Graduate Thesis Or Dissertation

Restoration of quadratically distorted images

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  • 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.
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