压缩感知的主要研究内容有信号的稀疏表达、观测矩阵的设计和信号恢复。精确的信号恢复算法是压缩感知中的关键。因此本文在压缩感知理论框架下研究恢复算法中的凸优化算法- Compressive sensing offers a variety of research fields, including signal sparse representation, sensing matrix design, signal reconstruction. Accurately signal reconstruction algoriths play a key role in compressive sensing. Hence, this thesis shows that a few of type algorithms of convex optimization with compressive sensing theory are investigated.