矩阵恢复的协方差矩阵估计算法

Covariance Matrix Estimation Algorithm for Matrix Recovery

研究受高斯噪声干扰的低秩矩阵恢复。根据高斯噪声的统计性质,引入了协方差矩阵估计模型,构造出针对高斯噪声模型的低秩矩阵恢复算法。该算法基于最小化协方差矩阵核范数求解低秩矩阵,利用奇异值分解理论推导出模型的最优解。该模型结合高斯混合模型能够达到非常好的估计效果。仿真实验表明,该模型具有更快的收敛速度和更好的估计结果。

The restoration of low rank matrices disturbed by Gaussian noise is studied.According to the statistical properties of Gaussian noise,the covariance matrix estimation model is introduced,and a low rank matrix restoration algorithm for Gaussian noise model is constructed.The algorithm is based on minimizing the nuclear norm of the covariance matrix to restore the low rank matrix,and the optimal solution of the model is derived by singular value decomposition theory.This model combined with Gaussian mixture model can achieve good estimation results.Simulation results show that the model has a faster convergence rate and better estimation results.