A Research On Data Denoising Method Based On Nonlinear Schr(?)dinger Equation

Data denoising is an important prerequisite for data analysis,and the ability to effectively eliminate noise from data directly affects the effective-ness of relevant data analysis algorithms.In order to make fuller use of the information provided by the data,it is expected to retain as much original information as possible while denoising,which places higher demands on data denoising algorithms.For this propose,this paper specifically analyzes the dynamic stochastic resonance effect in nonlinear optical systems based on the phenomenon that the presence of noise can enhance the signal energy due to the stochastic resonance effect,derives the nonlinear schrodinger equation to describe the signal propagation in this system,proposes a denoising model for 1-D data denoising.Further,the 1-D model is extended to 2-D form,and an image denoising algorithm is proposed based on the nonlinear schrodinger equation.Extensive experiments and comparisons with the other methods show that our algorithm achieves competitive performance.The specific con-tents are as follows:Chapter 2 introduces the stochastic resonance effects occurring in non-linear systems and gives the derivation of schrodinger equation for different system states,which provides the basis for the analysis of dynamical stochastic resonance in the following.Chapter 3 specifically analyzes the dynamical stochastic resonance effect occurring in nonlinear optical systems,describes the kinetic behavior of signal propagation in this system using nonlinear schrodinger equation,proposes a 1-D denoising model,and verifies the effectiveness of the method in 1-D data denoising and its advantages over some other methods through comparative experiments;then applies this model to 2-D image data denoising,and ana-lyzes the problems and shortcomings of the 1-D model in 2-D image denoising.Chapter 4 extends the 1-D model to 2-D form,constructs a model for 2-D image data denoising,and proposes an algorithm for 2-D image denoising in combination with other methods,and illustrates through comparative experi-ments that the method in this paper can more effectively in recovering detail information such as edges and textures in images while eliminating noise,and analyzes and verifies the advantages and shortcomings of this method in image denoising.