16.5 Implementation of WIPE at IRAM

In this section we describe the successive steps of the image reconstruction process as it is implemented now in the MAPPING program included in the IRAM software. For more information on this program, the reader is invited to read the last version of the Mapping CookBook.

The first step of the image reconstruction process is to define the object space $H_o$. This space is characterized by two key parameters: the extension $\Delta x$ of its field, and its resolution scale $\delta x = \Delta x/N$ (see Fig. 16.2). The procedure wipe_init is used to set these parameters properly.

The frequency coverage to be synthesized  $\mathcal{H}_s$ is defined with the aid of the procedure wipe_aper. This tool provides an interactive way of fitting an ellipse over the experimental frequency coverage generated by the experimental frequency list  $\mathcal{L}_e$ (see Fig. 16.4).

Once  $\mathcal{H}_s$ has been defined, the procedure wipe_beam is ready for computing the neat beam $\Theta _s$, as well as the dirty beam $\Theta_d$. The latter plays a key role in the action of the convolutor  $A^*_E A^{\vphantom{*}}_E$, while the Fourier transform of the former is involved in the definition of the data vector  $\Psi_{\! d}$ (cf. Eq. 16.9 and 16.10).

The last step in the image reconstruction process concerns the neat map. It is implemented in the wipe_solve command. Before the initialization of the reconstruction, the dusty map  $A^*\Psi_{\! d}$ is computed, and an optional support can be selected (this support plays the role of the clean box of CLEAN). As WIPE can be slow when reconstructing large images, it can be initialized with a few CLEAN iterations to quickly build a first object representation space $E$. When switching to WIPE, the program starts by optimizing the solution provided by CLEAN with the corresponding support. Then, at each iteration of WIPE, the support grows, and for a given and fixed object representation space $E$, the normal equation 16.16 is solved by using the conjugate gradient method, which also provides the condition number $\kappa _E$ of $A_E$. When leaving WIPE, a final smoothing of the current object support is performed, removing (through an appropriate morphological analysis) the details of the reconstructed image smaller than the resolution limit of the reconstruction process. The final reconstructed image $\Phi _E$ is the function minimizing the objective functional 16.13 on that support.

The control of the robustness of the reconstruction process is performed through an additional step with the wipe_error command. This procedure computes with a fine accuracy the final condition number $\kappa _E$, as well as the eigenvalues and the critical eigenmodes of  $A^*_E A^{\vphantom{*}}_E$. One of the aims of this last step is to check that the features present in the reconstructed image are not artefacts. This can be done by comparing these features with those of the critical eigenmodes. When there exists a certain similitude (between these features), it is then recommended to restart the process with a lower resolution, so that the final solution be more stable and reliable.