Research On Fractional Order Model For Signal Denoising

Spectral peaks contain important physical or chemical properties.Since signal is usually contaminated with noise during data acquisition,it is necessary to smooth the peak signal in subsequent analysis,such as derivative spectrum analysis.Once the peak is over-smoothed,it is difficult to recover in the subsequent analysis process,which affects the peak detection results.Therefore,for the smoothing of spectral signals,a challenging task is to protect spectral peaks while reducing noise.Based on the classical diffusion model and the regularization model,combined with fractional calculus theory,three new smoothing models--time fractional diffusion model,space fractional diffusion model and fractional regularization model are proposed.For the onedimensional signals,the numerical algorithm and model parameters of the proposed models are discussed in detail.The specific work is as follows:(1)The time fractional diffusion model is proposed by replacing the time derivative in the classical diffusion model with the fractional derivative.Through the discretization of Caputo fractional derivative,the explicit difference algorithm and semi-implicit difference algorithm for sub-diffusion and super-diffusion are given.In order to achieve peak-preserving smoothing,a natural idea is that the diffusion intensity decreases with the peak height.Therefore,a diffusion function is given by using the spectral peak signal as the reference signal and its parameters are discussed.In addition,the influence of time fractional order on smoothing performance is also analyzed.By comparing with the classical non-linear diffusion model and common smoothing method,the result shows that the time fractional diffusion model has better smoothing performance,and the time fractional diffusion model has better peak-preserving effect in smoothing the spectral peak signal.(2)A spatial fractional diffusion model is proposed by replacing the second derivative of the spatial variables of the nonlinear diffusion model with the fractional derivative.The explicit difference algorithm and semi-implicit difference algorithm of the model are given by the fractional Riesz derivative.The influence of spatial fractional order on smoothing performance is discussed.The smoothing performance of classical nonlinear diffusion model,time fractional order diffusion model and common smoothing methods are compared.The validity of the spatial fractional order diffusion model is verified by the simulation data and the actual data.(3)A fractional-order regularization model is proposed by replacing the first-order derivative in the regularization model with fractional-order derivative.The numerical algorithm of the model is given according to the definition of Grünwald-Letnikov.The influence of differential order on smoothing performance and the selection of optimal parameters are discussed.The research results show that the fractional order model has better peak-preserving smoothing performance than the integer order model.The corresponding research results can be used for peak detection of analytical signals and improve the accuracy of peak detection.