutter background

The adaptive subspace detector in system-dependent clutter background (SDC-ASD) is proved to be able to improve the detection performance for deterministic target detection in the authors' previous study. However, the exact performance of the SDC-ASD for fluctuating target detection is still unknown. In this study, with the aid of matrix decomposition theory, the analytical performance of the SDC-ASD for detecting fluctuating target is considered and assessed. At the design stage, the rigorous mathematical derivation processes for the exact theoretical detection performance of the SDC-ASD for fluctuating target detection is derived. The theoretical results, which have explicitly expressions for both the false alarm probability and the detection probability, not only provide an effective mathematical method to analyse the fluctuating target detection performance, but also can further simplify the deterministic target detection assessments. At the analysis stage, Monte Carlo simulations are resorted to validate the analytical results. Numerical experiments are conducted to assess the effectiveness of the SDC-ASD for fluctuating target detection. Results show that the SDC-ASD, by dealing separately with the clutter and the noise, performs the best in comparison with its published counterparts, i.e. the generalised likelihood ratio detectors, the adaptive matched filters, the adaptive subspace detectors and the low-rank detectors based on sample covariance matrix. (Less)

Multiframe GLRT-Based Adaptive Detection of Multipixel Targets on a Sea Surface

Ship-based automatic video/infrared detection of small floating objects on a sea surface remains a challenge. We developed the GLRT-based adaptive multiframe detector for multipixel targets embedded in the channel Gaussian noise plus the background Gaussian clutter with unknown covariance matrix using a sequence of images as input data. We used video spatial-temporal patches called bricks to characterize both the target appearance and parameters estimates of the background clutter. The proposed detector is based on the return model from a sea surface in the presence of a floating object. The proposed algorithm combines the multipixel adaptive subspace detector (ASD) and adaptive multipixel background-plus-noise power change detector in a unique scheme. Experiments on simulated data and real video demonstrate the ability of the proposed detector and show that this detector considerably outperforms the known ASD, especially in a real-life situation, when the size, shape, and position of the object are unknown. We used four different types of real targets in the experiment, and the proposed detector shows better performance than the ASD, the modified mean subtraction filter and focused correlation detector. We evaluated the performance degradation in the presence of the mismatches between the actual and designed one-lag correlation coefficient of background.

Design and performance analysis of adaptive subspace detectors in orthogonal interference and gaussian noise

In this paper, we consider the problem of detecting a multichannel signal in the presence of interference. The signal lies in a known subspace but with unknown coordinate. The interference is assumed to be orthogonal to the signal in the whitened space. We propose an effective detector, according to the criterion of the generalized likelihood ratio test (GLRT). The proposed GLRT has better detection performance than the corresponding Rao andWald tests. Remarkably, it is found that the GLRT in the presence of orthogonal interference has the same form as that in the absence of interference. However, the orthogonal interference does affect the detection performance of the detector. We derive closed-form expressions of the probabilities of detection and false alarm for the proposed detector, which are verified by Monte Carlo simulations.

Acoustic mode travel time variability in the Philippine Sea

During the 2009 NPAL (North Pacific Acoustic Laboratory) PhilSea deep water acoustic propagation experiment, a low frequency source transmitted broadband chirps to a mid-water spanning hydrophone array at a distance of 185 km every three hours for approximately one month. In addition, transmissions took place every five minutes during some time periods. The source and the receiver array contained conductivity and temperature sensors. The motions of the source and receiver moorings were measured using long-baseline acoustic navigation systems. The experiment site was oceanographically dynamic and contained significant internal tide activity. This work builds a model to compare the acoustic and oceanographic variabilities. The acoustic observations are used to estimate the mode travel times, and then related to the internal tide displacements at the source and the receiver arrays. This paper presents the work in three parts. The first part uses matched subspace detectors to estimate the mode travel times. The second uses the environmental observations to build an internal tide model. The third constructs a linear perturbation model to relate the internal tides to the adiabatic mode travel times. The discrepancies between the model and the observations are attributed to factors such as limitations of the perturbation model for the travel times, range variability not accounted for in the adiabatic mode propagation, and signal processing issues.

