Accelerating the cosmic microwave background map-making procedure through preconditioning

Szydlarski, Mikołaj; Grigori, Laura; Stompor, R.

doi:10.1051/0004-6361/201323210

Cited by 10 publications

(32 citation statements)

References 42 publications

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“…With simple preconditioners, these methods typically converge in a few hundred iterations for CMB data sets. With a more carefully design preconditioner, the number of iterations can be greatly reduced (Naess & Louis 2014;Szydlarski et al 2014), but the preconditioner must be tuned carefully to fit the characteristics of the CMB survey (using e.g. a typical scanning pattern).…”

Section: Introductionmentioning

confidence: 99%

Cosmic Microwave Background Mapmaking with a Messenger Field

Huffenberger

Næss

2018

ApJ

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We apply a messenger field method to solve the linear minimum-variance mapmaking equation in the context of Cosmic Microwave Background (CMB) observations. In simulations, the method produces sky maps that converge significantly faster than those from a conjugate gradient descent algorithm with a diagonal preconditioner, even though the computational cost per iteration is similar. The messenger method recovers large scales in the map better than conjugate gradient descent, and yields a lower overall χ 2 . In the single, pencil beam approximation, each iteration of the messenger mapmaking procedure produces an unbiased map, and the iterations become more optimal as they proceed. A variant of the method can handle differential data or perform deconvolution mapmaking. The messenger method requires no preconditioner, but a high-quality solution needs a cooling parameter to control the convergence. We study the convergence properties of this new method, and discuss how the algorithm is feasible for the large data sets of current and future CMB experiments.

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Section: Introductionmentioning

confidence: 99%

Cosmic Microwave Background Mapmaking with a Messenger Field

Huffenberger

Næss

2018

ApJ

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“…thousand iterations. Such a behavior is indeed expected in linear systems for which the system matrix is (numerically) nearly singular (Hanke 1995;Szydlarski et al 2014).…”

Section: Reconstructed Sky Mapsmentioning

confidence: 72%

“…Consequently, the solution of the inverse problem either in Eqs. (22) or in (23) would ideally be found using some iterative linear equations solvers such the preconditioned conjugate gradient method (PCG; e.g., de Gasperis et al 2005;Cantalupo et al 2010;Szydlarski et al 2014). However, convergence of these iterative solvers may be hard to attain if the matrices are not well conditioned.…”

Section: The Meta-pixel Approachmentioning

confidence: 99%

“…In general the principal difficulty in the GLS estimator is in solving the inverse problem, which requires an inversion of a large system matrix. Performing this inversion explicitly (e.g., Borrill 1999;Stompor et al 2001) has become very difficult as the number of sky pixels in the surveys increases: the iterative solution has therefore become the standard practice (e.g., Wright et al 1996;Doré et al 2001;de Gasperis et al 2005;Cantalupo et al 2010;Dünner et al 2013;Szydlarski et al 2014).…”

Section: Introductionmentioning

confidence: 99%

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Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example

Poletti

Fabbian

Jeune

et al. 2017

A&A

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Analysis of cosmic microwave background (CMB) datasets typically requires some filtering of the raw time-ordered data. For instance, in the context of ground-based observations, filtering is frequently used to minimize the impact of low frequency noise, atmospheric contributions and/or scan synchronous signals on the resulting maps. In this work we have explicitly constructed a general filtering operator, which can unambiguously remove any set of unwanted modes in the data, and then amend the map-making procedure in order to incorporate and correct for it. We show that such an approach is mathematically equivalent to the solution of a problem in which the sky signal and unwanted modes are estimated simultaneously and the latter are marginalized over. We investigated the conditions under which this amended map-making procedure can render an unbiased estimate of the sky signal in realistic circumstances. We then discuss the potential implications of these observations on the choice of map-making and power spectrum estimation approaches in the context of B-mode polarization studies. Specifically, we have studied the effects of time-domain filtering on the noise correlation structure in the map domain, as well as impact it may have on the performance of the popular pseudospectrum estimators. We conclude that although maps produced by the proposed estimators arguably provide the most faithful representation of the sky possible given the data, they may not straightforwardly lead to the best constraints on the power spectra of the underlying sky signal and special care may need to be taken to ensure this is the case. By contrast, simplified map-makers which do not explicitly correct for time-domain filtering, but leave it to subsequent steps in the data analysis, may perform equally well and be easier and faster to implement. We focused on polarization-sensitive measurements targeting the B-mode component of the CMB signal and apply the proposed methods to realistic simulations based on characteristics of an actual CMB polarization experiment, POLARBEAR. Our analysis and conclusions are however more generally applicable.

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“…It is also a basis for a construction of more advanced preconditioners (e.g. Szydlarski et al 2014). The block-diagonal preconditioner is derived by replacing the noise covarianceN −1 f in Eq.…”

Section: Block-diagonal Preconditionermentioning

confidence: 99%

Accelerating linear system solvers for time-domain component separation of cosmic microwave background data

Papež

Grigori

Stompor

2020

A&A

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Component separation is one of the key stages of any modern, cosmic microwave background (CMB) data analysis pipeline. It is an inherently non-linear procedure and typically involves a series of sequential solutions of linear systems with similar, albeit not identical system matrices, derived for different data models of the same data set. Sequences of this kind arise for instance in the maximization of the data likelihood with respect to foreground parameters or sampling of their posterior distribution. However, they are also common in many other contexts. In this work we consider solving the component separation problem directly in the measurement (time) domain, which can have a number of important advantageous over the more standard pixel-based methods, in particular if non-negligible time-domain noise correlations are present as it is commonly the case. The time-domain based approach implies, however, significant computational effort due to the need to manipulate the full volume of time-domain data set. To address this challenge, we propose and study efficient solvers adapted to solving time-domain-based, component separation systems and their sequences and which are capable of capitalizing on information derived from the previous solutions. This is achieved either via adapting the initial guess of the subsequent system or through a so-called subspace recycling, which allows to construct progressively more efficient, two-level preconditioners. We report an overall speed-up over solving the systems independently of a factor of nearly 7, or 5, in the worked examples inspired respectively by the likelihood maximization and likelihood sampling procedures we consider in this work. Key words. Numerical methods -linear systems solvers -cosmic microwave background data analysis -component separation Data model.As mentioned earlier we consider a component separation procedure performed directly on the time-domain data as measured by the instrument thus avoiding performing any prior, explicit map-making procedure. For this we need to relate the data directly to amplitudes of the component maps in the predefined sky pixels as these maps are the targeted outcome of the component separation procedure. We assume that for each frequency the time-domain data are made of sequences of consecutive observations registered by all detectors operating at this frequency and concatenated together, we can write,where s is the unknown vector of the component amplitudes and the star indicates that those are their actual values, n f is an (unknown) noise vector, and the number of the frequency channels, n freq , is assumed to be larger than that of the components, Article number, page 2 of 17 J. Papež, L. Grigori, R. Stompor: Accelerating linear system solvers for time domain component separation of CMB data

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Accelerating the cosmic microwave background map-making procedure through preconditioning

Cited by 10 publications

References 42 publications

Cosmic Microwave Background Mapmaking with a Messenger Field

Cosmic Microwave Background Mapmaking with a Messenger Field

Making maps of cosmic microwave background polarization for B-mode studies: the POLARBEAR example

Accelerating linear system solvers for time-domain component separation of cosmic microwave background data

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