New robust methods for superresolving signal recovery and bandlimited signal extrapolation.
Item
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Title
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New robust methods for superresolving signal recovery and bandlimited signal extrapolation.
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Identifier
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AAI8914796
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identifier
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8914796
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Creator
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Stojancic, Mihajlo M.
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Contributor
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Adviser: George Eichmann
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Date
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1988
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Electronics and Electrical | Engineering, General
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Abstract
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The reconstruction of signals and images degraded by a linear, frequency low-pass degradation operator, or obscured due to a finite space (time) observation interval, is an ill-posed problem. This thesis focuses on the developing of new robust methods to alleviate the aforementioned problem. In particular three different methods are proposed. First, based on a new constrained associative memory (CAM) method, the reconstruction (restoration) of an arbitrary binary object from an image, degraded by a linear shift-invariant (LSI) or a linear shift-variant (LSV) degradation operator, in the presence of strong noise, is achieved. Using an appropriate training set of signals, related ideally by a perfect degradation operator inverse, the CAM method yields a general one-step impulsive-type inverse filter in a form of two dimensional array of coefficients. Computer simulation results of the reconstruction of 1D and 2D signals and images, degraded by LSI and LSV systems, in the presence of strong noise, are presented. Second, a new iterative method, based on the weighted least-square (WLS) and best linear unbiased estimate (BLUE) algorithms, is presented. This algorithm focuses on designing a suitable symmetric weighting matrix that will, without disturbing the system consistency, perform an implicit filtering of the system degradation operator singular values (SV). A specific SV filter performs twofold function; it compensates for the ill-conditioning of the system degradation operator by decreasing its matrix condition number and by improving the low-to-high-order SV ration it improves the convergence rate of a recursive computation of the object signal estimate. Last, a new algorithm for the extrapolation in the space domain of a partially observed low space-bandwidth product (SBP) sequence, or equivalently, the resolution of the Fourier spectra in the frequency domain, in the presence of appreciable noise, is developed. Using an approach similar to the Simulated Annealing method the extrapolated sequence samples are constructed from variable size elementary grains. The new iterative algorithm, at each iteration step, based on a random number generator, decides both the sample position to be considered, and the sign of a grain that might be added to the current sample value. A variable size sample update in each iteration step is either accepted or rejected in accordance with an appropriate decision rule. Several simulation examples, for the extrapolation of low SBP sinusoidal and other arbitrary sequences and in the presence of high level of noise, are presented.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
