| Summary: | 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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