Abstract: 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.