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