Abstract:

Inspired by an interesting idea of Cai and Zhang, we formulate and prove
the convex k-sparse decomposition of vectors that is invariant with respect to the
l_1 norm. This result fits well in discussing compressed sensing problems under the
Restricted Isometry property, but we believe it also has independent interest. As an
application, a simple derivation of the RIP recovery condition δk + θk,k < 1 is presented.

Key words: Convex k-sparse decomposition , l_1 minimization , Restricted isometry
property , Sparse recovery