信号的SVD重建模型及其应用

Signal reconstruction model based on SVD and its application

以大数据低秩逼近与噪声消除问题为背景,针对信号近似表示与重建需要,提出信号在奇异值分解(SVD)基础上的低秩逼近线性模型。为使模型能够处理一维信号,从结构相似的角度出发引入3种结构矩阵构建模型,分析各自的结构特点;讨论信号SVD重建的通用算法及信号去噪声应用方法。进行SVD阈值去噪声及低秩逼近与小波阈值收缩去噪声的对比实验,实验结果表明了该模型在直观效果和均方误差、信噪比等统计特征方面的实用性。

In the background of low-rank approximation and noise-elimination for big data,aiming at the needs of signal approximation and reconstruction,a linear low-rank approximation model based on singular value decomposition（SVD）of signal was presented.To handle one-dimensional signal with the SVD approximation model,three structural matrix-construction models were introduced from the perspective of structure similarity,and their structural characteristics were analyzed.Then,the general signal reconstruction algorithm and signal denoising application methods were described.Finally,through the contrast experiments of SVD low rank approximation method and wavelet threshold shrinkage denoising method,the visual effect and the meansquared error,signal to noise ratio and other statistical characteristics verify the practicability of the model.