压缩感知理论与非凸优化方法研究

针对某些信号带宽较宽导致难以直接采样的问题,压缩感知理论提供了一种可行的低速采样方法。信号在特定变换域中拥有稀疏表示,通过低速采样得到少量的投影值,已经包含了重构所需的重要信息。利用压缩感知理论从投影值中重构出稀疏向量,进而重建原信号。同时介绍一种基于非凸优化的压缩感知重构算法。相比L1范数的凸优化和无稀疏约束的L2范数,非凸优化的Lp范数拥有对稀疏性更强的约束。实验结果表明,使用压缩感知理论可以显著降低对信号的采样速率,而使用非凸优化算法可以取得更好的重构效果。

Research on Compressed Sensing Theory and Non-convex Optimization Method

Due to the wider bandwidth,some signals are difficult to sample directly.To solve this problem,compressed sensing （CS） provides a feasible way with lower sampling speed.Signals have sparse representation in specific transformation domain.A few projection values obtained through low-speed sampling have already contained the important information for reconstruction. The sparse vector is reconstructed from the projection values based on CS and the original signal is reestablished.A CS reconstruction algo-rithm based on non-convex optimization is also introduced.Comparing to the convex optimization of L1-norm and non-sparse restriction of L2-norm,Lp-norm of non-convex optimization has stronger restriction on sparseness.Experimental results show that CS theory reduces the sampling speed of signal significantly,while the non-convex optimization algorithm has better reconstruction performance.