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A sparse signal reconstruction perspective for source localization with sensor arrays

We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the /spl lscr//sub 1/-norm. A number of recent theoretical results on sparsifying properties of /spl lscr//sub 1/ penalties justify this choice. Explicitly enforcing the sparsity of the representation is motivated by a desire to obtain a sharp estimate of the spatial spectrum that exhibits super-resolution. We propose to use the singular value decomposition (SVD) of the data matrix to summarize multiple time or frequency samples. Our formulation leads to an optimization problem, which we solve efficiently in a second-order cone (SOC) programming framework by an interior point implementation. We propose a grid refinement method to mitigate the effects of limiting estimates to a grid of spatial locations and introduce an automatic selection criterion for the regularization parameter involved in our approach. We demonstrate the effectiveness of the method on simulated data by plots of spatial spectra and by comparing the estimator variance to the Crame/spl acute/r-Rao bound (CRB). We observe that our approach has a number of advantages over other source localization techniques, including increased resolution, improved robustness to noise, limitations in data quantity, and correlation of the sources, as well as not requiring an accurate initialization.

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.

Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization

We develop a method for the formation of spotlight-mode synthetic aperture radar (SAR) images with enhanced features. The approach is based on a regularized reconstruction of the scattering field which combines a tomographic model of the SAR observation process with prior information regarding the nature of the features of interest. Compared to conventional SAR techniques, the method we propose produces images with increased resolution, reduced sidelobes, reduced speckle and easier-to-segment regions. Our technique effectively deals with the complex-valued, random-phase nature of the underlying SAR reflectivities. An efficient and robust numerical solution is achieved through extensions of half-quadratic regularization methods to the complex-valued SAR problem. We demonstrate the performance of the method on synthetic and real SAR scenes.

A nonparametric statistical method for image segmentation using information theory and curve evolution

In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use level-set methods to implement the resulting evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Furthermore, our method, which does not require any training, performs as good as methods based on training.

Homotopy continuation for sparse signal representation

We explore the application of a homotopy continuation-based method for sparse signal representation in overcomplete dictionaries. Our problem setup is based on the basis pursuit framework, which involves a convex optimization problem consisting of terms enforcing data fidelity and sparsity, balanced by a regularization parameter. Choosing a good regularization parameter in this framework is a challenging task. We describe a homotopy continuation-based algorithm to find and trace efficiently all solutions of basis pursuit as a function of the regularization parameter. In addition to providing an attractive alternative to existing optimization methods for solving the basis pursuit problem, this algorithm can also be used to provide an automatic choice for the regularization parameter, based on prior information about the desired number of non-zero components in the sparse representation. Our numerical examples demonstrate the effectiveness of this algorithm in accurately and efficiently generating entire solution paths for basis pursuit, as well as producing reasonable regularization parameter choices. Furthermore, exploring the resulting solution paths in various operating conditions reveals insights about the nature of basis pursuit solutions.

Distributed fusion in sensor networks

This paper presents an overview of research conducted to bridge the rich field of graphical models with the emerging field of data fusion for sensor networks. Both theoretical issues and prototyping applications are discussed in addition to suggesting new lines of reasoning.

Sparse Representation in Structured Dictionaries With Application to Synthetic Aperture Radar

Sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently. In this paper, we develop a new, heuristic, graph-structured, sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries and whose dictionary elements can be arranged in a hierarchy. Around this algorithm, we construct a methodology for advanced image formation in wide-angle synthetic aperture radar (SAR), defining an approach for joint anisotropy characterization and image formation. Additionally, we develop a coordinate descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation using that dictionary. The motivation is to characterize a phenomenon in wide-angle SAR that has not been given much attention before: migratory scattering centers, i.e., scatterers whose apparent spatial location depends on aspect angle. Finally, we address the topic of recovering solutions that are sparse in more than one objective domain by introducing a suitable sparsifying cost function. We encode geometric objectives into SAR image formation through sparsity in two domains, including the normal parameter space of the Hough transform.

Drowsy driver detection through facial movement analysis

The advance of computing technology has provided the means for building intelligent vehicle systems. Drowsy driver detection system is one of the potential applications of intelligent vehicle systems. Previous approaches to drowsiness detection primarily make preassumptions about the relevant behavior, focusing on blink rate, eye closure, and yawning. Here we employ machine learning to datamine actual human behavior during drowsiness episodes. Automatic classifiers for 30 facial actions from the Facial Action Coding system were developed using machine learning on a separate database of spontaneous expressions. These facial actions include blinking and yawn motions, as well as a number of other facial movements. In addition, head motion was collected through automatic eye tracking and an accelerometer. These measures were passed to learning-based classifiers such as Adaboost and multinomial ridge regression. The system was able to predict sleep and crash episodes during a driving computer game with 96% accuracy within subjects and above 90% accuracy across subjects. This is the highest prediction rate reported to date for detecting real drowsiness. Moreover, the analysis revealed new information about human behavior during drowsy driving.

Nonparametric methods for image segmentation using information theory and curve evolution

We present a novel information theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution, and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use fast level set methods to implement the resulting evolution The evolution equations are based on nonparametric statistics, and have an intuitive appeal. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems.

A Sparsity-Driven Approach for Joint SAR Imaging and Phase Error Correction

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data, which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. Phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm, where each iteration of which consists of consecutive steps of image formation and model error correction. Experimental results show the effectiveness of the approach for various types of phase errors, as well as the improvements that it provides over existing techniques for model error compensation in SAR.