  Standard compressive sensing results state that to exactly recover an s
sparse signal in R^p, one requires O(s. log(p)) measurements. While this bound
is extremely useful in practice, often real world signals are not only sparse,
but also exhibit structure in the sparsity pattern. We focus on
group-structured patterns in this paper. Under this model, groups of signal
coefficients are active (or inactive) together. The groups are predefined, but
the particular set of groups that are active (i.e., in the signal support) must
be learned from measurements. We show that exploiting knowledge of groups can
further reduce the number of measurements required for exact signal recovery,
and derive universal bounds for the number of measurements needed. The bound is
universal in the sense that it only depends on the number of groups under
consideration, and not the particulars of the groups (e.g., compositions,
sizes, extents, overlaps, etc.). Experiments show that our result holds for a
variety of overlapping group configurations.
