Related papers: Optimal Polyspectra Estimation
We extend the pure pseudo-power-spectrum formalism proposed recently in the context of the Cosmic Microwave Background polarized power spectra estimation by Smith (2006) to incorporate cross-spectra computed for multiple maps of the same…
Accurate covariance matrices are required for a reliable estimation of cosmological parameters from pseudo-power spectrum estimators. In this work, we focus on the analytical calculation of covariance matrices. We consider the case of…
Based on realistic simulations, we propose an hybrid method to reconstruct the lensing potential power spectrum, directly on PLANCK-like CMB frequency maps. It implies using a large galactic mask and dealing with a strong inhomogeneous…
Cosmic Microwave Background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise…
We discuss the derivation of the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps. The method is computationally convenient and it provides unbiased estimates under very broad assumptions. We…
A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing…
We describe a sampling method to estimate the polarized CMB signal from observed maps of the sky. We use a Metropolis-within-Gibbs algorithm to estimate the polarized CMB map, containing Q and U Stokes parameters at each pixel, and its…
Over the past decade, the gravitational lensing of the Cosmic Microwave Background (CMB) has become a powerful tool for probing the matter distribution in the Universe. The standard technique used to reconstruct the CMB lensing signal…
Strong foreground contamination in high resolution CMB data requires masking which introduces statistical anisotropies and renders a full maximum likelihood analysis numerically intractable. Standard analysis methods like the pseudo-C_l…
We describe a fast, optimal estimator for measuring angular bispectra between two correlated weakly non-Gaussian fields ($Y$ and $Z$) from observational datasets, based on a separable modal bispectrum expansion. Our methodology is…
Over the next decade, improvements in cosmological parameter constraints will be driven by surveys of large-scale structure. Its inherent non-linearity suggests that significant information will be embedded in higher correlations beyond the…
The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…
After the precise observations of the Cosmic Microwave Background (CMB) anisotropy power spectrum, attention is now being focused on the higher order statistics of the CMB anisotropies. Since linear evolution preserves the statistical…
We explore a systematic approach to the analysis of primordial non-Gaussianity using fluctuations in temperature and polarization of the Cosmic Microwave Background (CMB). Following Munshi & Heavens (2009), we define a set of power-spectra…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
The estimation of modal parameters from a set of noisy measured data is a highly judgmental task, with user expertise playing a significant role in distinguishing between estimated physical and noise modes of a test-piece. Various methods…
We present an optimization scheme for the focal plane of a multi-frequency CMB B-modes experiment with a fixed number of detectors and apply it to the specific case of LSPE experiment. Optimal focal planes are identified on the ground of…
We present ECLIPSE (Efficient Cmb poLarization and Intensity Power Spectra Estimator), an optimized implementation of the Quadratic Maximum Likelihood (QML) method for the estimation of the power spectra of the Cosmic Microwave Background…
We reexamine the evidence of the hemispherical power asymmetry, detected in the CMB WMAP data using a new method. At first, we analyze the hemispherical variance ratios and compare these with simulated distributions. Secondly, working…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…