The goal of this research is to develop models, estimation techniques, and computational algorithms for inverse problems arising in geophysics, and in particular in reservoir characterization. Although large volumes of data may be available in these problems, they do not sufficiently determine the underground structure under study. We are studying the use of stochastic models and nonlinear constraints to decrease this uncertainty.

Our goal is to develop optimal techniques and efficient algorithms in three areas of imaging: (1) image reconstruction from partial information, (2) acquisition of time-varying images, (3) visualization of vector fields. We are studying nonlinear techniques for tomographic with limited angle data, blind image restoration, and for other ill-posed inverse problems. We are also developing a systematic theory for designing minimum rate sampling patterns. We are developing algorithms for segmentation and maximally informative display of vector-valued images, such as are acquired in multispectral or multimodality remote sensing and diagnostic imaging. This research has applications in biomedical imaging; video; remote sensing and surveillance; and geophysics.

This project is a fundamental study of imaging from sparse Fourier data, with an emphasis on 3-D synthetic aperture radar (SAR). In SAR, as in most other important computed imaging applications, it is often impossible or prohibitively expensive to collect dense data sets that completely define the image. Our goal is to explore the use of various frequency and spatial domain constraints to obtain a unique and stable solution from sparse data sets. Specifically, our objectives are to characterize the fundamental limitations of various acquisition and constraint combinations and to develop efficient algorithms for image acquisition and formation in these circumstances. The methods will be validated for the 3-D SAR scenario.

We use the term HCI in a very broad sense to include communication between person and computer as well as communication between persons via computer. An example of the former is a person using a workstation, an example of the latter is tele-collaboration. We are investigating a variety of issues related to the use of computer vision in HCI. These include: facial feature extraction and tracking, determining 3-D head pose, facial movement modeling, analysis, and synthesis, hand gesture recognition, human body motion analysis, and person identification.

We are studying a number of challenging issues in image/video data indexing and retrieval. Of particular interest are similarity-based retrieval where similarity measures are based on image content such as color, texture, shape, and layout; mapping of high-level concepts to low-level image features; and how to deal with data and query uncertainties.

Our goal is to investigate image/video representation and compression schemes that are suitable for data storage, retrieval, and display. Performance criteria will be based not only on compression factors, but also on scalability, interoperability, and ease of manipulation with compressed data. Under study are fractal coding, wavelet/morphological coding, and 3-D model-based methods.

This project investigates how the learning process in adaptive digital filters is disturbed by hardware failures and how to design filters and adaptive algorithms that can continue operating in the presence of such failures. Adaptive systems are capable of adjusting parameters to reduce a specified error criterion. It has been shown that whenever a hardware failure occurs that increases the error, the system will attempt to compensate for this failure by further self-adjustment. Recently this research has concentrated on compensating broader classes of hardware errors and on applying adaptive fault tolerance to adaptive filters of the infinite impulse response class.

The structure of the input autocorrelation matrix in Volterra second-order adaptive filters for general colored Gaussian input processes has been analyzed to determine how to best formulate a computationally efficient, fast adaptive algorithm. It was shown that when the input signal samples are ordered properly within the input data vector, the autocorrelation matrix of quadratic filter inherits a block diagonal structure, with some of the subblocks also having diagonal structure. Some new results in developing and evaluating computationally efficient quasi-Newton adaptive algorithms have been obtained that take advantage of the sparsity and unique structure of the correlation matrix that results from this formulation.

This project is investigating the design of an adaptive equalizer-on-a-chip for the equalization of magnetic recording channels. A design based on combining a residue number system architecture with a block LMS adaptive algorithm is being evaluated for its potential to a design that achieves sufficiently high operating speeds for magnetic disk applications, while having simple enough circuit requirements to be fabricated as a monolithic VLSI component. Special attention is being devoted to the management of short word length finite precision arithmetic and its effect on the learning characteristic of the equalizer. This project involves both VLSI design and fabrication.

Communication system performance is often degraded by imperfections of the channel. When additive noise and nonideal channel characteristics are unknown prior to transmission, adaptive equalizers are used to compensate for these imperfections and improve overall performance. For highly correlated received sequences, the convergence rate of the equalizer is a strongly limiting factor. This project aims to develop novel schemes employing preconditioned conjugate gradient (PCG) optimization for channel equalization. Results have been obtained to illustrate that, compared to an LMS equalizer, the PCG equalizer provides significantly improved performance for algorithms which minimize the mean squared error and constant modulus error criteria.

New adaptive and statistically optimal time-frequency analysis methods are being developed for improved processing of nonstationary signals. The class of problems for which time-frequency-based detection is being characterized and optimal kernels for detection are being derived. New adaptive time-frequency representations for high-resolution visual characterization of signals are also under development. These methods are being applied to problems in condition assessment for machinery monitoring and fault detection, mine classification, and transient detection and analysis.

This research project is developing signal processing methods based on overdetermined basis decompositions for estimating the relative energies of individual components of complex signals and for component separation and recovery. Such an approach can decompose a signal with multiple overlapped, nonorthogonal components onto different basis elements, thereby separating them in situations in which standard filtering approaches or orthogonal basis decompositions cannot.

Research in this area is still in its infancy, and we propose to further develop the theory behind these methods and to apply them to the problem of energy partitioning and other promising navy applications.

We are investigating synthetic aperture radar (SAR) as a means of imaging runways through fog and cloud cover from an approaching aircraft. Current radars with traditional signal processing are incapable of providing the resolution required at long ranges, because of the wide beam widths of the antennas employed. Our approach uses the changes in angular aspect of points in the airport scene, provided by the motion of the aircraft, to produce high-resolution imagery from return signals collected by a conventional radar.

Denotes principal investigator.

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Professor Narendra Ahuja (center) and graduate students Manoj Aggarwal and Andres Castano work with the 3-D display system Immers adesk in the Computer Vision and Robotics Laboratory at the Beckman Institute. (Photo: Thompson-McClellan)

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In the Coordinated Science Laboratory, Professor Steve Kang (right) discusses MPEG4 VLSI projects with his graduate assistants Ketan Patel and James Stroming. (Photo: Thompson-McClellan)

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Professor Bruce Hajek (second from right) listens as graduate students Vijay Subramanian, Dakshi Agrawal, and Liping (Julia) Zhu discuss providing a high-quality end-to-end multimedia connection over a heterogeneous network. (Photo: Thompson-McClellan)

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Professor Tamer Basar (right rear) holds a work session in the Decision and Control Laboratory on the performance of robust control algorithms with (clockwise from left) graduate research assistants Suzanne Landry and Gordal Arslan, undergraduate Victor Hsu, and graduate research assistant Ross Blauwkamp. (Photo: Thompson-McClellan)

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Professors Pierre Moulin (left) and David Munson (center right) discuss facial modeling with their students. The work is being done in the Image Formation and Processing Laboratory in the Beckman Institute. (Photo: Thompson-McClellan)