In this paper, the joint support recovery of several sparse signals whose supports exhibit similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals. The measurement noise is assumed additive, Gaussian, and admits different variances for each sparse signal that is measured. Using the theory of compressed sensing, the performance of simultaneous orthogonal matching pursuit (SOMP) is analyzed for the envisioned signal model. The cornerstone of this paper is a novel analysis method upper bounding the probability that SOMP recovers at least one incorrect entry of the joint support during a prescribed number of iterations. Furthermore, the probability of SOMP failing is investigated whenever the number of sparse signals being recovered simultaneously increases and tends to infinity. In particular, convincing observations and theoretical results suggest that SOMP committing no mistake in the noiseless case does not guarantee the absence of error in the noisy case whenever the number of acquired sparse signals scales to infinity. Finally, simulation results confirm the validity of the theoretical results.
In a SMV setting, full support recovery guarantees for OMP with bounded noise signals as well as with Gaussian noises have been proposed in @cite_15 . This work also provides criteria on the stopping criteria to guarantee that OMP terminates after having picked all the correct atoms. This contribution has then been slightly refined in @cite_10 to provide conditions independent of the particular support that is to be recovered.
@cite_15 @cite_10
2169380424 2091893102
In this paper, we consider orthogonal matching pursuit (OMP) algorithm for multiple measurement vectors (MMV) problem. The robustness of OMPMMV is studied under general perturbations—when the measurement vectors as well as the sensing matrix are incorporated with additive noise. The main result shows that although exact recovery of the sparse solutions is unrealistic in noisy scenario, recovery of the support set of the solutions is guaranteed under suitable conditions. Specifically, a sufficient condition is derived that guarantees exact recovery of the sparse solutions in noiseless scenario. This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level O(k), then OMP can stably recover a k-sparse signal in 2-norm under measurement noise. For compressed sensing applications, this result implies that in order to uniformly recover a k-sparse signal in Rd, only O(k lnd) random projections are needed. This analysis improves some earlier results on OMP depending on stronger conditions that can only be satisfied with Ω(k2 lnd) or Ω(k1.6 lnd) random projections.