1 May 1990 M-estimators in robust nonlinear image restoration
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Abstract
Most image formation systems involve a built-in nonlinear transformation. Furthermore, many image processing applications involve longtailed noise processes, which introduce outliers in the gray-level distribution of the image. The performance of conventional restoration algorithms is highly degraded by such noise processes. A robust-design approach aims to eliminate the effects of outliers in the performance of the algorithm. The concept of M-estimation leads to robust estimators, which, however, require iterative evaluation. Such estimators have been employed in recursive image restoration, mainly for the robust parameter identification. In this paper, the exploitation of M-estimators in iterative nonlinear restoration algorithms is considered. These algorithms are designed to optimize the robust least-squares-error criterion, which limits the effects of large residuals through an influence function. The robust version of the steepest-descent (SD) algorithm is introduced. This algorithm overcomes the linear search required by the basic SD technique through a particular procedure for the selection of the iteration parameter. Based on the convergence analysis of this algorithm a new influence function, the redescending nonzero function, is introduced. Structural modifications of the robust SD technique result in two hybrid SD algorithms, which achieve fast convergence without degrading the quality of the final estimate. The algorithms introduced can be easily implemented through Fourier transform techniques. The convergence properties of the robust algorithms are rigorously studied through their singular-value analysis and the global convergence theorem. The application of these algorithms on image restoration problems is demonstrated through examples.
Michael E. Zervakis, Anastasios N. Venetsanopoulos, "M-estimators in robust nonlinear image restoration," Optical Engineering 29(5), (1 May 1990). https://doi.org/10.1117/12.55614
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