Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBayesian CMB foreground separation with a correlated log-normal model
128
0
0.0
(
0
)
Authors
Niels Oppermann
Ask ChatGPT about the research
No Arabic abstract
The extraction of foreground and CMB maps from multi-frequency observations relies mostly on the different frequency behavior of the different components. Existing Bayesian methods additionally make use of a Gaussian prior for the CMB whose correlation structure is described by an unknown angular power spectrum. We argue for the natural extension of this by using non-trivial priors also for the foreground components. Focusing on diffuse Galactic foregrounds, we propose a log-normal model including unknown spatial correlations within each component and cross-correlations between the different foreground components. We present case studies at low resolution that demonstrate the superior performance of this model when compared to an analysis with flat priors for all components.
rate research
Read More
We propose a Bayesian approach to joint source separation and restoration for astrophysical diffuse sources. We constitute a prior statistical model for the source images by using their gradient maps. We assume a t-distribution for the gradient maps in different directions, because it is able to fit both smooth and sparse data. A Monte Carlo technique, called Langevin sampler, is used to estimate the source images and all the model parameters are estimated by using deterministic techniques.
Key to any cosmic microwave background (CMB) analysis is the separation of the CMB from foreground contaminants. In this paper we present a novel implementation of Bayesian CMB component separation. We sample from the full posterior distribution using the No-U-Turn Sampler (NUTS), a gradient based sampling algorithm. Alongside this, we introduce new foreground modelling approaches. We use the mean-shift algorithm to define regions on the sky, clustering according to naively estimated foreground spectral parameters. Over these regions we adopt a complete pooling model, where we assume constant spectral parameters, and a hierarchical model, where we model individual spectral parameters as being drawn from underlying hyper-distributions. We validate the algorithm against simulations of the LiteBIRD and C-BASS experiments, with an input tensor-to-scalar ratio of $r=5times 10^{-3}$. Considering multipoles $32leqellleq 121$, we are able to recover estimates for $r$. With LiteBIRD only observations, and using the complete pooling model, we recover $r=(10pm 0.6)times 10^{-3}$. For C-BASS and LiteBIRD observations we find $r=(7.0pm 0.6)times 10^{-3}$ using the complete pooling model, and $r=(5.0pm 0.4)times 10^{-3}$ using the hierarchical model. By adopting the hierarchical model we are able to eliminate biases in our cosmological parameter estimation, and obtain lower uncertainties due to the smaller Galactic emission mask that can be adopted for power spectrum estimation. Measured by the rate of effective sample generation, NUTS offers performance improvements of $sim10^3$ over using Metropolis-Hastings to fit the complete pooling model. The efficiency of NUTS allows us to fit the more sophisticated hierarchical foreground model, that would likely be intractable with non-gradient based sampling algorithms.
We develop a method to infer log-normal random fields from measurement data affected by Gaussian noise. The log-normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders of magnitude. We use the formalism of minimum Gibbs free energy to derive an algorithm that uses the signals correlation structure to regularize the reconstruction. The correlation structure, described by the signals power spectrum, is thereby reconstructed from the same data set. We show that the minimization of the Gibbs free energy, corresponding to a Gaussian approximation to the posterior marginalized over the power spectrum, is equivalent to the empirical Bayes ansatz, in which the power spectrum is fixed to its maximum a posteriori value. We further introduce a prior for the power spectrum that enforces spectral smoothness. The appropriateness of this prior in different scenarios is discussed and its effects on the reconstructions results are demonstrated. We validate the performance of our reconstruction algorithm in a series of one- and two-dimensional test cases with varying degrees of non-linearity and different noise levels.
GroundBIRD is a ground-based experiment for the precise observation of the polarization of the cosmic microwave background (CMB). To achieve high sensitivity at large angular scale, we adopt three features in this experiment: fast rotation scanning, microwave kinetic inductance detector (MKID) and cold optics. The rotation scanning strategy has the advantage to suppress $1/f$ noise. It also provides a large sky coverage of 40%, which corresponds to the large angular scales of $l sim 6$. This allows us to constrain the tensor-to-scalar ratio by using low $l$ B-mode spectrum. The focal plane consists of 7 MKID arrays for two target frequencies, 145 GHz and 220 GHz band. There are 161 pixels in total, of which 138 are for 144 GHz and 23 are for 220 GHz. This array is currently under development and the prototype will soon be evaluated in telescope. The GroundBIRD telescope will observe the CMB at the Teide observatory. The telescope was moved from Japan to Tenerife and is now under test. We present the status and plan of the GroundBIRD experiment.
The Internal Linear Combination (ILC) component separation method has been extensively used to extract a single component, the CMB, from the WMAP multifrequency data. We generalise the ILC approach for separating other millimetre astrophysical emissions. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalised ILC methods, implemented on a needlet frame, is tested on simulations of Planck mission observations, for which we successfully reconstruct a low noise estimate of emission from astrophysical foregrounds with vanishing CMB and SZ contamination.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
