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A simulated globular star cluster for the WFC of HST before the servicing mission has been used as a test case. The image was retrieved from a set of test data created for image restoration work in the ST ScI anonymous FTP area.
The image contains 470 stars with approximately the maximum and minimum
pixel values (2500 and 10 DN, respectively),
covering a range of magnitude of 6. A standard
(not subsampled) PSF is used. The image size is 256256 pixels.
Convergence speed is expressed in terms of the number of FFTs needed to obtain
the final MEM solution. The number listed in Table 1 is decomposed
into two factors as (the total number of iterations) (the number of
FFTs per iteration). cmem is the latest version of my MEM program.
Values of
and 3000 correspond to the most frequent model
updating and no model updating, respectively. Comparisons have been made
with the lucy task (Richardson-Lucy method) in the
IRAF/STSDAS package and MEM/MemSys5, a commercial software package.
From the table we can see that the convergence is speeded up dramatically because of model updating. With this technique, cmem converges fastest.
In Fig. 2 ``Difference'' gives the stars' magnitudes estimated from the true image (``True magnitude'') minus those from the restored image. The radius for aperture photometry is 3 pixels. Without errors in photometry, the points would lie on a horizontal line as additionally drawn in each plot. Without bias, the points would symmetrically distribute below and above the line.
In Fig. 2 we see that the restored image C by lucy
exhibits quite good linearity in photometry. cmem with model updating
(A) is comparable to lucy except near the fainter end of the
magnitude range where cmem shows some systematic errors. The extreme
differences between A and C are and
mag.
The result in the case of no model updating (Fig. 2B) is
noticeably worse. The result from MEM/MemSys5 historic (D) is
worse still. The rather large amount of offset in D is due partly to
the lack of total power constraint in the program. (The total power errors
correspond to offsets of 0.011, 0.017, 0.035 and 0.12 in A, B,
C, and D, respectively.) The extreme differences are /
mag between B and C, and
/
mag between D and
C. Intermediate values of differences are scattered to a much greater
degree compared with those between A and C.