Sparse sampling recovery by greedy algorithms

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.