Phase Transitions in Oblivious Compressed Sensing
05 February 2017
In this paper we study the phase transition thresholds for oblivious compressed sensing, namely a noisy compressed sensing problem solved, unawarely or reluctantly, as a noiseless system. Modeling the unaccounted for noise as Gaussian and given a certain measurement rate, the maximal input sparsity allowing for stable decoding is derived, in the large-system limit, for a general Lp-norm decoder. The obliviousness penalty, with respect to the noise-aware threshold, is explicitly quantified.
