Abstract
We discuss the problem of sparse representation of domains in ℝd. We demonstrate how the recently developed general theory of greedy approximation in Banach spaces can be used in this problem. The use of greedy approximation has two important advantages: (1) it works for an arbitrary dictionary of sets used for sparse representation and (2) the method of approximation does not depend on smoothness properties of the domains and automatically provides a near optimal rate of approximation for domains with different smoothness properties. We also give some lower estimates of the approximation error and discuss a specific greedy algorithm for approximation of convex domains in ℝ2.
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