A Target Detection Method Based on Low-Rank Regularized Least Squares Model for Hyperspectral Images

Target detection plays an important role in the field of hyperspectral image (HSI) remote sensing. In this letter, a novel matched subspace detector based on low-rank regularized least squares (LRLS-MSD) is proposed for hyperspectral target detection. As pixels in an HSI have global correlation and can be represented in subspace, the low-rank regularization is introduced in the least squares model. An effective algorithm is presented to solve the problem. Then, the detection results are generated according to the generalized likelihood ratio test with statistical hypotheses. The experimental results suggest an advantage of the low-rank regularization over other classical target detection methods.

Iterative Strategies for Aftershock Classification in Automatic Seismic Processing Pipelines

Aftershock sequences following very large earthquakes present enormous challenges to near‐real‐time generation of seismic bulletins. The increase in analyst resources needed to relocate an inflated number of events is compounded by failures of phase‐association algorithms and a significant deterioration in the quality of underlying, fully automatic event bulletins. Current processing pipelines were designed a generation ago, and, due to computational limitations of the time, are usually limited to single passes over the raw data. With current processing capability, multiple passes over the data are feasible. Processing the raw data at each station currently generates parametric data streams that are then scanned by a phase‐association algorithm to form event hypotheses. We consider the scenario in which a large earthquake has occurred and propose to define a region of likely aftershock activity in which events are detected and accurately located, using a separate specially targeted semiautomatic process. This effort may focus on so‐called pattern detectors, but here we demonstrate a more general grid‐search algorithm that may cover wider source regions without requiring waveform similarity. Given many well‐located aftershocks within our source region, we may remove all associated phases from the original detection lists prior to a new iteration of the phase‐association algorithm. We provide a proof‐of‐concept example for the 2015 Gorkha sequence, Nepal, recorded on seismic arrays of the International Monitoring System. Even with very conservative conditions for defining event hypotheses within the aftershock source region, we can automatically remove about half of the original detections that could have been generated by Nepal earthquakes and reduce the likelihood of false associations and spurious event hypotheses. Further reductions in the number of detections in the parametric data streams are likely, using correlation and subspace detectors and/or empirical matched field processing.

GLRT subspace detection of multi-pixel targets with known and unknown spatial parameters in presence of signal-dependent background power

The video/infrared images captured at long range usually have low brightness and low contrast objects of interest with respect to surrounding background clutter. In this work, we design and analyze two detectors relying on the general likelihood ratio test (GLRT) to detect weak barely discernible multi-pixel objects with known (the first detector) and unknown shape, size and position (the second detector). The derived algorithms combine the multi-pixel matched subspace detector and multi-pixel background-plus-noise power change detector in a unique scheme. The numerical simulations and real experiments show that the first detector considerably outperforms the second one, especially in real-word situation, when the size, shape and position of the object are unknown. Finally, we compare the performances of the proposed detectors to the performances of the recently proposed modified mean subtraction filter and focused correlation (FC) detector.

A Framework of Target Detection in Hyperspectral Imagery Based on Blind Source Extraction

A framework based on the blind source extraction (BSE) algorithm is proposed to detect targets in remotely sensed hyperspectral images. The mean square cross prediction error (MSCPE)-based BSE method is used as the kernel algorithm where the autoregressive (AR) parameters of the targets' spectra are utilized as priors. Numerical simulations show that the proposed framework highlights the desired signal, suppresses the backgrounds, and is able to detect the distribution of the target. In the experiments, the data from the Rochester Institute of Technology (RIT) were used to evaluate the framework. The proposed method achieved a better performance in the tradeoff between the PD and the PFA with subpixel target detection compared with the constrained energy minimization (CEM), the adaptive cosine estimator (ACE), the matched filter (MF), the generalized likelihood ratio test (GLRT), the adaptive matched subspace detector (AMSD), and the orthogonal subspace projection (OSP).

