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Paper: Image Restoration Using the Damped Richardson-Lucy Iteration
Volume: 61, Astronomical Data Analysis Software and Systems III
Page: 292
Authors: White, R. L.
Abstract: The most widely used image restoration technique for optical astronomical data is the Richardson-Lucy (RL) iteration. The RL method is well-suited to optical and ultraviolet because it converges to the maximum likelihood solution for Poisson statistics in the data, which is appropriate for astronomical images taken with CCD or photon-counting detectors. Images restored using the RL iteration have good good photometric linearity and can be used for quantitative analysis, and typical RL restorations require a manageable amount of computer time. Despite its advantages, the RL method has some serious shortcomings. Noise amplification is a problem, as for all maximum likelihood techniques. If one performs many RL iterations on an image containing an extended object such as a galaxy, the extended emission develops a ``speckled'' appearance. The speckles are the result of fitting the noise in the data too closely. The only limit on the amount of noise amplification in the RL method is the requirement that the image not become negative. The usual practical approach to limiting noise amplification is simply to stop the iteration when the restored image appears to become too noisy. However, in most cases the number of iterations needed is different for different parts of the image. Hundreds of iterations may be required to get a good fit to the high signal-to-noise image of a bright star, while a smooth, extended object may be fitted well after only a few iterations. Thus, one would like to be able to slow or stop the iteration automatically in regions where a smooth model fits the data adequately, while continuing to iterate in regions where there are sharp features (edges or point sources). The need for a spatially adaptive convergence criterion is exacerbated when CCD readout noise is included in the RL algorithm (Snyder, Hammoud, & White, 1993, JOSA A , 10 , 1014), because the rate of convergence is then slower for faint stars than for bright stars. This paper will describe a new image restoration iteration that dramatically reduces noise amplification while retaining the good characteristics and efficiency of the RL method. The method is based on a modified form of the Poisson likelihood function that is flatter in the vicinity of a good fit. The resulting iteration is very similar to the RL iteration, but with a new spatially adaptive damping factor that prevents noise amplification in regions of the image where a smooth model provides an adequate fit to the data; thus, I call this the damped RL iteration . The damped iteration converges as fast or faster than the RL method. Results will be shown for both simulated data and Hubble Space Telescope images.
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