Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torresani Uncertainty Principle

Let \τₙ\ₙ₌₁^∞ and \ωₘ\ₘ₌₁^∞ be two modular Parseval frames for a Hilbert C*-module E. Then for every x ∈ E\0\, we show that {align}{UE} \|θ_τ x \|_0 \|θ_ω x \|_0 ≥ {1}{n, m ∈ N \| τ_n, ω_m \|^2}. {align} We call Inequality ({UE}) as {Noncommutative Donoho-Stark-Elad-Bruckstein-Ricaud-Torr\'{e}sani Uncertainty Principle}. Inequality ({UE}) is the noncommutative analogue of breakthrough Ricaud-Torr\'{e}sani uncertainty principle [IEEE Trans. Inform. Theory, 2013]. In particular, Inequality ({UE}) extends Elad-Bruckstein uncertainty principle [IEEE Trans. Inform. Theory, 2002] and Donoho-Stark uncertainty principle [SIAM J. Appl. Math., 1989].