Noncommutative Donoho-Elad-Gribonval-Nielson-Fuchs Sparsity Theorem

Breakthrough Sparsity Theorem, derived independently by Donoho and Elad [Proc. Natl. Acad. Sci. USA, 2003], Gribonval and Nielson [IEEE Trans. Inform. Theory, 2003] and Fuchs [IEEE Trans. Inform. Theory, 2004] says that unique sparse solution to NP-Hard ₀-minimization problem can be obtained using unique solution of P-Type ₁-minimization problem. In this paper, we derive noncommutative version of their result using frames for Hilbert C*-modules.