Abstract-The goal of (stable) sparse recovery is to recover a k-sparse approximation x * of a vector x from linear measurements of x. Specifically, the goal is to recover for some constant C and norm parameters p and q. It is known that, for p = q = 1 or p = q = 2, this task can be accomplished using m = O(k log(n/k)) non-adaptive measurements [3] and that this bound is tight [9] , [12] , [28] . In this paper we show that if one is allowed to perform measurements that are adaptive , then the number of measurements can be considerably reduced. Specifically, for C = 1+ and p = q = 2 we show rounds. This is a significant improvement over the best possible nonadaptive bound. • A scheme with m = O( 1 k log(k/ ) + k log(n/k)) measurements that uses two rounds. This improves over the best possible non-adaptive bound. To the best of our knowledge, these are the first results of this type.
When the measurements may be constructed adaptively, there is a scheme with t = O(k log log(n/k)) REF .
On the Power of Adaptivity in Sparse Recovery
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Mathematics Computer Science