{"arxiv_id":"astro-ph/0403098","incoming":{"papers":35,"sentences":61,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":12,"sentences":17,"quotes":[{"arxiv_id":"0903.3634","title":"CMB Polarization and Temperature Power Spectra Estimation using Linear Combination of WMAP 5-year Maps","url":"/paper/0903.3634","section":"Method","sentence":"The weights are obtained using the empirical covariance matrix, $Ĉ_l$, by the relationship, ( [ref] ) [equation]","intent_p":0.98,"contests_p":null},{"arxiv_id":"2309.08170","title":"A Constrained NILC method for CMB B mode observations","url":"/paper/2309.08170","section":"Constrained Needlet ILC","sentence":"The weights for minimizing the variance of the resulting map with the constraints can be solved using Lagrange multipliers [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"2608.28487","title":"Enhancing Cosmological Constraints from Foreground-Cleaned CMB Maps Using Large-Scale Structure 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currently and aiming at understanding all the major foreground components, seems to bode well for its future applications.","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":15,"sentences":17,"quotes":[{"arxiv_id":"2308.03412","title":"Non-parametric maximum likelihood component separation for CMB polarization data","url":"/paper/2308.03412","section":"Introduction","sentence":"Among others, the most extensively studied are based on the empirical modeling of the foreground SEDs in parametric methods [ref] , on statistical properties of the foreground in the Internal Linear Combination (ILC) [ref] and Independent Component Analysis (ICA) [ref] techniques, and on the definition of internal or external foreground templates in template fitting methods [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2505.14644","title":"Minimizing Contaminant Leakage in Internal Linear Combination Maps Using a Data-Driven 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