Image reconstruction and modeling

Popular image reconstruction methods include maximum likelihood and maximum entropy. There is a unique maximum-likelihood estimator (MLE) of the X-ray sky brightness distribution given a distribution of photons and a point spread function. It is calculated by a procedure known as the Lucy-Richardson algorithm in astronomy, and as the EM Algorithm in statistics and other fields. This algorithm is guaranteed to approach the MLE with each iteration. Maximum entropy reconstruction, on the other hand, has a free parameter (effectively the S/N of the dataset, often hidden from the user) and poorly defined stopping rules (too many interations hurt rather than help). It is a Bayesian method.
P. Broos informs us there are two sources of PSFs for this effort, but warns of two problems: First, the aspect solution (or artificial +/- 1 pixel blurring introduced by the CXC pipeline) will create a slighter broader PSF than provided by models of the Chandra mirrors. This problem might be ignored off-axis or for cases where the signal is not extremely strong.
MARX simulations. One might use a Gaussian rather than unresolved source model, but there is no recommended sigma. For an accurate reconstruction, particularly off-axis where the PSF is assymetrical, it is necessary to rotate the MARX PSF. See Scott Koch for techniques to do this.

CIAO program mkpsf. The PSF libras needed by mkpsf are discussed here and are installed at Penn State at /bulk/raid2/axaflib/software/ascds/caldb/acis/cpf /2dpsf/. The program interpolates between available PSFs and rotates the result to match your field.

IDL routines maxlik.pro and maxent.pro are available. Here we first make an appropriate point spread function, and then run the deconvolution routines:

G. Chartas provides an IDL script that extracts a subimage and performs an maximum likelihood deconvolution using the appropriate simulated PSF. For two or more observations, the resulting deconvolved images are aligned and coadded.
Create an ASCII file with exposure times, X and Y locations of the source, source offsets in Z and Y (in arcmin), and roll angle. These quantities are found in the FITS header of the events file. Example of an entry in file "infile1": Copy the following IDL programs and parameter files into your directory: xdeconv.pro, xdeconv.par, and par_get.pro. Edit the parameter file xdeconv.par with a UNIX editor or with Run the program: Note: Neither maximum likelihood nor maximum entropy may be very effective for restoring very diffuse structures where the PSF contribution is negligible.

A. Ptak has developed a sophisticated two-dimensional image modeling procedure, XIMGFIT. It permits the use to specify any combination of analytical spatial structures (e.g. elliptical Gaussians, constant backgrounds), for which parameters are determined by least-squares minimization. A point spread function can be specified for deconvolution, user models can be added, model simulation and subtraction are provided. The code is written in Python and Tcl, and uses a genetic algorithm for efficient minimization and FFTs for convolutions. A comprehensive manual with examples is available.