基于线性规划的分段平滑信号的复原算法

随着物联网技术的发展，人们大量地通过传感器获取现实生活及自然界中的信息，但由于种种原因，传输过程中信号会有失真。因此，要得到反映某物理特性真实原始的信号很困难。从失真的观测信号中恢复原始信号一直是信号处理领域的热点之一，而信号复原最需要解决的问题是解的不唯一性。基于“总有界变差”思想，利用分段平滑的性质，提出带总观测误差约束的信号复原模型。通过引入松弛因子，将有约束的不可微优化问题转化为有约束的线性规划问题。仿真实验结果表明，信号复原的效果明显要好于传统的Wiener滤波和Richardson-Lucy方法。 

Sectionally smooth signal recovery based on linear programming algorithm

With the development of Internet of Things,information from the real life or the nature is largely got through the sensors,but for various reasons,which will lead to the distortion of the signal when transmitted.Therefore,it is very difficult to reflect the physical characteristics of an original signal.Signal recovery from the distorted original signals is always one of the hot spots of the signal processing domain,however,the problem of solution’ s non-uniqueness is still the most pressing issue to signal recovery.By using the sectionally smooth’s property and relaxation factor,this paper puts forward a signal recovery model with observation error constraints based on the idea of "total bounded variation".With the proposed model,optimization process of non-differentiable constrained problem can be transformed into a nonlinear programming problem with constraints.The simulation results demonstrate that the effect of the signal recovery is clearly better than the traditional Wiener filter and Richardson-Lucy method.