Results

To illustrate the use of the algorithm to control noise amplification, we have reconstructed a 256256 pixels planetary nebula simulation for the PC camera prepared by R. Hanisch at ST ScI. The PSF has a similar radius to the ring of the planetary nebula. The images combine background, a diffuse object, and several bright stars. Fig. 1 (left) shows the raw image.

We have reconstructed the raw image using the FMAPEVAR algorithm with a space variant parameter. We set for the background, for the diffuse planetary nebula and a high value for the bright stars of allowing the algorithm to reach maximum likelihood in the stars.

Fig. 1 (right) shows the result of this three-channel restoration. We obtained a smooth background, a well reconstructed nebula, and sharp images of the stars. We suppressed the noisy amplification in the background and in the nebula, while fully developing the images of the stars.

In order to compare the new algorithm with the constant approach and to study the photometric properties of the restoration, we made two restorations of the raw image using a constant value of and a constant respectively. Since this is a simulated image, we can quantitatively study the restorations with respect to the true unblurred image. For the restorations, we computed the percentage of energy recovered in a 77 box located in the background, the ring, the central star and the brightest star.

Fig. 2 shows the results. The restoration with constant only has correct photometry for the background. The restoration with constant performs well in the background and in the ring (although the background is too noisy in the restoration) but the photometry is poor in the stars because the stars are not properly developed. However, the restoration with variable in three channels performs much better in the stars, while maintaining the quality the photometry in the ring and the background. We obtained an accuracy better than 95%(or 0.05 mag.) for the whole image. We adjusted the values of the variable approximately without any local cross-validation or segmentation. Thus, by using an optimum adjustment it is possible to obtain even better photometry.