1. Jean Ballet, CEA Saclay
GSFC, 31 May 2006
All-sky source search
Aim: Look for a fast method to find sources over the whole sky
MR_FILTER
Optimal filter
Combining energy bands
Iteration

2. All-sky source search. MR_FILTER
MR_FILTER is an all-purpose wavelet algorithm developed at Saclay by J.L. Starck.
Works on cartesian images.
Special mode for Poisson statistics
Output is a smoothed image, keeping only significant positive structures
2nd step to locate excesses (SExtractor)
Accepts background model in input
Currently used as place holder in catalog generation

3. All-sky source search. Optimal filter
Generalization of the idea of convolving an image with the (known) PSF, to account for a structured background
Filter is PSF/(1+BKG) in Fourier space
Works on cartesian images (same filter over entire image)
Accounts for Poisson statistics
Sky partitioned into 11 pieces (2 CAR in Galactic plane up to +/- 10°, 4 CAR or AIT at mid-latitudes up to 45°, 2 ARC around the poles above 45°). Avoids too much geometrical distortion, and adapts the filter to local conditions

4. Optimal filter 2
Variance is computed at each point, knowing the background shape (use number of photons from the image under the filter when larger). But not Gaussian distribution.
Signal / dispersion at each point is converted into an effective gaussian significance depending on the local density of counts and the filter shape (same principle as is used in wavelet methods for each coefficient). Entire image can be converted assuming background is locally flat (then same conversion everywhere)

5. Putting energy bands together
Simplest solution is to run algorithm over each energy band separately and merge source lists.
Merging source lists
Estimate position error. In the checkout 3 simulation, it was found that the formula 1.8 HWHM / significance + pixelsize / 2.5 provides a reasonable estimate of the (1 σ) position error, where HWHM is the half width at half maximum of the PSF in the band
Start from high energy (best PSF), identify with lower energy sources using tolerance 3 times larger, keep only unambiguous associations. Combine positions and errors using as weight 1/sigma^2, where sigma is the position error itself.

6. All-sky source search. Iteration
Methods based on filtering have trouble finding weak sources in the wings of bright ones (because they generate ripples around sources).
The solution is to iterate. After the bright sources have been detected, they can be modelled and entered into the diffuse emission.
Start with merged source lists
Feed to likelihood pipeline, to weed out non significant sources
Run the band likelihood pipeline, to get accurate flux in each band even for sources which do not have a power law spectrum
Run gtmodelmap on the large images used by the source detection methods, readjusting the diffuse emission to account for the bright sources
All those steps take quite long

7. All-sky source search. Comparison
Energy band from 100 to 300 MeV, toward North Galactic pole
gtmodelmap on the basis of the result of the band likelihood pipeline (sources only)
Map with coordinate grid is with MR_FILTER source list
Map without coordinates is with optimal filter source list
Differences in source position, and a few faint sources

8. Iteration: MR_FILTER
Energy band from 3 to 100 GeV, toward (l,b) = (90,0) in the Galactic plane.
Size of the image is about 60 x 20°
Same color coding before and after iteration
Many excesses not confirmed by likelihood, bright sources leave secondaries

9. Iteration: optimal filter
Energy band from 3 to 100 GeV, toward the Galactic center.
Size of the image is about 40 x 20°
Same color coding before and after iteration (0 to 5 sigma)
Very bright sources removed already, fainter sources go away nicely

10. Putting energy bands together 2
A better solution is to add log(likelihood) values (before applying threshold).
Galactic center region, 40 x 30°
4 bands
Several scales are visible
Transform significance maps into probability, add log(probability), correct the distribution for the number of bands, transform back to significance
The broad PSF at low energy adds a complication. A true source can induce false detections in its vicinity (via its low energy wings). Therefore do it only after all 1st pass sources have been removed

11. Source detection studies
Jean Ballet, CEA Saclay
GSFC, 31 May 2006
Source detection studies
Investigated 2 imaging based methods
MR_FILTER improved. Works well (in combination with SExtractor), but does not provide source significance.
Optimal filter works all right. Finds fewer sources (hopefully fewer spurious sources), but returns source significance.
Energy band combination is promising
Is iteration worth the cost in computing time ?