The problem of the restoration of quadratically distorted images is considered in this investigation, based upon the fact that images formed by partially coherent illuminations are related quadratically to the amplitude of the object. Two of the most important problems in image restoration are: 1) determining the degradation characteristics of the degraded image and 2) developing restoration algorithms. Among the two classes of inverse problems, one for system identification and the second for image restoration, only the means to solve the latter are presented in this study. Since the present problem is represented by the second-order term of a Volterra series expansion, multidimensional Volterra filter theory is presented with emphasis on the properties of two-dimensional quadratic filter. The mathematics of inverse problems is presented for the purpose of image restoration, and the novel algorithms which are simple and easy to implement and robust to the ill-conditioned system in comparison to the existing algorithms are proposed. Since quadratically distorted imaging systems preclude a closed-form solution, approximate solutions are obtained through application of the proposed iterative and noniterative schemes. Images restored approximately by the proposed algorithms can be improved substantially by the use of a Newton-Raphson iteration scheme. Two typical regularization methods are presented and the truncated singular-value decomposition method is applied for the noisy image restoration. Regularized iterative restoration schemes for the noisy image restoration are also considered. Simulation examples for different issues are presented. / Graduation date: 1991

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This paper presents a set of Image Registration, Image Integration, interpolation and image restoration and other technology, the number of low-resolution images synthesized high-resolution image. Relative to the existing image fusion technology, the method provided in this paper has more advantages, such as: (1) high-precision value; (2)low computation cost; (3)a compact system; (4) applicable to noise images; (5) robotic and automatic performance.

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The splitting-integrating method(SIM) is well suited to the inverse transformations of digital images and patterns in 2D, but it encounters some difficulties involving nonlinear solutions for the forward transformation. New techniques are explored in this thesis to bypass the nonlinear solution process completely, to save CPU time, and to be more flexible for general and complicated transformations T, such as the harmonic model which convert the original shape of images and patterns to other arbitrary shapes. In this thesis, the finite element method (FEM) are used to seek the approximate transformation of the harmonic model. The new methods of image transformation are applied to human face. To describe the face boundary, we use the method combining Lagrange polynomial and Hermite interpolation seeking for the corresponding grid points besides the fixed ones. The greyness of images under geometric transformations by the splitting-integrating method has the error bounds, O(H)+O(H/N^2) as using the piecewise bilinear interpolations (u =1), for smooth images, where H(<<1) is mesh resolution of an optical scanner, and N is the division number of a pixel split into N^2 sub-pixels. Furthermore, there often occur in practical applications the discontinuity images whose greyness jump is a minor portion of the entire image, e.g., the piecewise continuous images but with the interior and exterior boundary of greyness jumps, or the continuous pictures accompanied with a finite number of isolated pixels. For this kind of discontinuous images, the error bounds are also derived in this thesis to be $O(H^{eta})+O(H^{eta}/N^2), ~ eta in (0,1]$ as $mu =1$. The image greyness made before was always assumed to be smooth enough, this error analysis is significant for geometric image transformations.

Texte remanié de: Tesis de doctorado--Teología biblica--Rome--Pontificia Universidad Gregoriana, 2004. / Bibliogr. p. 385-406.

Thesis(M.S.)--Case Western Reserve University, 2009 / Title from PDF (viewed on 2010-01-28) Department of Electrical Engineering and Computer Science -- Electrical Engineering Includes abstract Includes bibliographical references and appendices Available online via the OhioLINK ETD Center

Thesis (Ph.D.) -- University of Texas at Arlington, 2008.

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains x, 105 p. Includes abstract and vita. Advisor: W. Bruce Walsh, Dept. of Psychology. Includes bibliographical references (p. 92-101).

Includes bibliographical references (p. 81-90).