DOIAbstract
AbstractIn this note, we address the theoretical properties of Δp, a class of compressed sensing decoders that rely on ℓp minimization with 0<p<1 to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. In particular, we extend the results of Candès, Romberg and Tao (2006) [3] and Wojtaszczyk (2009) [30] regarding the decoder Δ1, based on ℓ1 minimization, to Δp with 0<p<1. Our results are two-fold. First, we show that under certain sufficient conditions that are weaker than the analogous sufficient conditions for Δ1 the decoders Δp are robust to noise and stable in the sense that they are (2,p) instance optimal for a large class of encoders. Second, we extend the results of Wojtaszczyk to show tha...
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