The orthogonal matching pursuit (OMP) is a popular decoder to recover sparse signal in compressed sensing. Our aim is to investigate the theoretical properties of OMP. In particular, we show that the OMP decoder can give (p, q) instance optimality for a large class of encoders with 1 ≤ p ≤ q ≤ 2 and (p, q) ≠ (2, 2).
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