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Weak gravitational lensing is an invaluable tool for understandingfundamental cosmological physics. An unresolved issue in weak lensing cosmologyis to accurately reconstruct the lensing convergence $\kappa$ maps fromdiscrete shear catalog with survey masks, which the seminal Kaiser-Squire (KS)method is not designed to address. We present the Accurate Kappa ReconstructionAlgorithm for masked shear catalog (AKRA) to address the issue of mask. AKRA isbuilt upon the prior-free maximum likelihood mapmaking method (or the unbiasedminimum variance linear estimator). It is mathematically robust in dealing withmask, numerically stable to implement, and practically effective in improvingthe reconstruction accuracy. Using simulated maps with mask fractions rangingfrom 10\% to 50\% and various mask shapes, we demonstrate that AKRA outperformsKS at both the map level and summary statistics such as the auto power 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 powerspectrum, and therefore avoids the Wiener filter related biases at both the maplevel and cross-correlation statistics. If we only use the reconstructed map inthe unmasked regions, the reconstructed $C_\kappa$ is accurate to $1\%$ orbetter and $1-r_\ell \lesssim 1\%$ (excluding $\ell$ at the smallest scalesinvestigated), even for extreme cases of mask fraction and shape. As the firststep, the current version of AKRA only addresses the mask issue and thereforeignores complexities such as curved sky and inhomogeneous shape measurementnoise. AKRA is capable of dealing with these issues straightfowrardly, and willbe addressed in the next version.

Accurate Kappa Reconstruction Algorithm for masked shear catalog (AKRA)