Mathematical Problems and Adaptive Algorithms for Imaging in Random Media

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BorceaDMS-0907746 The project is concerned with sensor array imaging in heterogeneous (cluttered) richly scattering media. It is motivated by applications in reflection seismology, ultrasonic nondestructive evaluation, ground-foliage penetrating radar, and synthetic aperture radar. Mathematically, the study is on inverse problems for the wave equation with rapidly fluctuating wave speed, due to numerous small heterogeneities in clutter. The goal is to locate (image) strong reflectors buried in clutter, using measurements of the scattered waves at remote arrays of sensors. Because the clutter inhomogeneities are not known and they cannot be estimated from the array data, they are modeled with random processes. The work is divided in three main themes: (1) Filtering random media effects for array imaging in heavy clutter. (2) Optimal subspace projection methods for selective illumination and imaging with array sensors in random media. (3) Robust and efficient imaging methods for persistent surveillance synthetic aperture radar. All problems are new and challenging, they involve theory, extensive numerical simulations, and algorithm development in realistic setups, motivated by applications. Sensor array imaging is an important technology in oil exploration, earthquake prediction, nondestructive evaluation of materials, radar, persistent surveillance of complex urban scenes, and elsewhere. Progress in sensor technology has improved dramatically the ability to collect new types of data and vast amounts of it. The current imaging technology is inadequate, specially in highly heterogeneous (cluttered), low visibility environments. The project is concerned with the development of new imaging methodologies that can adaptively mitigate the clutter effects and the uncertainty in the data, and can optimize sensor array illumination waveforms for achieving the best possible images.