ERA-Net_ASTRONET Call 2008_Compressed Sensing for Herschel (CSH)

The Herschel satellite will be launched in early 2009 and - being the biggest space telescope ever built - it will explore the far-infrared universe with unprecedented sensitivity. Operational and power budget constraints severely limit communication with the satellite and result in an allowed data rate that is typically 16 times smaller than the raw science output of the PACS photometer. For this reason, relatively drastic measures have been included in the on-board software, involving lossy steps like averaging as well as lossless data compression techniques. These data processing steps have a negative side-effect: Due to the averaging process the data obtained in the continuous scanning mode are significantly degraded in both spatial resolution and signal quality. However, recent advances in mathematics and information theory have given rise to a technique termed "Compressed Sensing", which offers the potential for restoring the full capacities of the PACS photometer while achieving the high compression factor required to downlink the data. The principle behind is to already combine the compression step during measurement. Compressed Sensing uses the mathematical concepts of sparsity and incoherence to accurately reconstruct data that have been undersampled by the measurement process. The sensing step in such a Compressed Sensing scheme consists of a projection onto incoherent measurement ensembles. For this purpose we have recently shown that the noiselet transform fulfills the specific requirements of the Herschel/PACS mission. The sensing algorithm is the smallest component, yet it needs careful attention as it has to be added as a separate compression mode to the flight software. The advantage of Compressed Sensing is that it is perfectly suitable for a space experiment because it is simple yet very efficient and it runs with minimal CPU load and memory requirements. Reconstruction of the original data can be achieved by solving a convex optimization problem. Although Compressed Sensing is a very young field of research, a number of algorithms are already available for this purpose. We have successfully developed an approach based on iterative thresholding, in which we can take additional properties of the detector and the observed target into account, without needing to modify the sensing algorithm. That way we can still improve on the reduction scheme even beyond Herschel`s expected lifetime. By adding Compressed Sensing to the Herschel/PACS mission we provide the best data reduction scheme for scanned observations to the community and demonstrate the feasibility of the technique to other missions and remote sensing applications.

The Herschel Space Observatory was launched in 2009 to observe the Universe in the far-infrared. Due to the novelty of its detectors, the generation of scientific data from the measured material is exceptionally difficult. In addition to that, Herschel uses lossy reduction steps in order to be able to downlink the data to the ground. Within the project Compressed Sensing for Herschel, a novel way to measure data was investigated, which is able to deliver better results. With this technique, the losses in the data can be avoided und the calculation of the final images can be done in one big reconstruction step. This technique, which is based on recent developments in Mathematics, was tested by us in the Herschel mission, and we could show the applicability of it to space projects. The new method achieves equal results than classical measurement and in many cases we could improve the quality of the information contained. Another important result of the project is that we can apply the new reduction steps also to old data and derive better results from that. Data which are acquired with Compressed Sensing cannot be simply transformed into images, but they have to be reconstructed in a more intricate way. This has to consider the modeling of the instrument. That way instrumental effects such as motion blur for instance can be considered. Since this requires extensive computation, the reconstruction software was implemented on the supercomputer of our institute. The way how we deal with image defects turned out to be very effective. As a consequence, we provided imaging data in several international collaborations. These data would have not been useful otherwise. The reconstruction of the data is achieved by solving a convex optimization problem. That way we can consider detector effects a posteriori without having to make changes to the measurement process. Thus, we can further improve the observations, even past the operational lifetime of Herschel. By adding Compressed Sensing to the Herschel/PACS mission we provide an alternative data reduction scheme for scanned observations to the community and demonstrate the feasibility of the technique to other space missions and remote sensing applications.