## A SUPer REsolution Mapmaker for Extended emission

SUPREME is a generic name for mapmakers for extended emission based on a realistic physical instrument model and regularized inversion. A first development has been performed by T. Rodet et al IEEE 2, 5 (2008) for the infrared slit spectrograph on board the Spitzer Space Telescope. F. Orieux et al A&A 539, A38 (2012) have proposed the first super-resolution mapmaker for the SPIRE instrument of the Herschel observatory, tested for simulated and real data. The current version of SUPREME, developed by H. Ayasso et al (hal-00765929), is based on an unsupervised Bayesian approach with enhanced beam and offset models. B. Hasnoun, member of the Integrated Data And Operation Center at IAS (IDOC), has exported the original Matlab code to Java and prepared a HIPE plugin.

SUPREME is an ambitious pluridisciplinary research projet for map-making where several research codes have been already developed. For instance, the estimate of hyperparameters and instrument parameters has been presented with a Bayesian framework by F. Orieux et al A&A 549, A83 (2013). Moreover, Ayasso et al proposed an unsupervised mapmaker for point and extend sources mixture. Furthermore other improvements are expected in the future (1/f corrections, use for other instruments, …).

### Model of the data

In a map-making problem, one tries to restore the sky $x$ given several observations $y$ and instrument model $H$. The forward model is written as

$$y = Hx + n + o$$

where $n$ is the noise (including error modeling) added to the data and $o$ an offset. The instrument model $H = UC$ is a linear operator containing $U$ the pointing matrix and $C$ is a convolution matrix accounting for the instrument optics, the bolometers and the electronics.

### Inversion

SUPREME tackles the map-making question in an inverse problem framework. The instrument model, which must be as realistic as possible, contains convolutions and low-pass systems. The inverse problem is ill-posed and this is particularly true when super-resolution is intended. Thus, a naive inversion, such as a least-squares solution, would lead to an unacceptably noisy and unstable solution.

A usual class of solutions relies on regularization, i.e. the introduction of prior information on the unknown object $x$ to compensate for the lack of information in the data. A consequence of regularization is that reconstruction methods are specific to a class of sky maps, according to the introduced information (i.e. extended emission or point-sources).