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

Breakthrough Sparsity Theorem, derived independently by Donoho and Elad Proc. Natl. Acad. Sci. USA, 2003, Gribonval and Nielsen 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.