一种基于快速随机投影的矩阵填充方法

A MATRIX COMPLETION METHOD BASED ON FAST RANDOM PROJECTION

为了解决在矩阵填充过程中的高维度和高计算成本的问题,提出一种基于快速随机投影的矩阵填充方法(FRPMC)。利用对矩阵的随机投影的方式对需要填充的矩阵进行降维,然后构造SVD的近似模型来重构矩阵来实现矩阵填充的功能。通过仿真实验证明了该算法的可行性。与其他一些传统算法进行对比,FRPMC在图像恢复的实验中图片恢复的峰值信噪比和运行时间均比奇异值阈值法、加速近邻梯度法和增广拉格朗日乘子法要好。

To solve the problem of high dimensionality and high computational cost in matrix completion, we a proposed matrix completion method based on fast random projection(FRPMC). The dimension of the matrix to be completed was reduced by random projection, and then the approximate model of SVD was constructed to reconstruct the matrix to realize the function of matrix completion. The feasibility of the algorithm is proved by simulation experiments. Compared with other traditional algorithms, FRPMC has better PSNR and running time in image restoration experiments than SVT, APG and ALME.