On the ℓ 1-Norm Invariant Convex k-Sparse Decomposition of Signals

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 δ k +θ k,k