Tricky stuff

Turning now to the tricky instrumental stuff, what has been solved since the last meeting? First, I'll discuss instrument-related problems, then I'll turn to algorithms.

PSF poorly known: Solved.

Either find PSF by blind deconvolution or by using one of the new PSF prediction codes (Redding).

Under-sampling of focal-plane: Not much said here.

Signal-to-noise ratio: Solved.

Strangely, this was a big worry three years ago. I think that this represents a set of then-unresolved concerns over the effect of the PSF halo on imaging weak sources. We now know that for weak, point-like sources the answer is to simply increase the observing time proportionately to the loss in Strehl ratio. For complex sources, we know that the answer is much more complicated.

Cosmic rays: Solved.

The signature of cosmic rays is that no PSF halo is seen. Working algorithms to exploit this fact exist (Adorf). Ironically, it seems that this signature will disappear after the servicing mission (Biretta).

Readout noise: Solved.

Several algorithms now account for readout noise in the formal description of the measurement equation (Núñez and Llacer; Snyder).

Field rotation: Solved.

Joint deconvolution of several epochs does the trick. The coupling with undersampling must still be a problem, though it was not discussed as such.

Object color variations: Not solved.

Since the PSF changes with wavelength, objects of different colors observed with a wide-band filter will have different PSFs. This seems to have vanished from consideration.

Photometry bias: Solved.

Some of the deconvolution algorithms can be forced to have less bias (Lucy) or one can use a photometry package (e.g., DAOPHOT) directly (Stetson).

Spatially variant PSF: Not solved.

Some progress in understanding but no well-used working algorithms. (Hunt and McNown; Adorf). From my experience tackling an SVPSF in radio interferometry, I would advise investigators to look at a number of different approachs carefully before implementing any one method. The computational issues tend to dominate and one has to think carefully about how to best solve the relevant equations. In radio interferometry, although the equations become more tractable by embedding the imaging in a three-dimensional space, the optimum computational solution comes from using local approximations to the PSF.

Null-space stuff, e.g., mottling in RL: Solved.

The RL algorithm produces mottled images if allowed to iterate too long. There seem to be a number of ad hoc ways around this problem (White). CLEAN also produces strange stuff in the null-space (i.e., unsampled regions of Fourier space) but the main effect seems to be easily-recognizable stripes in the image plane.

Performance limits: Solved.

The Cramér-Rao bound work is very interesting (Gonsalves). Also, the incorporation of the error analysis into deconvolution looks promising (Bouyoucef, Roques, and Fraix-Burnet).

Multi-channeling: Solved.

Both MEM and RL can handle multiple constraint images.