Lee C. Potter

Sparsity and Compressed Sensing in Radar Imaging

Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.

Attributed scattering centers for SAR ATR

High-frequency radar measurements of man-made targets are dominated by returns from isolated scattering centers, such as corners and flat plates. Characterizing the features of these scattering centers provides a parsimonious, physically relevant signal representation for use in automatic target recognition (ATR). In this paper, we present a framework for feature extraction predicated on parametric models for the radar returns. The models are motivated by the scattering behaviour predicted by the geometrical theory of diffraction. For each scattering center, statistically robust estimation of model parameters provides high-resolution attributes including location, geometry, and polarization response. We present statistical analysis of the scattering model to describe feature uncertainty, and we provide a least-squares algorithm for feature estimation. We survey existing algorithms for simplified models, and derive bounds for the error incurred in adopting the simplified models. A model order selection algorithm is given, and an M-ary generalized likelihood ratio test is given for classifying polarimetric responses in spherically invariant random clutter.

A GTD-based parametric model for radar scattering

This paper presents a new approach to scattering center extraction based on a scattering model derived from the geometrical theory of diffraction (GTD). For stepped frequency measurements at high frequencies, the model is better matched to the physical scattering process than the damped exponential model and conventional Fourier analysis. In addition to determining downrange distance, energy, and polarization, the GTD-based model extracts frequency dependent scattering information, allowing partial identification of scattering center geometry. We derive expressions for the Cramer-Rao bound of this model; using these expressions, we analyze the behavior of the new model as a function of scatterer separation, bandwidth, number of data points, and noise level. Additionally, a maximum likelihood algorithm is developed for estimation of the model parameters. We present estimation results using data measured on a compact range to validate the proposed modeling procedure. >

Statistical prediction of task execution times through analytic benchmarking for scheduling in a heterogeneous environment

In this paper, a method for estimating task execution times is presented in order to facilitate dynamic scheduling in a heterogeneous metacomputing environment. Execution time is treated as a random variable and is statistically estimated from past observations. This method predicts the execution time as a function of several parameters of the input data and does not require any direct information about the algorithms used by the tasks or the architecture of the machines. Techniques based upon the concept of analytic benchmarking/code profiling are used to characterize the performance differences between machines, allowing observations from dissimilar machines to be used when making a prediction. Experimental results are presented which use actual execution time data gathered from 16 heterogeneous machines.

Maximum mutual information principle for dynamic sensor query problems

In this paper we study a dynamic sensor selection method for Bayesian filtering problems. In particular we consider the distributed Bayesian Filtering strategy given in [1] and show that the principle of mutual information maximization follows naturally from the expected uncertainty minimization criterion in a Bayesian filtering framework. This equivalence results in a computationally feasible approach to state estimation in sensor networks. We illustrate the application of the proposed dynamic sensor selection method to both discrete and linear Gaussian models for distributed tracking as well as to stationary target localization using acoustic arrays.

A parametric model for synthetic aperture radar measurements

We present a parametric model for radar scattering as a function of frequency and aspect angle. The model is used for analysis of synthetic aperture radar measurements. The estimated parameters provide a concise, physically relevant description of measured scattering for use in target recognition, data compression and scattering studies. The scattering model and an image domain estimation algorithm are applied to two measured data examples.

Compressive imaging using approximate message passing and a Markov-tree prior

We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a hidden Markov tree (HMT) but, unlike other works, ours is based on loopy belief propagation (LBP). For LBP, we adopt a recently proposed “turbo” message passing schedule that alternates between exploitation of HMT structure and exploitation of compressive-measurement structure. For the latter, we leverage Donoho, Maleki, and Montanaris recently proposed approximate message passing (AMP) algorithm. Experiments with a large image database suggest that, relative to existing schemes, our turbo LBP approach yields state-of-the-art reconstruction performance with substantial reduction in complexity.

Fast bayesian matching pursuit

A low-complexity recursive procedure is presented for minimum mean squared error (MMSE) estimation in linear regression models. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both an approximate MMSE estimate of the parameter vector and a set of high posterior probability mixing parameters. Emphasis is given to the case of a sparse parameter vector. Numerical simulations demonstrate estimation performance and illustrate the distinctions between MMSE estimation and MAP model selection. The set of high probability mixing parameters not only provides MAP basis selection, but also yields relative probabilities that reveal potential ambiguity in the sparse model.

RFI suppression for ultra wideband radar

An estimate-and-subtract algorithm is presented for the real-time digital suppression of radio frequency interference (RFI) in ultrawideband (UWB) synthetic aperture radar (SAR) systems used for foliage- and ground-penetrating imaging. The algorithm separately processes fixed- and variable-frequency interferers. Excision of estimated targets greatly reduces bias in RFI estimates, thereby reducing target energy loss and sidelobe levels in SAR imagery. Performance is demonstrated on data collected with the Army Research Laboratorys UWB rail SAR.

Model-based classification of radar images

A Bayesian approach is presented for model-based classification of images with application to synthetic-aperture radar. Posterior probabilities are computed for candidate hypotheses using physical features estimated from sensor data along with features predicted from these hypotheses. The likelihood scoring allows propagation of uncertainty arising in both the sensor data and object models. The Bayesian classification, including the determination of a correspondence between unordered random features, is shown to be tractable, yielding a classification algorithm, a method for estimating error rates, and a tool for evaluating the performance sensitivity. The radar image features used for classification are point locations with an associated vector of physical attributes; the attributed features are adopted from a parametric model of high-frequency radar scattering. With the emergence of wideband sensor technology, these physical features expand interpretation of radar imagery to access the frequency- and aspect-dependent scattering information carried in the image phase.