4 Application to ISOCAM data

4.1 ISOCAM point source reconstruction

   

Table 2: Flux estimation from MVM and MVM + deconvolution (MVMD)

Real Flux	MVM Flux	MVMD Flux	MVM Error	MVM Error (%)	MVMD Error	MVMD Error (%)
7	7.35	5.96	5.00	14.82	0.35	1.03
12	12.66	12.62	5.51	5.21	0.66	0.62
17	17.57	18.41	3.37	8.30	0.57	1.41
22	21.68	23.42	1.41	6.46	0.31	1.42
27	26.18	28.43	3.00	5.31	0.81	1.43
32	30.74	33.44	3.93	4.51	1.25	1.44
37	35.28	38.45	4.64	3.93	1.71	1.45
42	39.91	43.46	4.95	3.49	2.08	1.46
47	44.60	48.47	5.09	3.13	2.39	1.47
52	49.24	53.48	5.29	2.85	2.75	1.48
57	53.93	58.49	5.37	2.61	3.06	1.49
62	58.67	63.49	5.36	2.41	3.32	1.49
67	63.42	68.50	5.33	2.24	3.57	1.50
72	68.14	73.51	5.35	2.09	3.85	1.51
77	72.93	78.51	5.27	1.96	4.06	1.51
82	77.70	83.52	5.23	1.85	4.29	1.52
87	82.47	88.52	5.20	1.75	4.52	1.52
92	87.24	93.53	5.16	1.66	4.75	1.53
97	92.02	98.53	5.13	1.58	4.97	1.53
102	96.84	103.5	5.05	1.50	5.15	1.53

Figure 3: Abell 1689: left, ISOCAM source detection (isophotes) overplotted on an optical image (NTT, band V). The ISOCAM image is a raster observation at 7 $\mu$m. Right, ISOCAM source detection using the PSF (isophotes) overplotted on the optical image. Compared to the left panel, it is clearly easier to identify the detected infrared sources in the optical image

A simulation was performed in order to analyse how well the flux is estimated. A point source (using ISOCAM 6 arcsec lens PSF) was simulated, with a constant background (value of 100), and uniform Gaussian noise (sigma = 1). The integrated flux of the sources varies from 7 to 102. Table 2 gives the results of this simulation. The first column gives the real flux, the second column the flux found using MVM, and the third column the flux found using MVM plus the deconvolution (MVMD). The photometry is clearly improved using MVMD. Another aspect of MVMD is that the error is relatively constant, whatever the flux of the source.

Figure 4: XMM model simulation. Upper left, position of the point sources. The flux is the same on each radial line. Upper right, simulated data with Poisson noise. The background is $\sim 0.1$ counts/pixel. Bottom left and right shows respectively the result of the detection by the MVM with and without the PSF model

4.2 Abell 1689 ISOCAM data

Figure 3 (left) shows the detections (isophotes) obtained using the MVM method without deconvolution on ISOCAM data. The data were collected using the 6 arcsec lens at 6.75 $\mu$m. This was a raster observation with 10 s integration time, 16 raster positions, and 25 frames per raster position. The noise is non-stationary, and the detection of the significant wavelet coefficients was carried out using the root mean square error map $R_\sigma(x,y)$ by the method described in Starck et al. (1999). The isophotes are overplotted on an optical image (NTT, band V) in order to identify the infrared source. Figure 3 (right) shows the same treatment but using the MVM method with deconvolution. The objects are the same, but the photometry is improved, and it is clearly easier to identify the optical counterpart of the infrared sources.