ROBUST SUPERRESOLVING RESTORATION WITH APPLICATIONS.
Item
-
Title
-
ROBUST SUPERRESOLVING RESTORATION WITH APPLICATIONS.
-
Identifier
-
AAI8119665
-
identifier
-
8119665
-
Creator
-
MAMMONE, RICHARD JAMES.
-
Contributor
-
G. Eichmann
-
Date
-
1981
-
Language
-
English
-
Publisher
-
City University of New York.
-
Subject
-
Engineering, Electronics and Electrical
-
Abstract
-
A new robust method of solving ill-conditioned problems is presented. The method employs a priori constraints on the estimate, i.e. that the estimate, the first and/or higher order differences are bounded. The ill-conditioned system is reduced by elimination of the effectively redundant equations. This provides a reduction in computational complexity and acts to stabilize the inversion problem.;Since the resulting reduced system of equations is under-determined, there are many possible "solutions." We shall select that particular vector for the solution which yields the minimal norm of the residual error. Since this solution vector is of the same dimension as the effective rank, the method prefers restorations of inputs with sparse vector representations. The method is demonstrated in three applications: image processing, spectral estimation, and Apodization. Each application pertains to increasing the resolution of a measured signal. The resolution is increased beyond the limit imposed by the uncertainty principle of signal processing (superresolving). The method is demonstrated to be very effective in all three applications via computer simulations. The first chapter of this thesis contains material of an introductory nature. In Chapter 2 the contemporary methods of increasing resolution or equivalently extrapolating the spectrum of a signal are given. In general, these methods are found to be computationally very expensive and highly sensitive to noise. In Chapter 3, a new method of increasing the resolution of an image is presented. The method reduces the computational effort necessary to restore images degraded by an ill-conditioned operator. The restorations of noncoherent and coherent diffraction limited images are treated in detail. In Chapter 4, extrapolation in the time domain of a bandlimited signal is investigated. Alternately, the resolution of the frequency spectrum is increased. Thus, super-resolving spectral estimation is demonstrated. In Chapter 5, the design of a superresolving Apodization screen is presented. This screen will permit a spot-size of smaller circumference than previously possible. This smaller spot-size finds immediate application in the recent development of laser video discs. The video information is in the form of holes in the video disc. This Apodization will allow smaller holes to be burnt into the disc; thus discs of higher density can be made. Chapter 6 presents the general summary and conclusons obtained in the thesis. Future research is suggested in further applications of the algorithm presented.
-
Type
-
dissertation
-
Source
-
PQT Legacy CUNY.xlsx
-
degree
-
Ph.D.
-
Program
-
Engineering