Robust multipixel matched subspace detection with signal-dependent background power

A modified matched subspace detector (MSD) has been recently proposed for detecting a barely discernible object in an additive Gaussian background clutter using a single pixel in a sequence of digital images. In contrast to this detector designed for the subpixel object, we developed a generalized likelihood ratio approach to the detection of a multipixel object of unknown shape, size, and position in an additive signal-dependent Gaussian background and noise. The proposed detector modifies the MSD by adding the additional term proportional to the square of the difference between the background variances under two statistical hypotheses. The performances of these detectors are evaluated for the example scenario of two multipixel floating objects on the agitated sea surface. The crucial characteristic of the proposed detector is that prior knowledge of the target size, shape, and position is not required. Computer simulation and experimental results have shown that the proposed detector outperforms the MSD, especially in the case of weak and poorly contrasted objects of unknown shape, size, and position.

Performance prediction of subspace-based adaptive detectors with signal mismatch

For the problem of subspace signal detection, three adaptive detectors have been proposed in the past, namely, the subspace-based generalized likelihood ratio test, subspace-based adaptive matched filter, and adaptive subspace detector. In this paper we analyze their performance in the mismatch case, where the actual signal does not exactly lie in the nominal signal subspace. We derive their statistical distributions, and then obtain analytical expressions for the probabilities of detection and false alarm. It is shown that the signal mismatch has a significant effect on their detection performance through a quantity, which can be taken as a measure of the “distance” between the actual signal and the nominal signal subspace. These results extend the existing theory for rank-one signal detection in the mismatch case.

Automated detection of Antarctic blue whale calls.

This paper addresses the problem of automated detection of Z-calls emitted by Antarctic blue whales (B. m. intermedia). The proposed solution is based on a subspace detector of sigmoidal-frequency signals with unknown time-varying amplitude. This detection strategy takes into account frequency variations of blue whale calls as well as the presence of other transient sounds that can interfere with Z-calls (such as airguns or other whale calls). The proposed method has been tested on more than 105 h of acoustic data containing about 2200 Z-calls (as found by an experienced human operator). This method is shown to have a correct-detection rate of up to more than 15% better than the extensible bioacoustic tool package, a spectrogram-based correlation detector commonly used to study blue whales. Because the proposed method relies on subspace detection, it does not suffer from some drawbacks of correlation-based detectors. In particular, it does not require the choice of an a priori fixed and subjective template. The analytic expression of the detection performance is also derived, which provides crucial information for higher level analyses such as animal density estimation from acoustic data. Finally, the detection threshold automatically adapts to the soundscape in order not to violate a user-specified false alarm rate.

Matched signal detection on graphs: Theory and application to brain imaging data classification

Motivated by recent progress in signal processing on graphs, we have developed a matched signal detection (MSD) theory for signals with intrinsic structures described by weighted graphs. First, we regard graph Laplacian eigenvalues as frequencies of graph-signals and assume that the signal is in a subspace spanned by the first few graph Laplacian eigenvectors associated with lower eigenvalues. The conventional matched subspace detector can be applied to this case. Furthermore, we study signals that may not merely live in a subspace. Concretely, we consider signals with bounded variation on graphs and more general signals that are randomly drawn from a prior distribution. For bounded variation signals, the test is a weighted energy detector. For the random signals, the test statistic is the difference of signal variations on associated graphs, if a degenerate Gaussian distribution specified by the graph Laplacian is adopted. We evaluate the effectiveness of the MSD on graphs both with simulated and real data sets. Specifically, we apply MSD to the brain imaging data classification problem of Alzheimer's disease (AD) based on two independent data sets: 1) positron emission tomography data with Pittsburgh compound-B tracer of 30 AD and 40 normal control (NC) subjects, and 2) resting-state functional magnetic resonance imaging (R-fMRI) data of 30 early mild cognitive impairment and 20 NC subjects. Our results demonstrate that the MSD approach is able to outperform the traditional methods and help detect AD at an early stage, probably due to the success of exploiting the manifold structure of the data.

