谱图傅里叶变换与谱图小波变换基分析研究

Analysis and Study of Spectral Fourier Transform and Spectral Wavelet Transform Basis

卷积神经网络在欧氏数据上取得巨大成功之后,开始在图结构、几何流行等非欧数据上泛化。当前图卷积神经已成为研究热点。在数字图像去噪、压缩、增强、融合以及加密方面傅里叶变换与小波变换是不可或缺的处理手段,在图卷积神经中有卷积定理将傅里叶变换用于实现图上的卷积运算,谱图小波变换也只是实现了卷积的快速算法,都是围绕如何在图结构上做卷积而展开的研究,没有真正发挥其作用,大大限制了图卷积神经网络性能的发挥。该文对谱图傅里叶变换与谱图小波变换基进行分析研究,同时研究基与图结构之间的关系。实验表明通过谱图傅里叶变换和谱图小波变换可以获取图结构的特征信息,为谱图小波变换和谱图傅里叶变换更深入地与图卷积神经网络结合提供了参考。

After achieving great success in Euclidean data,convolutional neural network began to generalize on non-Euclidean data such as graph structure and geometric popularity.At present,the graph convolutional nerve has become a research hotspot.In the digital image denoising,compression,enhancement,fusion and encrypted,Fourier transform and wavelet transform are indispensable means of processing.There is a convolution theorem in the graph convolutional nerve to realize the convolution operation on the graph by spectral Fourier transform and fast convolution algorithm by spectral wavelet transform.The study is over how to convolutions on the graph structure,which does not really play its role and greatly limits the performance of the graph convolutional neural network.Therefore,we analyze and study the Fourier transform and wavelet transform basis of spectrogram and also the relationship between the basis and graph structure.The experiment shows that the characteristic information of the graph structure can be obtained by the Fourier transform and wavelet transform of the spectrum,which provides a reference for the deeper combination of the wavelet transform and Fourier transform of the spectrum with the convolutional neural network of the graph.