中文摘要：

1引言 1．1研究背景 压缩感知（CS）理论是2006年左右Donoho、Candes以及Tao在信号稀疏情形下提出的一种新的信息获取理论，而1998年Donoho在研究信号稀疏处理时提出了一种新的原理——基追踪原理，该模型是求解信号稀疏问题的一个有效的数学工具．

英文摘要：

Because of the introduction of ＂compressed sensing＂, the class of l1 regularized optimization problems has received much attention recently. With an equivalent form of the least squares problem and Bregman iterative methods, we give out a derivation of a new equivalent form of the A＋ linear Bregman iteration. Furthermore, combining with the alternating direction method, a new predictorcorrector method for solving the sparse least squares problem is proposed. Simultaneously, we prove the convergence of the new method. The paper ends with a report on numerical tests for the sparse signal recovery problem. The numerical results show that the new method is faster, more efficient and simpler than the A^＋ linear Bregman iterative method. At the same time, the new method can reduce the stagnation of the iterative procedure.