Restoration Methods Evaluated

The following restoration methods were evaluated. The central 200200 region of the restored images are shown in Fig. 3 for selected results.

1. Minimum norm. This technique is a linear constrained least squares method which minimizes the norm of the solution. It is solved using the method of Lagrange multipliers (Andrews and Hunt 1977). A reciprocal Lagrangian multiplier, , can be adjusted to control the smoothness of the solution or to satisfy chi-squared test for the solution. Results are evaluated with = 0.1, 0.01, and 0.001.

2. Five iteration minimized difference from the previous iteration. This is a constrained least-squares method which minimizes the norm of the difference of the solution from a trial solution (Twomey 1963). A reciprocal Lagrangian multiplier, , controls the amount of constraint. In our solution we have used the raw blurred image as the initial trial solution and performed 5 iterations. After each iteration, a new trial solution was set to the results of the previous iteration with a positivity constraint applied. Results are evaluated with = 0.1, 0.01, and 0.001.

3. Richardson-Lucy method. This technique is the Richardson-Lucy (R-L) maximum likelihood solution for Poisson statistics (Richardson 1972, Lucy 1974). Results were evaluated after 100, 300 and 1000 iterations.

4. Richardson-Lucy/Snyder. This method is the R-L method with the Snyder modification for non-Poisson read-out noise (Snyder 1990; Snyder, Hammoud, &White 1993). Results were evaluated after 100, 300 and 1000 iterations.

5. Maximum entropy method. This is the Image Reduction and Analysis Facility (IRAF) maximum entropy method (MEM) developed by Wu (1994). The results were evaluated after 100, 200 and 400 iterations.

6. Hybrid method. This approach minimizes the norm of difference of the restored image from a trial solution (Twomey 1963). The trial solution was selected as the results of 1000 iterations of the R-L/Snyder method. Results are evaluated with the reciprocal Lagrangian multiplier = 0.1, 0.01 and 0.001.