Pixel domain multi-resolution minimum variance painting of CMB maps

TL;DR

This paper presents a new pixel domain minimum variance method for CMB map reconstruction that effectively handles missing data, reduces residuals, and is computationally efficient, enabling improved analysis of CMB datasets.

Contribution

It introduces an unbiased, multi-resolution minimum variance painting technique for CMB maps that improves residual reduction and computational efficiency over traditional methods.

Findings

Reduces residuals like EB-leakage in CMB maps

Achieves similar accuracy with lower computational cost ($rom O(N_{side}^6)$ to O(N_{side}^3)$)

Provides a foundation for future minimum variance CMB data analyses

Abstract

This work introduces an unbiased minimum variance painting of the pixel domain CMB maps for both the missing and available sky regions. In the missing region, it generates CMB realizations that have identical statistical properties to the expected CMB signal; and in the available region, it significantly alleviate the unwanted residuals, e.g., the residual of EB-leakage. The time cost of this method follows $\sim$$ O(N_{side}^3)$ ($N_{side}$ is the map resolution parameter), which is similar to the fast spherical harmonic transforms and is much better than the traditional minimum variance method that follows $\sim$$O(N_{side}^6)$. This method is the basis of a series of minimum variance estimations for analyzing CMB datasets, and more works based on it will follow in the future.