Recovering rank-one matrices via rank-r matrices relaxation
11:20:00 - 12:20:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
In this paper, a relaxation is employed to nonconvex alternating minimization methods to recover the rank-one matrices. A generic measurement matrix can be standardized to a matrix consisting of orthonormal columns. To recover the rank-one matrix, the standardized frames are used to select the matrix with the maximal leading eigenvalue among the rank-$r$ matrices. Empirical studies are conducted to validate the effectiveness of this relaxation approach. In this work, we discuss one theoretical result: In the case of Gaussian random matrices with a sufficient number of nearly orthogonal sensing vectors, the singular vector corresponding to the least singular value is close to the unknown signal, and thus it can be a good initialization for the nonconvex minimization algorithm.