Instabilities in the optimal regularization parameter relating to image recovery problems

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The reconstruction of an object from an image formed by an idealized optical system is considered. The problem is well known to be ill posed, and so Tikhonov regularization is applied. An ensemble of additive Gaussian noise vectors at several signal-to-noise ratios is used to exhibit variations in the optimal Tikhonov regularization parameter. It is shown that the abrupt and rapid decrease in the magnitude of the eigenvalues of the imaging kernels causes instability in the optimal regularization parameter. This instability dramatically affects the generalized cross-validation estimator for the optimal regularization parameter. © 1992 Optical Society of America.

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Journal of the Optical Society of America A: Optics and Image Science, and Vision