A robustized vector recursive stabilizer algorithm for image restoration

Abstract

The ill-posed problem of object reconstruction (or band-limited extrapolation) is reformulated in the framework of the general linear model in new recursive parametric forms. The resultant algorithms are shown to be natural stabilizers of the inherent instabilities of both the iterative and noniterative reconstruction/band-limited extrapolation methods. Both robustized and unrobustized versions of the algorithms are given. The recursive algorithms provide immunity to measurement noise outliers in burst noise of high variance. Unlike procedures suggested previously, these methods eliminate the need for stopping rule constraints and ensure convergence of the algorithms. The recursive formulation of the noniterative method of band-limited extrapolation is also found to be adaptable to multidimensional image restoration. Computer simulations verify the theory and demonstrate the computational efficiency of the method. © 1980 Academic Press, Inc.