A splitting-based iterative method for sparse reconstruction

Abstract

In this paper, we study a ℓ1-norm regularized minimization method for sparse solution recovery in compressed sensing and X-ray CT image reconstruction. In the proposed method, an alternating minimization algorithm is employed to solve the involved ℓ1-norm regularized minimization problem. Under some suitable conditions, the proposed algorithm is shown to be globally convergent. Numerical results indicate that the presented method is effective and promising.