This paper studies the convergence of the adaptively iterative thresholding(AIT) algorithm for compressed sensing. We first introduce a generalizedrestricted isometry property (gRIP). Then we prove that the AIT algorithmconverges to the original sparse solution at a linear rate under a certain gRIPcondition in the noise free case. While in the noisy case, its convergence rateis also linear until attaining a certain error bound. Moreover, as by-products,we also provide some sufficient conditions for the convergence of the AITalgorithm based on the two well-known properties, i.e., the coherence propertyand the restricted isometry property (RIP), respectively. It should be pointedout that such two properties are special cases of gRIP. The solid improvementson the theoretical results are demonstrated and compared with the knownresults. Finally, we provide a series of simulations to verify the correctnessof the theoretical assertions as well as the effectiveness of the AITalgorithm.
展开▼
