An RIP Condition for Exact Support Recovery With Covariance-Assisted Matching Pursuit - Ge, Huanmin; Wang, Libo; Wen, Jinming; Xian, Jun (IEEE signal processing letters, 2019)
The covariance-assisted matching pursuit (CAMP) algorithm has recently been proposed for recovering sparse signals \boldsymbol {f} from noisy linear measurements based on a priori knowledge of the covariance and mean of the nonzero coefficients of \boldsymbol {f} . It utilizes the a priori knowledge by incorporating the Gauss-Markov theorem into the orthogonal matching pursuit (OMP) algorithm and has a significantly better reconstruction performance than OMP. This letter develops sufficient conditions of exact support recovery of any k -sparse signals \boldsymbol {f} via CAMP in k iterations, under the \ell _2 -bounded and Gaussian noises. These sufficient conditions are based on the restricted isometry constant of the sensing matrix and minimum magnitude of the nonzero elements of \boldsymbol {f} , and are much better than the existing ones.