Stochastic gravitational wave background mapmaking using regularized deconvolution

Obtaining a faithful source intensity distribution map of the sky from noisy data demands incorporating known information of the expected signal, especially when the signal is weak compared to the noise. We introduce a widely used procedure to incorporate these priors through a Bayesian regularization scheme in the context of mapmaking of the anisotropic stochastic GW background. Specifically, we implement the quadratic form of a regularizing function with varying strengths of regularization and study its effect on image restoration for different types of the injected source intensity distribution in simulated LIGO data. We find that regularization significantly enhances the quality of reconstruction, especially when the intensity of the source is weak, and it dramatically improves the stability of deconvolution. We further study the quality of reconstruction as a function of the regularization constant. While in principle this constant is dependent on the dataset, we show that the deconvolution process is robust against the choice of the constant, as long as it is chosen from a broad range of values obtained by the method presented here.