Iterative Weighted Group Thresholding Method for Group Sparse Recovery

This article proposes a novel iterative weighted group thresholding method for group sparse recovery of signals from underdetermined linear systems. Based on an equivalent weighted group minimization problem with ℓ
^p
_p
-norm (0 <; p ≤ 1), we derive closed-form solutions for a subproblem with respect to some specific values of p when using the proximal gradient method. Then, we design the corresponding algorithmic framework, including stopping criterion and the method of nonmonotone line search, and prove that the solution sequence generated by the proposed algorithm converges under some mild conditions. Moreover, based on the proposed algorithm, we develop a homotopy algorithm with an adaptively updated group threshold. Extensive computational experiments on the simulated and real data show that our approach is competitive with state-of-the-art methods in terms of exact group selection, estimation accuracy, and computation time.