Regularized iterative and non-iterative procedures for object restoration from experimental data

A regularized algorithm for the recovery of band-limited signals from noisy data is described. The regularization is characterized by a single parameter. Iterative and non-iterative implementations of the algorithm are shown to have useful properties, the former offering the advantage of flexibility and the latter a potential for rapid data processing. Comparative results, using experimental data obtained in laser anemometry studies with a photon correlator, are presented both with and without regularization. © 1983 Taylor & Francis Ltd.

Regularized iterative and noniterative procedures for object restoration in the presence of noise :an error analysis

An analysis is carried out, using the prolate spheroidal wave functions, of certain regularized iterative and noniterative methods previously proposed for the achievement of object restoration (or, equivalently, spectral extrapolation) from noisy image data. The ill-posedness inherent in the problem is treated by means of a regularization parameter, and the analysis shows explicitly how the deleterious effects of the noise are then contained. The error in the object estimate is also assessed, and it is shown that the optimal choice for the regularization parameter depends on the signal-to-noise ratio. Numerical examples are used to demonstrate the performance of both unregularized and regularized procedures and also to show how, in the unregularized case, artefacts can be generated from pure noise. Finally, the relative error in the estimate is calculated as a function of the degree of superresolution demanded for reconstruction problems characterized by low space–bandwidth products.