An RIP Condition for Exact Support Recovery With Covariance-Assisted Matching Pursuit

• Published in: IEEE signal processing letters Vol. 26; no. 3; pp. 520 - 524
• Main Authors: Ge, Huanmin, Wang, Libo, Wen, Jinming, Xian, Jun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Covariance; Covariance matrices; Covariance-assisted matching pursuit (CAMP); Gauss-Markov theorem; Gaussian noise; Markov processes; Matched pursuit; Matching; Matching pursuit algorithms; Noise measurement; Recovery; restricted isometry property (RIP); Sensors; Signal processing algorithms; Sparse matrices; sparse recovery
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2019.2896543

The covariance-assisted matching pursuit (CAMP) algorithm has recently been proposed for recovering sparse signals <inline-formula><tex-math notation="LaTeX">\boldsymbol {f}</tex-math></inline-formula> from noisy linear measurements based on a priori knowledge of the covariance and mean of the nonzero coefficients of <inline-formula><tex-math notation="LaTeX">\boldsymbol {f}</tex-math></inline-formula>. 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 <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula>-sparse signals <inline-formula><tex-math notation="LaTeX">\boldsymbol {f}</tex-math></inline-formula> via CAMP in <inline-formula><tex-math notation="LaTeX">k</tex-math></inline-formula> iterations, under the <inline-formula><tex-math notation="LaTeX">\ell _2</tex-math></inline-formula>-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 <inline-formula><tex-math notation="LaTeX">\boldsymbol {f}</tex-math></inline-formula>, and are much better than the existing ones.