7 Conclusion

We have shown that the source detection can be combined with a deconvolution when using wavelet based methods such as the Multiscale Vision Model. This leads to the reconstruction of deconvolved objects. The main advantages of this approach are:

• Faint extended objects can be detected as well as point sources;
• The analysis does not require background estimation. (We know that if the background varies spatially, its estimation becomes a non-trivial task and may produce large errors in object photometry);
• Objects are easier to identify in the deconvolved map;
• Morphological parameters (gallaxy ellipticity and so on) are more accurate;
• Since each object is deconvolved separately, a spatially variable point spread function can easily be taken into account;
• Very large images can be deconvolved.

We may note that observing, in practice, requires consideration of issues prior to, or beyond, what has been considered in this work. Examples include: extensive detector imperfections, the managing of multiple wavelength observations, observations requiring knowledge of physical phenomena. All of these produce observational errors, which we have not considered. Our aim has instead been to futher deconvolution and detection technologies. Towards this end, we have considered a wide range of practical observing cases, but certainly not all.

The software used in this paper is based on that described in Starck et al. (1998) and is implemented in the MR/1 multiresolution analysis environment available through the website http://www.multiresolution.com

Acknowledgements

We would like to thank Dan Harris, CfA, for the simulated Chandra data. This work was partially supported by U.S.A. National Science Foundation grant DMS 98-72890 (KDI).