The Iteratively Reweighted L₁ Algorithm And Conjugate Gradient Method For The Reconstruction Of Two Sparse Signals

This paper discusses the recovery of sparse signal.Sparse signal has a wide range of applications in compressed sensing,medical imaging,face recognition and other fields.Therefore,studying the reconstruction algorithm of sparse signal has important theoret-ical significance and application value.The main contents of this paper are as follow:1.A new sparse signal reconstruction model is proposed using the log sparse function,and it is transformed into an unconstrained least square problem.Then,the iteratively reweighted l₁ algorithm is used to solve our problem.We prove the convergence of the algorithm under suitable assumptions.Finally,we perform numerical experiments to test the effect of our method.We compare our algorithm with Gist algorithm and IRLS algorithm.And the numerical results show that our method has less CPU time and iterations.2.The complementary function is introduced into the l₁ norm model of signal reconstruction.The Fischer-Burmeister complementary function is used as a bridge to transform the l₁ norm model into an unconstrained optimization problem.Then,the transformed objective function is coerciveness.So we can get the boundedness of the level set.Then,we use the PRP three-term conjugate gradient method proposed by Zhang L,Zhou W to solve our problem.We also prove the global convergence of the algorithm.Numerical experiments are carried out under four observation matrices,and numerical results are provided.