Weighted one-norm minimization with inaccurate support estimates: Sharp analysis via the null-space property

摘要: We study the problem of recovering sparse vectors given possibly erroneous support estimates. First, we provide necessary and sufficient conditions for weighted l 1 minimization to successfully recovery all signals whose estimate is sufficiently accurate. relate these analogous ones minimization, showing that they are equivalent when 50% accurate but easier satisfy more than Second, quantify this improvement, bounds on number Gaussian measurements ensure, with high probability, succeeds. The resulting can be significantly less what needed ensure via minimization. Finally, illustrate our results numerical experiments.