Drift removal by means of alternating least squares with application to Herschel data

We consider the problem of reconstructing an image observed with a linear, noisy instrument, the output of which is affected by a drift too, causing a slowly varying deviation of the readouts from the baseline level. Since the joint estimation of the image and the drift, which is the optimal approach, is demanding for large data, we consider an alternative approach, where we remove the drift and the noise in two separate steps. In particular, we remove the drift by means of Least Squares (LS) and the noise by means of Generalised Least Squares (GLS). Moreover, we introduce an efficient drift removal algorithm, based on Alternating Least Squares (ALS), and carry out an analysis which proves convergence and gives geometrical insight. Finally, we apply the approach to the Herschel satellite data, discussing the performance and showing that nearly optimal results are achieved.