Accurate kappa reconstruction algorithm for masked shear catalog

Weak gravitational lensing is an invaluable tool for understanding fundamental cosmological physics. An unresolved issue in weak lensing cosmology is to accurately reconstruct the lensing convergence $\kappa$ maps from discrete shear catalog with survey masks, which the seminal Kaiser-Squire (KS) method is not designed to address. We present the accurate kappa reconstruction algorithm for masked shear catalog (AKRA) to address the issue of mask. AKRA is built upon the prior-free maximum-likelihood map making method (or the unbiased minimum variance linear estimator). It is mathematically robust in dealing with mask, numerically stable to implement, and practically effective in improving the reconstruction accuracy. Using simulated maps with mask fractions ranging from 10% to 50% and various mask shapes, we demonstrate that AKRA outperforms KS at both the map level and summary statistics such as the autopower spectrum $C_{\kappa }$ of the reconstructed map, its cross-correlation coefficient $r_{\ell }$ with the true $\kappa$ map, the scatter plot and the localization measure. Unlike the Wiener filter method, it adopts no priors on the signal power spectrum, and therefore avoids the Wiener filter related biases at both the map level and cross-correlation statistics. If we only use the reconstructed map in the unmasked regions, the reconstructed $C_{\kappa }$ is accurate to 1% or better and $1-r_{\ell }\lesssim 1\%$, even for extreme cases of mask fraction and shape. As the first step, the current version of AKRA only addresses the mask issue and therefore ignores complexities such as curved sky and inhomogeneous shape measurement noise. AKRA is capable of dealing with these issues straightforwardly, and will be addressed in the next version.