Hyrum S. Anderson

Joint deconvolution and classification with applications to passive acoustic underwater multipath

This paper addresses the problem of classifying signals that have been corrupted by noise and unknown linear time-invariant (LTI) filtering such as multipath, given labeled uncorrupted training signals. A maximum a posteriori approach to the deconvolution and classification is considered, which produces estimates of the desired signal, the unknown channel, and the class label. For cases in which only a class label is needed, the classification accuracy can be improved by not committing to an estimate of the channel or signal. A variant of the quadratic discriminant analysis (QDA) classifier is proposed that probabilistically accounts for the unknown LTI filtering, and which avoids deconvolution. The proposed QDA classifier can work either directly on the signal or on features whose transformation by LTI filtering can be analyzed; as an example a classifier for subband-power features is derived. Results on simulated data and real Bowhead whale vocalizations show that jointly considering deconvolution with classification can dramatically improve classification performance over traditional methods over a range of signal-to-noise ratios.

Training a support vector machine to classify signals in a real environment given clean training data

When building a classifier from clean training data for a particular test environment, knowledge about the environmental noise and channel should be taken into account. We propose training a support vector machine (SVM) classifier using a modified kernel that is the expected kernel with respect to a probability distribution over channels and noise that might affect the test signal. We compare the proposed expected SVM to an SVM that ignores the environment, to an SVM that trains with multiple random samples of the environment, and to a quadratic discriminant analysis classifier that takes advantage of environment statistics (Joint QDA). Simulations classifying narrowband signals in a noisy acoustic reverberation environment indicate that the expected SVM can improve performance over a range of noise levels.

Gamut Expansion for Video and Image Sets

A semi-automated gamut expansion method is proposed for transforming the colors of video and images to take advantage of extended-gamut displays. In particular, a custom color transformation is learned from an experts enhancement of a single image on an extended gamut display. This methodology allows for the gamut-expansion to be defined in a contextually appropriate way. From the user-enhanced image, we compare defining the gamut expansion by one linear transformation, or by a multi-dimensional LUT which we learn via local linear regression. We show that using the estimated multi-dimensional LUT with tri-linear interpolation (a standard workflow for ICC profiles and color management modules) leads to significantly more pleasant reproduction of skin tones and bright saturated colors.

Channel-Robust Classifiers

A key assumption underlying traditional supervised learning algorithms is that labeled examples used to train a classifier are drawn i.i.d. from the same distribution as test samples. This assumption is violated when classifying a test sample whose statistics differ from the training samples because the test signal is the output of a noisy linear time-invariant system, e.g., from channel propagation or filtering. We assume that the channel impulse response is unknown, but can be modeled as a random channel with finite first and second-order statistics that can be estimated from sample impulse responses. We present two kernels, the expected and projected RBF kernels, that account for the stochastic channel. Compared to the strategy of virtual examples, an SVM trained with the proposed kernels requires dramatically less training time, and may perform better in practice. We also extend the joint quadratic discriminant analysis (joint QDA) classifier, which also accounts for a stochastic channel, to a local version that reduces model bias. Results show the proposed methods achieve state-of-the-art performance and significantly faster training times.

Classifying linear system outputs by robust local Bayesian quadratic discriminant analysis on linear estimators

We consider the problem of assigning a class label to the noisy output of a linear system, where clean feature examples are available for training. We design a robust classifier that operates on a linear estimate, with uncertainty modeled by a Gaussian distribution with parameters derived from the bias and covariance of a linear estimator. Class-conditional distributions are modeled locally as Gaussians. Since estimation of Gaussian parameters from few training samples can be illposed, we extend recent work in Bayesian quadratic discriminant analysis to derive a robust local generative classifier. Experiments show a statistically significant improvement over prior art.

Joint Deconvolution and Classification for Signals with Multipath

For many sensing modalities such as sonar, received signals are corrupted by multipath and can be challenging for automatic classification systems. An approach to jointly deconvolve and classify such signals is proposed. Specifically, a filter is estimated that minimizes the distortion between the received signal and a set of training signals, then the received signal is assigned to the class that corresponds to the training signal whose estimated filter is most sparse. Simulations compare the new method with blind deconvolution using Cabrellis algorithm followed by a correlation-based nearest neighbor classifier. Results indicate that joint deconvolution and classification performs similarly to blind deconvolution in the presence of severe noise, and outperforms blind deconvolution at low and moderate noise levels.

Joint deconvolution and imaging

We investigate a Wiener fusion method to optimally combine multiple estimates for the problem of image deblurring given a known blur and a corpus of sharper training images. Nearest-neighbor estimation of high frequency information from training images is fused with a standard Wiener deconvolution estimate. Results show an improvement in sharpness and decreased artifacts compared to either the standard Wiener filter or the nearest-neighbor reconstruction.

Maximum Likelihood Signal Classification using Second-Order Blind Deconvolution Probability Model

We address the problem of classifying a signal that has been corrupted by an unknown linear time-invariant filter. This problem is common in remote-sensing and non-destructive evaluation applications wheremultipath and spreading are prevalent. A traditional approach is blind deconvolution to estimate the original signal, followed by classification of the estimated signal. Blind deconvolution is an ill-posed estimation problem, and if only a classification is needed, then we hypothesize it is an unnecessary step. We present an alternative maximum likelihood classifier that uses second-order probability models for the original signal and the unknown corrupting filter. The resulting quadratic discriminant analysis classifier is shown to perform well over a range of signal-to-noise ratios for two different models of multipath, and in all cases performs consistently better than a standard blind deconvolution method followed by a quadratic discriminant analysis classifier.

Robust sequential classification of tracks

We present a robust probabilistic method to classify targets based on their tracks. As is customary in supervised learning problems, it is assumed that example tracks from various classes are available to train a classifier. We present an optimal but computationally intensive sequential solution, and show that a computationally feasible naive Bayes approximation works better than ignoring sequential information. We show how to take into account the uncertainty of the track, as quantified by the error covariance matrix from a Kalman tracker, using the recently proposed expected maximum likelihood rule coupled with a robust local Bayesian discriminant analysis classifier. In addition, we propose an expected maximum a posterior rule to take test sample uncertainty into account for classifiers that model the posterior, and use it to define a robust kernel classifier. Simulations with a Kalman tracker show significantly improved performance by taking into account the tracked state covariance.

Classification of shallow water passive sonar signals using stochastic channel model.

This paper addresses the problem of classifying passive sonar signals propagating in shallow water channels. A key problem is that such signals are corrupted by noise and multipath, which we model stochastically in terms of the expected multipath and noise, and the variance of the multipath and noise. We assume that free‐field (e.g., deep water) training signals are available. We show that for classification, the accuracy can be improved by not committing to an estimate of the channel or signal, but rather by marginalizing out the channel and noise uncertainty. Specifically, we propose variants of the quadratic discriminant analysis (QDA) classifier and the support vector machine classifier (SVM) that probabilistically account for the unknown channel effects, and which avoid ill‐posed deconvolution. The proposed classifiers can work either directly on a time signal or on subband power features. Results on simulated data and real Bowhead whale vocalizations show that we can significantly improve classifica...