Sparse Recovery by Non-convex Optimization -- Instance Optimality

  title={Sparse Recovery by Non-convex Optimization -- Instance Optimality},
  author={Rayan Saab and {\"O}zg{\"u}r Yilmaz},
In this note, we address the theoretical properties of ∆p, 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 [4] and Wojtaszczyk [30] regarding the decoder ∆1, based on l 1 minimization, to ∆p with 0 < p < 1. Our results are two-fold. First, we show that under certain sufficient conditions that are… CONTINUE READING
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