6 Conclusions

In this paper we report the development of a Bayesian algorithm with entropy prior (FMAPE) that uses a space-variant balancing hyperparameter. In order to define the hyperparameters, we have used a segmentation technique based on the wavelet decomposition and artificial neural networks. We have found the Kohonen self-organizing maps quite suitable for clasification of astronomical objects, although it is important that the network implementation be carefully done with regards to plane normalization and randomization of the input vectors.

The combined use of the FMAPE algorithm and the segmentation allows us to obtain different degrees of smoothing in different regions of the image. This implies a variation in resolution in the reconstruction that can prevent amplification of noise while maintaining the photometric accuracy in the whole image (background, diffuse objects and stars).

In astronomical image reconstruction there are two basic requirements: 1 - the recovery of the object shape and 2 - the recovery of the correct brightness of the objects without amplifying the noise. The second requirement is largely related to the correctness of the residuals between the data and the projection of the solution. The method described here goes a long way towards satisfying those two needs.

We would like to conclude by indicating that we continue working on the better understanding of what the FMAPE requires from the segmentation and from the hyperparameter assignment steps with a view to provide a reliable method for reconstruction of images with a wide range of intensity values. Since there is no proof of uniqueness of the solutions obtained by the FMAPE with space-variant hyperparameters, we also need to explore the effects of using different starting images, different initial values for the hyperparameters and updating schemes.

Acknowledgements

We would like to thank Jean Luc Starck for the use of his wavelet decomposition package for this research. We also would like to thank an anonymous referee who made a careful revision and whose comments had helped us to increase notably the quality of this paper. This work was supported in part by the DGICYT Ministerio de Educación y Ciencia (Spain) under grants Nos. BP94-0905, BP95-1031-A and PB97-0903. Partial support was also obtained from the D.G.U. Generalitat de Catalunya and from the Gaspar de Portola Catalan Studies Program of the University of California and Generalitat de Catalunya. J. Llacer's work is supported by the U.S. Department of Energy under contract No. DE-AC03-76SF00098.