CAJ | 학술논문

针对奇异值分解在信号降噪时有效秩的选择问题，提出一种基于矩阵秩最小化和统计修正的信号降噪方法。首先，利用矩阵秩最小化理论将奇异值有效秩选择问题转化为秩的约束优化问题；然后，通过凸优化求解，得到干净信号的 Hankel 矩阵，实现一次降噪；最后，根据奇异值子集标准差对干净信号 Hankel 矩阵进行统计修正，进一步优化降噪效果。模拟信号和真实信号的实验结果表明：该方法可以有效的消除脉冲干扰和高斯噪声，能够最大限度的降低信号均方误差，提高信噪比，增强了奇异值分解在信号降噪中的通用性。
침대기이치분해재신호강조시유효질적선택문제，제출일충기우구진질최소화화통계수정적신호강조방법。수선，이용구진질최소화이론장기이치유효질선택문제전화위질적약속우화문제；연후，통과철우화구해，득도간정신호적 Hankel 구진，실현일차강조；최후，근거기이치자집표준차대간정신호 Hankel 구진진행통계수정，진일보우화강조효과。모의신호화진실신호적실험결과표명：해방법가이유효적소제맥충간우화고사조성，능구최대한도적강저신호균방오차，제고신조비，증강료기이치분해재신호강조중적통용성。
Aiming at the selection problem of effective ranks in singular value decomposition for signal denoising,a signal denoising method based on matrix rank minimization and statistical modification was proposed.Firstly,the effective rank selection problem of singular value decomposition was transformed into a constrained optimization problem of rank by using the matrix rank minimization theory.Secondly,Hankel matrix of a clean signal was obtained with a convex optimization to realize the first noise reduction.At last,the statistical correction was performed for the clean signal's Hankel matrix with subset standard deviation of a singular value to further optimize the noise reduction effect.The simulated signal and real signal test results showed that the method can effectively eliminate pulse noise and Gaussian noise;at the same time,the method can reduce the maximum signal mean square error and improve the signal-to-noise ratio;so the method can enhance the universality of singular value decomposition in signal denoising.