Nick Klausner

Detection of Spatially Correlated Time Series From a Network of Sensor Arrays

This paper addresses the problem of testing for the independence among multiple ( ≥ 2) random vectors. The generalized likelihood ratio test tests the null hypothesis that the composite covariance matrix of the channels is block-diagonal, using a generalized Hadamard ratio. Using the theory of Gram determinants, we show that this Hadamard ratio is stochastically equivalent to a product of scalars, which are independently drawn from a beta distribution under the null hypothesis. This result is then used to derive an asymptotic null distribution, which can be used to identify an appropriate threshold when the sample support is large. These results are then extended to the problem of detecting the presence of spatially correlated time series when each observer employs an array of sensors. Assuming wide-sense stationary processes in both time and space, the likelihood ratio is shown to involve a Hadamard ratio of an estimated cross-spectral matrix at every frequency/wavenumber pair. The proposed detector is compared to several alternative detectors, using simulated space-time fields.

Target detection in M-disparate sonar platforms using multichannel hypothesis testing

The use of multiple disparate sonars allows one to exploit a high resolution sonar with good target definition while taking advantage of the clutter suppressing abilities of a low resolution broadband sonar co-registered over the same region to provide potentially much better detection and classification performance comparing to those of the single sonar cases. In this paper the standard Neyman-Pearson detector is extended to the dual disparate sonar case allowing target detection across two sensory platforms simultaneously. For three disparate sonar platforms, two detectors are implemented with the final decisions being fused. Test results of the proposed methods on a data set of underwater side-scan sonar imagery are presented. This database contains data from 3 different side-scan sonars, namely one high frequency sonar and two broadband sonars, operating at three different frequencies and bandwidths. The data was collected in different bottom conditions and contains various mine-like and non-mine-like objects with varying degree of difficultly and bottom clutter. Test results illustrate the effectiveness of the proposed detection system in terms of probability of detection, false alarm rate, and the receiver operating characteristic (ROC) curve.

Underwater target detection from multi-platform sonar imagery using multi-channel coherence analysis

This paper introduces a new target detection method for multiple disparate sonar platforms. The detection method is based upon multi-channel coherence analysis (MCA) framework which allows one to optimally decompose the multichannel data to analyze their linear dependence or coherence. This decomposition then allows one to extract MCA features which can be used to discriminate between two hypotheses, one corresponding to the presence of a target and one without, through the use of the log-likelihood ratio. Test results of the proposed detection system were applied to a data set of underwater side-scan sonar imagery provided by the Naval Surface Warfare Center (NSWC), Panama City. This database contains data from 4 disparate sonar systems, namely one high frequency (HF) sonar and three broadband (BB) sonars coregistered over the same area on the sea floor. Test results illustrate the effectiveness of the proposed multi-platform detection system in terms of probability of detection, false alarm rate, and receiver operating characteristic (ROC) curves.

K-SVD dictionary learning using a fast OMP with applications

K-SVD method has recently been introduced to learn a specific dictionary matrix that best fits a set of training data vectors. K-SVD is flexible in that any preferred pursuit method of sparse coding can be used to represent the data. In this paper, we show how K-SVD method can be used in conjunction with a fast orthogonal matching pursuit implemented using orthogonal projection updating. Geometric interpretation of this learning is also presented. The method was then applied to underwater target detection problem using a dual-channel sonar imagery data.

Space-time coherence and its exact null distribution

This paper considers the problem of testing for the independence among multiple (≥ 2) random vectors with each random vector representing a time series captured at one sensor. Implementing the Generalized Likelihood Ratio Test involves testing the null hypothesis that the composite covariance matrix of the channels is block-diagonal through the use of a generalized Hadamard ratio. Using the theory of linear prediction and its connection with Gram determinants, it is shown that this generalized Hadamard ratio can be written as a product of scalars which are independently drawn from a beta distribution under the null hypothesis. This result is useful from a Monte Carlo analysis standpoint in that it is much more computationally efficient to form a product of scalar beta random variables than it is to compute the determinant of complex Wishart matrices.

