Abstract

A method is reported for bringing about more rapid and complete convergence of the equations that implement the minimum-negativity constraint. The method utilizes an improved spatial function constructed by leaving the negative values intact and replacing the positive values with the differences between their values for the present and previous iteration. (This difference is found to converge after several iterations.) The advantage of this new spatial function is that convergence may be obtained for recalcitrant data using fast approximate procedures requiring the FFT. Several improvements were made in restoring inverse-filtered data. One is to impose an upper bound constraint (in the form of a tapered window) on the Fourier spectrum most degraded by noise and other errors. This provides stability, and the window can be used on the starting estimate and all succeeding iterations. Errors in the low frequency spectrum (below the cutoff radius) are determined and corrected by a slight modification of the restoration procedure described in this paper. Results are shown for simulated CO₂ interferograms, experimental interferometer data, and experimental IRAS data.

© 1990 Optical Society of America

Fast algorithm for implementing the minimum-negativity constraint for Fourier spectrum extrapolation. Part 2

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