  We introduce a novel approach to reconstruct dark matter mass maps from weak
gravitational lensing measurements. The cornerstone of the proposed method lies
in a new modelling of the matter density field in the Universe as a mixture of
two components:(1) a sparsity-based component that captures the non-Gaussian
structure of the field, such as peaks or halos at different spatial scales; and
(2) a Gaussian random field, which is known to well represent the linear
characteristics of the field.Methods. We propose an algorithm called MCALens
which jointly estimates these two components. MCAlens is based on an
alternating minimization incorporating both sparse recovery and a proximal
iterative Wiener filtering. Experimental results on simulated data show that
the proposed method exhibits improved estimation accuracy compared to
state-of-the-art mass map reconstruction methods.
