  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 regularisation scheme
in the context of map-making of the anisotropic stochastic GW background
(SGWB). Specifically, we implement the quadratic form of regularizing function
with varying strength 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 dramatically improves the stability of deconvolution. We further study the
quality of reconstruction as a function of regularization constant. While in
principle this constant is dependent on the data set, 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.
