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