Multi-sonar target detection using multi-channel coherence analysis

The use of multiple disparate platforms in many remote sensing and surveillance applications allows one to exploit the coherent information shared among all sensory systems thereby potentially reducing the risk of making single-sensory biased detection and classification decisions. This paper introduces a target detection method based upon multi-channel coherence analysis (MCA) framework which optimally decomposes the multi-channel data to analyze their linear dependence or coherence. This decomposition then allows one to extract MCA features that can be used to implement a coherence-based detector. This detector is applied to a data set of underwater side-scan sonar imagery provided by the Naval Surface Warfare Center Panama City Division. This database contains data from 2 disparate sonar systems, namely one high frequency (HF) sonar and one broadband (BB) sonar coregistered over the same region on the sea floor. Test results illustrate the effectiveness of the proposed multi-platform detection system in terms of probability of detection, false alarm rate, and receiver operating characteristic (ROC) curves.

Detection of Underwater Targets Using a Subspace-Based Method With Learning

This paper introduces a new subspace-based detection method for multichannel (high frequency and broadband) synthetic aperture sonar (SAS) imagery. An image-dependent dictionary learning method is applied to form the appropriate dictionary matrices for representing target and nontarget image snippets. The hypothesis testing is done by forming a test statistic that relies on the residual error power ratio in representing an unknown image snippet using the target and nontarget dictionary matrices. To avoid the computational bottleneck in most dictionary learning methods, a new recursive method is introduced which does not require any matrix inversion or singular value decomposition (SVD). The proposed detection method was then implemented and benchmarked against a matched subspace detection method for detecting mine-like objects. Results are then presented on two sonar imagery data sets collected in two geographically disparate locations.

Saddlepoint Approximations for Correlation Testing Among Multiple Gaussian Random Vectors

This letter considers the problem of threshold selection for a correlation test among multiple (≥2) random vectors. The generalized likelihood ratio test (GLRT) for this problem uses a generalized Hadamard ratio to test for block diagonality in a composite covariance matrix. As the number of realizations used to estimate the composite covariance matrix grows large, the null distribution of the likelihood ratio statistic converges to a chi-squared distribution which can be used to prescribe thresholds needed to achieve a desired false alarm rate in high sample support situations. However, this asymptotic distribution can be slow to converge, making its use dubious in many practical scenarios. To address this problem, this letter uses saddlepoint approximations for the null distribution of the generalized Hadamard ratio. Simulations are provided to demonstrate the saddlepoint approximations ability to achieve a desired false alarm probability, even in situations with low sample support.

Detection in multiple disparate systems using multi-channel coherence analysis

This paper presents a coherence-based detection method for multiple disparate sensing systems using the multi-channel coherence analysis (MCA) framework. MCA provides an optimal coordinate system for multi-channel detection problems as it finds sets of one-dimensional mapping vectors that maximize the sum of the cross-correlations among all pair-wise combinations of channels. The standard detector for Gaussian random vectors is then cast into the MCA framework by developing the log-likelihood ratio and J-divergence measure. The proposed detection method is then tested on a data set consisting of sets of four side-scan sonar images coregistered over the same region on the seafloor and the results are compared with those of a multi-channel generalized likelihood ratio (GLR) detector.

Spatial correlation analysis using canonical correlation decomposition for sparse sonar array processing

This paper uses the canonical correlation decomposition (CCD) framework to investigate the spatial correlation of sources captured using two spatially separated sensor arrays. The relationship between the canonical correlations of the observed signals and the spatial correlation coefficients of the source signals are first derived, including an analysis of the changes seen in this relationship under certain noise level and array geometry assumptions. Additionally, simulation results are presented that demonstrate the effects of different noise levels and array geometries on the canonical correlations for the case of two uniform linear sparse arrays.