Browsing by Author "Tsogka, C."

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    Detection and Imaging in Strongly Backscattering Randomly Layered Media
    (2010-05) Alonso, R.; Borcea, L.; Papanicolaou, G.; Tsogka, C.
    Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and emphasizing the echoes from the reflectors that we wish to locate. We consider a detection and filtering approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm applies to general clutter, but its analysis depends on the model of the medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging.
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    Filtering Deterministic Layer Effects in Imaging
    (Society for Industrial and Applied Mathematics, 2012) Borcea, L.; del Cueto, F. Gonzalez; Papanicolaou, G.; Tsogka, C.
    Sensor array imaging arises in applications such as nondestructive evaluation of materials with ultrasonic waves, seismic exploration, and radar. The sensors probe a medium with signals and record the resulting echoes, which are then processed to determine the location and reflectivity of remote reflectors. These could be defects in materials such as voids, fault lines or salt bodies in the earth, and cars, buildings, or aircraft in radar applications. Imaging is relatively well understood when the medium through which the signals propagate is smooth, and therefore nonscattering. But in many problems the medium is heterogeneous, with numerous small inhomogeneities that scatter the waves. We refer to the collection of inhomogeneities as clutter, which introduces an uncertainty in imaging because it is unknown and impossible to estimate in detail. We model the clutter as a random process. The array data is measured in one realization of the random medium, and the challenge is to mitigate cumulative clutter scattering so as to obtain robust images that are statistically stable with respect to different realizations of the inhomogeneities. Scatterers that are not buried too deep in clutter can be imaged reliably with the coherent interferometric (CINT) approach. But in heavy clutter the signal-to-noise ratio (SNR) is low and CINT alone does not work. The “signal,” the echoes from the scatterers to be imaged, is overwhelmed by the “noise,” the strong clutter reverberations. There are two existing approaches for imaging at low SNR: The first operates under the premise that data are incoherent so that only the intensity of the scattered field can be used. The unknown coherent scatterers that we want to image are modeled as changes in the coefficients of diffusion or radiative transport equations satisfied by the intensities, and the problem becomes one of parameter estimation. Because the estimation is severely ill-posed, the results have poor resolution, unless very good prior information is available and large arrays are used. The second approach recognizes that if there is some residual coherence in the data, that is, some reliable phase information is available, it is worth trying to extract it and use it with well-posed coherent imaging methods to obtain images with better resolution. This paper takes the latter approach and presents a first attempt at enhancing the SNR of the array data by suppressing medium reverberations. It introduces filters, or annihilators of layer backscatter, that are designed to remove primary echoes from strong, isolated layers in a medium with additional random layering at small, subwavelength scales. These strong layers are called deterministic because they can be imaged from the data. However, our goal is not to image the layers, but to suppress them and thus enhance the echoes from compact scatterers buried deep in the medium. Surprisingly, the layer annihilators work better than intended, in the sense that they suppress not only the echoes from the deterministic layers, but also multiply scattered ones in the randomly layered structure. Following the layer annihilators presented here, other filters of general, nonlayered heavy clutter have been developed. We review these more recent developments and the challenges of imaging in heavy clutter in the introduction in order to place the research presented here in context. We then present in detail the layer annihilators and show with analysis and numerical simulations how they work.
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    Filtering Random Layering Effects in Imaging
    (2008-10) Borcea, L.; del Cueto, F. Gonzalez; Papanicolaou, G.; Tsogka, C.
    Objects that are buried deep in heterogeneous media produce faint echoes which are difficult to distinguish from the backscattered field. Sensor array imaging in such media cannot work unless we filter out the backscattered echoes and enhance the coherent arrivals that carry information about the objects that we wish to image. We study such filters for imaging in strongly backscattering, finely layered media. The fine layering is unknown and we model it with random processes. The filters use ideas from common seismic imaging techniques, such as normal move-out and semblance velocity estimation. These methods are based on the single scattering approximation, so it is surprising that the filters can annihilate the incoherent echoes produced by random media. The goal of the paper is to study theoretically and numerically this phenomenon.