Advanced GLS map-making for the Herschel's photometers

We discuss Generalised Least Squares (GLS) map-making for the data of the Herschel satellite's photometers, which is a difficult task, due to the many disturbances affecting the data, and requires appropriate pre- and post-processing. Taking an existing map-maker as a reference, we propose several advanced techniques, which can improve both the quality of the estimate and the efficiency of the software. As a main contribution we discuss two disturbances, which have not been studied yet and may be detrimental to the image quality. The first is a data shift, due to delays in the timing system or in the processing chain. The second is a random noise, termed pixel noise, due to the jitter and the approximation of the pointing information. For both these disturbances, we develop a mathematical model and propose a compensation method. As an additional contribution, we note that the performance can be improved by properly adapting the algorithm parameters to the data being processed and discuss an automatic setting method. We also provide a rich set of examples and experiments, illustrating the impact of the proposed techniques on the image quality and the execution speed