Xuejun Liao

Coded aperture compressive temporal imaging

We use mechanical translation of a coded aperture for code division multiple access compression of video. We discuss the compressed videos temporal resolution and present experimental results for reconstructions of > 10 frames of temporal data per coded snapshot.

Identification of ground targets from sequential high-range-resolution radar signatures

An approach to identifying targets from sequential high-range-resolution (HRR) radar signatures is presented. In particular, a hidden Markov model (HMM) is employed to characterize the sequential information contained in multiaspect HRR target signatures. Features from each of the HRR waveforms are extracted via the RELAX algorithm. The statistical models used for the HMM states are formulated for application to RELAX features, and the expectation-maximization (EM) training algorithm is augmented appropriately. Example classification results are presented for the ten-target MSTAR data set.

On Classification with Incomplete Data

We address the incomplete-data problem in which feature vectors to be classified are missing data (features). A (supervised) logistic regression algorithm for the classification of incomplete data is developed. Single or multiple imputation for the missing data is avoided by performing analytic integration with an estimated conditional density function (conditioned on the observed data). Conditional density functions are estimated using a Gaussian mixture model (GMM), with parameter estimation performed using both expectation-maximization (EM) and variational Bayesian EM (VB-EM). The proposed supervised algorithm is then extended to the semisupervised case by incorporating graph-based regularization. The semisupervised algorithm utilizes all available data-both incomplete and complete, as well as labeled and unlabeled. Experimental results of the proposed classification algorithms are shown

Video Compressive Sensing Using Gaussian Mixture Models

A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.

Detection of buried targets via active selection of labeled data: application to sensing subsurface UXO

When sensing subsurface targets, such as landmines and unexploded ordnance (UXO), the target signatures are typically a strong function of environmental and historical circumstances. Consequently, it is difficult to constitute a universal training set for design of detection or classification algorithms. In this paper, we develop an efficient procedure by which information-theoretic concepts are used to design the basis functions and training set, directly from the site-specific measured data. Specifically, assume that measured data (e.g., induction and/or magnetometer) are available from a given site, unlabeled in the sense that it is not known a priori whether a given signature is associated with a target or clutter. For N signatures, the data may be expressed as {x/sub i/,y/sub i/}/sub i=1,N/, where x/sub i/ is the measured data for buried object i, and y/sub i/ is the associated unknown binary label (target/nontarget). Let the N x/sub i/ define the set X. The algorithm works in four steps: 1) the Fisher information matrix is used to select a set of basis functions for the kernel-based algorithm, this step defining a set of n signatures B/sub n//spl sube/X that are most informative in characterizing the signature distribution of the site; 2) the Fisher information matrix is used again to define a small subset X/sub s//spl sube/X, composed of those x/sub i/ for which knowledge of the associated labels y/sub i/ would be most informative in defining the weights for the basis functions in B/sub n/; 3) the buried objects associated with the signatures in X/sub s/ are excavated, yielding the associated labels y/sub i/, represented by the set Y/sub s/; and 4) using B/sub n/,X/sub s/, and Y/sub s/, a kernel-based classifier is designed for use in classifying all remaining buried objects. This framework is discussed in detail, with example results presented for an actual buried-UXO site.

Application of the theory of optimal experiments to adaptive electromagnetic-induction sensing of buried targets

A mobile electromagnetic-induction (EM I) sensor is considered for detection and characterization of buried conducting and/or ferrous targets. The sensor maybe placed on a robot and, here, we consider design of an optimal adaptive-search strategy. A frequency-dependent magnetic-dipole model is used to characterize the target at EMI frequencies. The goal of the search is accurate characterization of the dipole-model parameters, denoted by the vector /spl Theta/; the target position and orientation are a subset of /spl Theta/. The sensor position and operating frequency are denoted by the parameter vector p and a measurement is represented by the pair (p, O), where O denotes the observed data. The parameters p are fixed for a given measurement, but, in the context of a sequence of measurements p may be changed adaptively. In a locally optimal sequence of measurements, we desire the optimal sensor parameters, p/sub N+1/ for estimation of /spl Theta/, based on the previous measurements (p/sub n/, O/sub n/)/sub n=1,N/. The search strategy is based on the theory of optimal experiments, as discussed in detail and demonstrated via several numerical examples.

Detection of Unexploded Ordnance via Efficient Semisupervised and Active Learning

Semi supervised learning and active learning are considered for unexploded ordnance (UXO) detection. Semi supervised learning algorithms are designed using both labeled and unlabeled data, where here labeled data correspond to sensor signatures for which the identity of the buried item (UXO/non-UXO) is known; for unlabeled data, one only has access to the corresponding sensor data. Active learning is used to define which unlabeled signatures would be most informative to improve the classifier design if the associated label could be acquired (where for UXO sensing, the label is acquired by excavation). A graph-based semi supervised algorithm is applied, which employs the idea of a random Markov walk on a graph, thereby exploiting knowledge of the data manifold (where the manifold is defined by both the labeled and unlabeled data). The algorithm is used to infer labels for the unlabeled data, providing a probability that a given unlabeled signature corresponds to a buried UXO. An efficient active-learning procedure is developed for this algorithm, based on a mutual information measure. In this manner, one initially performs excavation with the purpose of acquiring labels to improve the classifier, and once this active-learning phase is completed, the resulting semi supervised classifier is then applied to the remaining unlabeled signatures to quantify the probability that each such item is a UXO. Example classification results are presented for an actual UXO site, based on electromagnetic induction and magnetometer data. Performance is assessed in comparison to other semi supervised approaches, as well as to supervised algorithms.

Generalized Alternating Projection for Weighted-

We consider the group basis pursuit problem, which extends basis pursuit by replacing the

\ell_{2,1}

\ell_{1}

Minimization with Applications to Model-Based Compressive Sensing

norm with a weighted-