Signal Denoising In Both Time And Frequency Domains And Its Applications

Since the signal in reality is often contaminated by noise,the signal enhance-ment is needed and it is a basic problem in the field of signal processing.Signal denoising usually relies on relevant prior knowledge of both signal and noise.Signals and noise typically exhibit different properties in different transform domains,such as time and frequency domains.By using these prior knowledge and appropriate mathematical models,signal denoising can be achieved.Based on the smoothness of the signal time domain and the sparseness of the transform domain,firstly,the TV domain and the(?)norm are used to characterize smoothness and sparsity,respec-tively,and introduce it as regular terms into the denoising model for noise reduction,and using the decomposition characteristics of the compound proximity operator to give an effective Union Domain Denoising method.Secondly,aiming at the clip-ping effect of(?)1 norm in UDDN,this paper introduces the non-convex penalty,firm,instead of the sparsity of the(?)1 norm characterization signal in the transform do-main,and gives the solution algorithm based on the duality algorithm of proximity.The experimental results show that compared with the traditional wavelet denois-ing method,the union domain can make good use of the priors knowledge of the signal to obtain better denoising effect,and the non-convex penalty function not only eliminates the clipping effect due to sparseness,but also further introduces sparsity,the performance of the algorithm is further improved.