Abstract-This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the original sparse solution at a linear rate under certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated as compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm. Index Terms-Compressed sensing, iterative hard/soft thresholding algorithm, coherence, restricted isometry property
The work REF examines the convergence properties of an adaptive iterative thresholding algorithm in compressed sensing problem.
Linear Convergence of Adaptively Iterative Thresholding Algorithms for Compressed Sensing
IEEE Transactions on Signal Processing, 63(11):2957-2971, 2015
Mathematics Computer Science