  In this paper we analyze approximation and recovery properties with respect
to systems satisfying universal sampling discretization property and a special
incoherence property. We apply a powerful nonlinear approximation method -- the
Weak Chebyshev Greedy Algorithm (WCGA). We establish that the WCGA based on
good points for the $L_p$-universal discretization provides good recovery in
the $L_p$ norm. For our recovery algorithms we obtain both the Lebesgue-type
inequalities for individual functions and the error bounds for special classes
of multivariate functions. The main point of the paper is that we combine here
two deep and powerful techniques -- Lebesgue-type inequalities for the WCGA and
theory of the universal sampling dicretization -- in order to obtain new
results in sampling recovery.
