Linearized iterative least-squares (LIL): A parameter fitting algorithm for component separation in multifrequency CMB experiments such as Planck

We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency 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 result with the 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 the publicly available Planck data. Our algorithm is extremely fast, fitting 6 parameters to 7 lowest Planck channels at full resolution (50 million pixels) in less than 160 CPU-minutes (or few minutes running in parallel on 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 degeneracies between the parameters to the final errors on the parameters using Fisher matrix. One indirect application of LIL could be a front-end for Bayesian parameter fitting to find the maximum of the likelihood to be used as the starting point for the Gibbs sampling. We show for rare components, such as the carbon-monoxide emission, present in small fraction of sky, the optimal approach should combine parameter fitting with model selection. LIL may also be useful in other astrophysical applications which satisfy the quasi-linearity criteria.