A Remaining Proofs from Section 4

Here we provide proofs for all the results in Section 4 that were excluded in the main paper. For each of these results we dedicate a subsection that provides further details. Combining all these results from different subsections, in Appendix A.4 we provide the proof for our main result (Theorem 2.1). A.1 Properties of Convex Program and Proof of Lemma 4.3 Here we prove important properties of our convex program. In the remainder we prove and state interesting properties of this function that helps us construct sparse approximate solutions.