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Activity Number: 28 - SPEED: Statistical Computing and Statistics in Genomics Part 1
Type: Contributed
Date/Time: Sunday, August 7, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract #320906
Title: Using Krylov Subspace Methods for Large Scale Image Source Separation
Author(s): Simon P Wilson* and Dung P Pham and Kirk P Soodhalter
Companies: Trinity College Dublin and Trinity College Dublin and Trinity College Dublin
Keywords: Krylov subspace; Linear system; Factor analysis; Bayesian; Markov random field

Krylov subspaces are a well known approach to solving large linear systems such as occur in a diverse range of statistical methods. In this paper we explore their use in a large scale (dimension of the order 100 million) factor analysis or source separation problem associated with separating out the Cosmic Microwave Background from other sources in multi-channel all-sky images of the sky. A Bayesian method is used for inference with Gaussian Markov random field priors on the sources to regularize the solution and capture spatial smoothness. Two different approaches with the Krylov subspace, using a conjugate gradient optimisation and using the so-called Sylvester method, are compared. We demonstrate that posterior means of the CMB using Planck satellite data (the most detailed that we have so far) can be computed in minutes, opening up the prospect of being able to conduct extensive model checking and prior sensitivity experiments.

Authors who are presenting talks have a * after their name.

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