3,111 research outputs found
A bayesian approach to adaptive detection in nonhomogeneous environments
We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter
A Bayesian approach to filter design: detection of compact sources
We consider filters for the detection and extraction of compact sources on a
background. We make a one-dimensional treatment (though a generalization to two
or more dimensions is possible) assuming that the sources have a Gaussian
profile whereas the background is modeled by an homogeneous and isotropic
Gaussian random field, characterized by a scale-free power spectrum. Local peak
detection is used after filtering. Then, a Bayesian Generalized Neyman-Pearson
test is used to define the region of acceptance that includes not only the
amplification but also the curvature of the sources and the a priori
probability distribution function of the sources. We search for an optimal
filter between a family of Matched-type filters (MTF) modifying the filtering
scale such that it gives the maximum number of real detections once fixed the
number density of spurious sources. We have performed numerical simulations to
test theoretical ideas.Comment: 10 pages, 2 figures. SPIE Proceedings "Electronic Imaging II", San
Jose, CA. January 200
Knowledge-aided covariance matrix estimation and adaptive detection in compound-Gaussian noise
We address the problem of adaptive detection of a signal of interest embedded in colored noise modeled in terms of a compound-Gaussian process. The covariance matrices of the primary and the secondary data share a common structure while having different power levels. A Bayesian approach is proposed here, where both the power levels and the structure are assumed to be random, with some appropriate distributions. Within this framework we propose MMSE and MAP estimators of the covariance structure and their application to adaptive detection using the NMF test statistic and an optimized GLRT herein derived. Some results, also conducted in comparison with existing algorithms, are presented to illustrate the performances of the proposed algorithms. The relevant result is that the solutions presented herein allows to improve the performance over conventional ones, especially in presence of a small number of training data
Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism
Testing for the significance of a subset of regression coefficients in a
linear model, a staple of statistical analysis, goes back at least to the work
of Fisher who introduced the analysis of variance (ANOVA). We study this
problem under the assumption that the coefficient vector is sparse, a common
situation in modern high-dimensional settings. Suppose we have covariates
and that under the alternative, the response only depends upon the order of
of those, . Under moderate sparsity levels, that
is, , we show that ANOVA is essentially optimal under some
conditions on the design. This is no longer the case under strong sparsity
constraints, that is, . In such settings, a multiple comparison
procedure is often preferred and we establish its optimality when
. However, these two very popular methods are suboptimal, and
sometimes powerless, under moderately strong sparsity where .
We suggest a method based on the higher criticism that is powerful in the whole
range . This optimality property is true for a variety of designs,
including the classical (balanced) multi-way designs and more modern ""
designs arising in genetics and signal processing. In addition to the standard
fixed effects model, we establish similar results for a random effects model
where the nonzero coefficients of the regression vector are normally
distributed.Comment: Published in at http://dx.doi.org/10.1214/11-AOS910 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Seizure-onset mapping based on time-variant multivariate functional connectivity analysis of high-dimensional intracranial EEG : a Kalman filter approach
The visual interpretation of intracranial EEG (iEEG) is the standard method used in complex epilepsy surgery cases to map the regions of seizure onset targeted for resection. Still, visual iEEG analysis is labor-intensive and biased due to interpreter dependency. Multivariate parametric functional connectivity measures using adaptive autoregressive (AR) modeling of the iEEG signals based on the Kalman filter algorithm have been used successfully to localize the electrographic seizure onsets. Due to their high computational cost, these methods have been applied to a limited number of iEEG time-series (< 60). The aim of this study was to test two Kalman filter implementations, a well-known multivariate adaptive AR model (Arnold et al. 1998) and a simplified, computationally efficient derivation of it, for their potential application to connectivity analysis of high-dimensional (up to 192 channels) iEEG data. When used on simulated seizures together with a multivariate connectivity estimator, the partial directed coherence, the two AR models were compared for their ability to reconstitute the designed seizure signal connections from noisy data. Next, focal seizures from iEEG recordings (73-113 channels) in three patients rendered seizure-free after surgery were mapped with the outdegree, a graph-theory index of outward directed connectivity. Simulation results indicated high levels of mapping accuracy for the two models in the presence of low-to-moderate noise cross-correlation. Accordingly, both AR models correctly mapped the real seizure onset to the resection volume. This study supports the possibility of conducting fully data-driven multivariate connectivity estimations on high-dimensional iEEG datasets using the Kalman filter approach
An ABORT-like detector with improved mismatched signals rejection capabilities
In this paper, we present a GLRT-based adaptive detection algorithm for extended targets with improved rejection capabilities of mismatched signals. We assume that a set of secondary data is available and that noise returns in primary and secondary data share the same statistical characterization. To increase the selectivity of the detector, similarly to the ABORT formulation, we modify the hypothesis testing problem at hand introducing fictitious signals under the null hypothesis. Such unwanted signals are supposed to be orthogonal to the nominal steering vector in the whitened observation space. The performance assessment, carried out by Monte Carlo simulation, shows that the proposed dectector ensures better rejection capabilities of mismatched signals than existing ones, at the price of a certain loss in terms of detection of matched signals
Spectral Detection of Human Skin in VIS-SWIR Hyperspectral Imagery without Radiometric Calibration
Many spectral detection algorithms require precise ground truth measurements that are hand-selected in the image to apply radiometric calibration, converting image pixels into estimated reflectance vectors. That process is impractical for mobile, real-time hyperspectral target detection systems, which cannot empirically derive a pixel-to-reflectance relationship from objects in the image. Implementing automatic target recognition on high-speed snapshot hyperspectral cameras requires the ability to spectrally detect targets without performing radiometric calibration. This thesis demonstrates human skin detection on hyperspectral data collected at a high frame rate without using calibration panels, even as the illumination in the scene changes. Compared to an established skin detection method that requires calibration panels, the illumination-invariant methods in this thesis achieve nearly as good detection performance in sunny scenes and superior detection performance in cloudy scenes
Improving Hyperspectral Subpixel Target Detection Using Hybrid Detection Space
A Hyper-Spectral Image (HSI) has high spectral and low spatial resolution. As a result, most targets exist as subpixels, which pose challenges in target detection. Moreover, limitation of target and background samples always hinders the target detection performance. In this thesis, a hybrid method for subpixel target detection of an HSI using minimal prior knowledge is developed. The Matched Filter (MF) and Adaptive Cosine Estimator (ACE) are two popular algorithms in HSI target detection. They have different advantages in differentiating target from background. In the proposed method, the scores of MF and ACE algorithms are used to construct a hybrid detection space. First, some high abundance target spectra are randomly picked from the scene to perform initial detection to determine the target and background subsets. Then, the reference target spectrum and background covariance matrix are improved iteratively, using the hybrid detection space. As the iterations continue, the reference target spectrum gets closer and closer to the central line that connects the centers of target and background and resulting in noticeable improvement in target detection. Two synthetic datasets and two real datasets are used in the experiments. The results are evaluated based on the mean detection rate, Receiver Operating Characteristic (ROC) curve and observation of the detection results. Compared to traditional MF and ACE algorithms with Reed-Xiaoli Detector (RXD) background covariance matrix estimation, the new method shows much better performance on all four datasets. This method can be applied in environmental monitoring, mineral detection, as well as oceanography and forestry reconnaissance to search for extremely small target distribution in a large scene
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