Shearlet Transform Image Denoising Method Based On Meyer Wavelet

Digital image is used more and more widely in daily life and scientific research,but in the process of signal conversion and transmission,it will always be affected and interfered by the outside world,which makes the quality of the image decline.Therefore,it is necessary to study the method of image restoration.In recent years,because shearlet can be correlated with multi-resolution analysis and discretized to provide a more flexible method for image processing,the research of image denoising by shearlet transformation has become a hot topic.Generally,the shearlet uses ordinary wavelet as its basis function,and generates multidirectional multiresolution analysis function by shearing,translating and expanding the basis function.In order to get better simulation results,the smoothness of the basis function should be increased when the image is denoised by shearlet.Therefore,Meyer wavelet with better smoothness is often chosen as the basis function of shearlet in image denoising.However,the smoothness of Meyer wavelet is closely related to the sigmiod function selected by its scale function.It often appears in the form of polynomial sigmiod function,which is always finite derivable,but can not achieve full smoothness.Therefore,this paper proposes a construction method of fully smooth sigmiod function.Taking a sufficiently smooth non-polynomial sigmiod function as an example,it is applied as a new excitation function in BP neural network function approximation for simulation.Compared with the approximation of the BP neural network function of the excitation function,the sigmoid function of this paper has good approximation effect,high degree of agreement and less learning time.At the same time,the scale function of Meyer wavelet is obtained by using sufficiently smooth sigmiod function.Combined with multi-resolution analysis,Meyer wavelet is sufficiently smooth,has infinite vanishing moments and has faster attenuation speed.The constructed Meyer wavelet with sufficient smoothness is used for image denoising.Firstly,the Meyer wavelet constructed in this paper is selected as the basis function of shearlet,and the corresponding filter is obtained.Secondly,theimage with different degrees of Gaussian noise is decomposed at multi-scale,and the denoised image is obtained by inverse shearlet transform.Compared with the wavelet transform denoising and the commonly used Meyer wavelet shearlet denoising,it can be seen from the denoising performance evaluation index that the peak signal-to-noise ratio is relatively high and the mean square error is relatively small when using the Meyer wavelet shearlet transform constructed in this paper to denoise the image.At the same time,the texture and edge information of the image are better preserved.Therefore,this paper not only gives a method to construct a sufficiently smooth sigmiod function,which can be used as the excitation function of BP neural network to approximate the function effectively,but also provides an effective image denoising method by combining Meyer wavelet shearlet transform with Meyer wavelet,which is sufficiently smooth,has infinite order vanishing moments and has faster attenuation speed.