Results

Table 1 summarizes some distance measure results. These measures were computed both for the full image and for a 50 pixel sq. region centered on the star cluster, dominated by crowded star images. Thus, they are sensitive to different image properties. The full image measures asses the global goodness-of-fit, but in the particular image under study they are strongly sensitive to the sky background fit. The crowded region measures, on the other hand, are more sensitive to how well star images were fitted. The highest peak value is a measure on how close the brightest star's peak approached the truth value, and so it is also a goodness-of-fit measure for star images.

Algorithms are arranged in Table 1 in increasing order of execution speed. All algorithms were iterated up to the point where at least one of or just started to decrease. Most often this happened for the full image's , which is sensitive to spurious noise peaks introduced in the sky background. The exception is the Iterative/Recursive algorithm, which was run arbitrarily for 5 levels of recursion and 3 iterations at each level. -CLEAN was iterated to the level.

Visual inspection alone showed that the three algorithms: R-L, MEM0, and ILS+ are capable of very similar results. This is confirmed by the similar values for them. The solution obtained by the ILS+ algorithm, being a least-squares one, had the highest , as expected. R-L produced a somewhat better solution than MEM0, but at a considerable speed penalty. -CLEAN produced not so good results as the methods above, mostly because of the large PSF residuals left on the CLEAN+residual map. The RILS results show that inclusion of a spatially-adaptive smoothness constraint in the least-squares iteration actually decreased restoration quality.

Results also suggest that the ILS+ iteration is the most robust against PSF mismatches, followed by R-L and MEM0, which showed very similar degradations. -CLEAN was the most sensitive to PSF errors.

Figure 1 depict typical results from photometry with a small aperture. Results were also obtained for a subset of isolated (non-crowded) star images, using larger apertures up to pixel. This large-aperture data show that systematic zero-point shifts are a common feature of restored stellar images. Only the R-L iteration showed negligible zero-point shifts; all other algorithms showed mag shifts to either side of the zero-residual locus.

Restoration with PSF error led to an increased scatter and more confusion. Besides, large-aperture measurements showed measurable () slopes in R-L and MEM0 residuals. ILS+ showed only a slight increase in zero-point shift.

Comparison of results in Figure 1 with the ones in Figure 2 points to the existence of a trade-off between a particular algorithm's linearity, and its ability to control high-frequency noise buildup. Extreme cases are the Iterative Inverse and IR algorithms, which are very linear but do not control sky background noise, and RILS+, which produces very smooth backgrounds but at the cost of losing mag of light at the faint levels in this particular test image. R-L, MEM0 and ILS+ seem all to offer a reasonable compromise among these extremes.

Preliminary results from an ongoing study of photometric errors from aperture photometry in restored images suggests that restoration by R-L, MEM0 and ILS+ does not degrade the random error level in large-aperture photometry of isolated stars. There is marginal evidence that restoration may even decrease the random error in faint stars. This point needs more study, and of course a detailed comparison with sophisticated PSF-fitting techniques (Stetson 1993) is fundamental to answer the question: should stellar photometry be performed in restored or unrestored images ?