Linearized iterative least-squares (LIL): a parameter-fitting algorithm for component separation in multifrequency cosmic microwave background experiments such as Planck

Abstract

We present an efficient algorithm for least-squares parameter fitting, optimized for component separation in multifrequency cosmic microwave background (CMB) experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of the quasi-linear nature of the foreground model. We demonstrate our algorithm, linearized iterative least-squares (LIL), on the publicly available Planck sky model FFP6 simulations and compare our results with those of other algorithms. We work at full Planck resolution and show that degrading the resolution of all channels to that of the lowest frequency channel is not necessary. Finally, we present results for publicly available Planck data. Our algorithm is extremely fast, fitting six parameters to the seven lowest Planck channels at full resolution (50 million pixels) in less than 160 CPU minutes (or a few minutes running in parallel on a few tens of cores). LIL is therefore easily scalable to future experiments, which may have even higher resolution and more frequency channels. We also, naturally, propagate the uncertainties in different parameters due to noise in the maps, as well as the degeneracies between the parameters, to the final errors in the parameters using the Fisher matrix. One indirect application of LIL could be a front-end for Bayesian parameter fitting to find the maximum likelihood to be used as the starting point for Gibbs sampling. We show that for rare components, such as carbon monoxide emission, present in a small fraction of sky, the optimal approach should combine parameter fitting with model selection. LIL may also be useful in other astrophysical applications that satisfy quasi-linearity criteria.