亚高斯测量映射的限制等距性质

Restricted Isometric Property of Sub-Gaussian Measurement Mapping

信号恢复的充分条件是测量矩阵须满足限制等距性质,类比可知低秩矩阵恢复的充分条件是需要一个线性映射满足限制等距性质。线性映射与矩阵可以一一对应,因此本文通过一个与亚高斯测量映射一一对应的亚高斯矩阵,以建立亚高斯测量映射的限制等距性质,并得出秩最多为s的低秩矩阵可以进行稀疏恢复的结论。

The sufficient condition of vector sparse recovery is that the measurement matrix needs to meet the restricted isometric property.By analogy,it can be seen that the sufficient condition of low rank matrix recovery is that a linear mapping needs to meet the restricted isometric property.Linear mapping and matrix can correspond one-to-one.Therefore,this paper establishes the restricted isometric property of Sub-Gaussian measurement mapping through a Sub-Gaussian matrix corresponding to Sub-Gaussian measurement mapping one-to-one,and obtains that the low rank matrix with the most rank can be sparsely restored.