Abstract

A new means of bringing about more rapid and complete convergence of the nonlinear equations that implement the minimum-negativity constraint by summing over a modified spatial function (instead of only the negative values) was discovered. This improved spatial function was found by seeking a trend in succeeding major iterations of the equations that may be extrapolated into a future iteration. This new function replaced only those values between the negative regions that were previously set to zero. It was noted that this modified spatial function closely approximated the one given by Fourier transforming the true high-frequency values, which is evidently the reason for its success. A constant ratio between the sum of the new function that is substituted for the zeros and the sum of the negative values had to be maintained, however, to prevent divergence in the solution of the equations. The considerable advantage entailed by this new procedure is that convergence may be obtained for even the recalcitrant data with approximate procedures that use only the fast Fourier transform to perform the major calculations. Results are shown for field-widened interferometer data of 32K points and both simulated and experimental IRAS data of 64 × 64 pixels.

© 1988 Optical Society of America