  We study sparse approximation by greedy algorithms. We prove the
Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA), a
generalization of the Weak Orthogonal Matching Pursuit to the case of a Banach
space. The main novelty of these results is a Banach space setting instead of a
Hilbert space setting. The results are proved for redundant dictionaries
satisfying certain conditions. Then we apply these general results to the case
of bases. In particular, we prove that the WCGA provides almost optimal sparse
approximation for the trigonometric system in $L_p$, $2\le p<\infty$.
