A multi-level solver for Gaussian constrained CMB realizations

TL;DR

The paper introduces a multi-level solver that significantly accelerates the process of generating constrained Gaussian realizations of the CMB sky from noisy, partial data, outperforming traditional methods in speed and convergence.

Contribution

A novel multi-level solver for CMB data analysis that converges faster than existing conjugate gradient methods, enabling efficient high-precision realizations.

Findings

Achieves microKelvin accuracy in 3 W-cycles for Planck data

Reduces computational time to minutes per realization using multi-level approach

Outperforms conventional CG methods in convergence speed and accuracy

Abstract

We present a multi-level solver for drawing constrained Gaussian realizations or finding the maximum likelihood estimate of the CMB sky, given noisy sky maps with partial sky coverage. The method converges substantially faster than existing Conjugate Gradient (CG) methods for the same problem. For instance, for the 143 GHz Planck frequency channel, only 3 multi-level W-cycles result in an absolute error smaller than 1 microKelvin in any pixel. Using 16 CPU cores, this translates to a computational expense of 6 minutes wall time per realization, plus 8 minutes wall time for a power spectrum-dependent precomputation. Each additional W-cycle reduces the error by more than an order of magnitude, at an additional computational cost of 2 minutes. For comparison, we have never been able to achieve similar absolute convergence with conventional CG methods for this high signal-to-noise data set, even after thousands of CG iterations and employing expensive preconditioners. The solver is part of the Commander 2 code, which is available with an open source license at http://commander.bitbucket.org/.