Maximum margin metric learning based target detection for hyperspectral images

Target detection is one of the most important problems in hyperspectral image (HSI) processing. However, the classical algorithms depend on the specific statistical hypothesis test, and the algorithms may only perform well under certain conditions, e.g., the adaptive matched subspace detector algorithm assumes that the background covariance matrices do not include the target signatures, which seldom happens in the real world. How to develop a proper metric for measuring the separability between targets and backgrounds becomes the key in target detection. This paper proposes an efficient maximum margin metric learning (MMML) based target detection algorithm, which aims at exploring the limited samples in metric learning and transfers the metric learning problem for hyperspectral target detection into a maximum margin problem which can be optimized via a cutting plane method, and maximally separates the target samples from the background ones. The extensive experimental results with different HSIs demonstrate that the proposed method outperforms both the state-of-the-art target detection algorithms and the other classical metric learning methods.

Hundreds of Earthquakes per Day: The 2014 Guthrie, Oklahoma, Earthquake Sequence

Online Material: Gutenberg–Richter plot, b ‐values and associated p ‐values, magnitudes and number of detections per day, and earthquake catalog. A remarkable increase in seismic activity in Oklahoma since 2009 has been shown to correlate closely with enhanced hydrocarbon extraction and associated wastewater disposal; 99% of this recent Oklahoma earthquake activity has occurred within 15 km of a class II injection well (Ellsworth, 2013). In response to this increase in seismic activity, the U.S. Geological Survey (USGS) partnered with the Oklahoma Geological Survey (OGS) to exchange waveform data from permanent and temporary seismic stations to improve the cataloging of earthquake source parameters for a broad region of north–central Oklahoma. For a particularly persistent earthquake sequence near Guthrie, Oklahoma, a subspace detection method is applied to data from nearby seismic stations. This approach documents the occurrence of hundreds of readily detectable, highly similar, earthquakes per day, with rates occasionally exceeding 1000 earthquakes per day. Time‐varying changes in b ‐value appear episodic, suggesting a correlation with periods of reversible fault weakening and associated failure. Real‐time seismic monitoring typically uses automated transient detection‐based pickers to detect earthquakes and to define onset times of seismic phases. Such methods cannot reliably detect earthquake signals or time phases with low signal‐to‐noise, resulting in less complete earthquake catalogs than may be recovered by other means. Recognizing this limitation, recent studies of a suspected induced‐seismicity sequence near Youngstown, Ohio, used waveform template matching (Kim, 2013; Skoumal et al. , 2014) to significantly lower the detection threshold and to better characterize the spatiotemporal variability of seismicity. In this article, we build on these efforts using subspace detectors to objectively minimize the number of waveform templates required to fully characterize an earthquake sequence while increasing computational efficiency. Results demonstrate a new and scalable real‐time procedure to better detect and characterize the …

A novel framework for feature extraction in multi-sensor action potential sorting

BackgroundExtracellular recordings of multi-unit neural activity have become indispensable in neuroscience research. The analysis of the recordings begins with the detection of the action potentials (APs), followed by a classification step where each AP is associated with a given neural source. A feature extraction step is required prior to classification in order to reduce the dimensionality of the data and the impact of noise, allowing source clustering algorithms to work more efficiently. New methodIn this paper, we propose a novel framework for multi-sensor AP feature extraction based on the so-called Matched Subspace Detector (MSD), which is shown to be a natural generalization of standard single-sensor algorithms. ResultsClustering using both simulated data and real AP recordings taken in the locust antennal lobe demonstrates that the proposed approach yields features that are discriminatory and lead to promising results. Comparison with existing method(s)Unlike existing methods, the proposed algorithm finds joint spatio-temporal feature vectors that match the dominant subspace observed in the two-dimensional data without needs for a forward propagation model and AP templates. ConclusionsThe proposed MSD approach provides more discriminatory features for unsupervised AP sorting applications.