2 The data set

2.1 The observations

The tools we describe further were extensively tested on many sets of data in the framework of signal processing and communication. Their ability to give a pertinent solution to Eq. (1) was studied taking into account various conditions (Cardoso et al. 1999; Pajunen & Karhunen 2000). So, there is no point to give in this paper experiments on simulated data.

We chose to test BSS tools on HST images of the Seyfert radiogalaxy 3C 120. This object displays a one side radio jet, which has been optically identified (Lelièvre et al. 1994). The best HST observations were made with the Wide Field Planetary Camera 2 (WFPC2) through the filters F547M, F555W, F675W, and F814W by J. Westphal, on July 25th 1995. The exposure characteristics are given in Table 1.

 

 

Table 1: The characteristics of the studied images

Filter	Color	Exposure (s)
F547M	V1	$2\times 1100$
F555W	V	$2\times 1000$
F675W	R	$2\times 1100$
F814W	I	$2\times 1100$

The transmission profiles of the filters are drawn in Fig. 1.

Figure 1: The four filters used: F547M (full line), F555W (dashed line), F675W (dot-dashed line) and F814W (dotted line). The galaxy spectrum in the nuclear part (Oke et al. 1980) is superimposed on these profiles (dashed-dotted line)

The spectrum obtained by Oke et al. (1980) by a spectrophotometer is also plotted. F547M covers two strong [OIII] lines. F555W recovers F547M, the other part includes only the continuum. F675W covers H$_{\alpha}$ and F814W [OI] and [SIII] lines. Linear combinations of the observed images can display specific physical phenomena. We can determine their best combinations by applying Spectral Energy Distribution (SED) methods (Bolzonella et al. 2000). With SED the photometric information is transformed into physical parameters using spectral models. But for 3C 120 we have a mixing between stellar distributions, non-thermal emission from the nucleus and light from the ionized regions, and SED does not take into account this mixing. We expect from BSS to disentangle these various phenomena.

2.2 The data preparation

The central WFPC2 observations correspond to images of $800 \times 800$ pixels. The pixel size is $0.0455''\times 0.0455''$. We have extracted the central part of $256\times 256$ pixels, corresponding to a region of $11.6^{\prime\prime} \times 11.6^{\prime\prime}$.

The observations were made with a CCD receiver. The detector noise is low, and the photon noise is dominant in the galaxy region. As the noise is not stationary Gaussian, a generalized Anscombe transform (Murtagh et al. 1995) allowed us to stabilize its variance. A pixel value v is transformed by the relation:

$$% t={2\over \alpha}\sqrt{\alpha v+{3\over 8}\alpha^2+\sigma^2-\alpha g}$$ (2)

where $v=\gamma+\alpha n$, $\gamma$ is a Gaussian random variable, corresponding to the read-out noise of mean g and variance $\sigma^2$, while n is the number of photoevents in the pixel, $\alpha$ is then the gain of the CCD. $\gamma$, g and $\alpha$values are given in the HST/WFPC2 handbook.

For each resulting image, the background value is estimated and subtracted. Then the images (Fig. 2) can be considered clean enough to be processed by BSS algorithms.

Figure 2: HST/WFPC2 images of the radiogalaxy 3C 120 respectively obtained with the filters F547M, F555W, F675W and F814W. The images were processed in order to stabilize the noise variance

We note that the images were not linearly transformed. Roughly speaking we took their square roots (Eq. 2). By this transformation we destroyed the hypothetical linearity between the images and the sources as written in Eq. (1). We can imagine that this Eq. (1) constitutes only a working hypothesis. With the transformation given by Eq. (2), the dynamical amplitude is then reduced and the nucleus plays a smaller part in the computations. We do not search for a perfect photometric model, but we want to exhibit coherent image structures.