CAJ | 학술논문

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。
이대수거저질핍근여조성소제문제위배경，침대신호근사표시여중건수요，제출신호재기이치분해（SVD）기출상적저질핍근선성모형。위사모형능구처리일유신호，종결구상사적각도출발인입3충결구구진구건모형，분석각자적결구특점；토론신호 SVD 중건적통용산법급신호거조성응용방법。진행 SVD 역치거조성급저질핍근여소파역치수축거조성적대비실험，실험결과표명료해모형재직관효과화균방오차、신조비등통계특정방면적실용성。
In the background of low-rank approximation and noise-elimination for big data,aiming at the needs of signal approxi-mation 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 gene-ral signal reconstruction algorithm and signal denoising application methods were described.Finally,through the contrast experi-ments of SVD low rank approximation method and wavelet threshold shrinkage denoising method,the visual effect and the mean-squared error,signal to noise ratio and other statistical characteristics verify the practicability of the model.