一种近似稀疏信号的压缩传感重建方法

A Fast Reconstruction Method for Approximately Sparse Signal in Compressed Sensing

研究近似稀疏信号压缩传感数据的快速准确重建,提出一种基于分析模型的近似l0平滑函数重建方法ASL0.采用分析模型避免了合成模型的累计误差;引入近似l0范数使优化求解过程得以简化,保证了算法的快速实现.对一维分段平滑的合成信号进行了重建仿真,结果表明,采用ASL0重建信号质量好,算法复杂度低,适用于近似稀疏信号压缩感知数据的重建.

The fast and accurate reconstruction of approximately sparse signal in compressed sensing is investigated. A new method of ASL0 （smoothed l0 norm with analysis） is proposed based on analysis model and SL0. Analysis approach can avoid the accumulative errors caused by synthesis approach, and the smoothed l0 norm makes the optimization process simpler. The simulation results on one-dimension piece-wise smooth signals demonstrate that ASL0 can reconstruct the signal accurately and lower the computational complexity, which shows ASL0 method is suitable to be used to reconstruct the approximately sparse signals.