X-ray image filtering, and deconvolution

The galaxy cluster A2390 is at a redshift of 0.231. The first image above was obtained with the ROSAT X-ray spacecraft. The resolution is one arc second per pixel, with a total number of photons equal to 13506, based on an integration time of 8.5 hours. The background level is about 0.04 photons per pixel.

It is obvious that the image cannot be used directly and that some processing is required before any analysis. The standard method consists of convolving the image with a Gaussian. The second image above shows the result of doing this. With much residual noise, it is difficult to see any structure.

The final image above shows the image after wavelet filtering. Faint X-ray emission structures are seen, related to gravitational amplification phenomena obervable in the visible wavelength range.

The Beta Pictoris image (first image) was obtained by integrating on-source for 5 hours using a mid-infrared camera (TIMMI, on the ESO 3.6m telescope at La Silla, Chile). The raw image has a peak signal-to-noise ratio of 80. It is strongly blurred by a combination of seeing, diffraction (0.7 arcsec on a 3m-class telescope) and additive Gaussian noise. The initial disk shape has been lost following convolution with the point spread function. Thus we need to deconvolve the image to get the best information about the object - the exact profile and thickness of the disk - and subsequently to compare results to models of thermal dust emission.

Noise filtering alone will show up the disk quite well. For detection of faint structures in the disk, one can calculate that the use of such filtering on this image provides a gain of observing time of a factor of around 60. The deconvolved image (second image above) shows that the disk is extended at 10 microns and on close examination can be seen to be asymmetrical. The multiscale entropy method is more effective for regularizing than other standard methods, and leads to good reconstruction of the faintest structures of the dust disk.

To probe further

Image and Data Analysis: The Multiscale Approach, J-L Starck, F Murtagh and A Bijaoui, Cambridge University Press, 1998.