We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, in which empirical singular values below a threshold λ are set to 0. We study the asymptotic MSE (AMSE) in a framework where the matrix size is large compared to the rank of the matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. The AMSE-optimal choice of h...

We consider recovery of low-rank matrices from noisy data by hard thresholding of singular values, in which empirical singular values below a prescribed threshold λ are set to 0. We study the asymptotic MSE (AMSE) in a framework where the matrix size is large compared to the rank of the matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. The AMSE-optimal ...

In this paper, we study the low-rank tensor completion problem, where a high-order tensor with missing entries is given and the goal is to complete the tensor. We propose to minimize a new convex objective function, based on log sum of exponentials of nuclear norms, that promotes the low-rankness of unfolding matrices of the completed tensor. We show for the first time that the proximal operato...

Canyi Lu, Changbo Zhu, Chunyan Xu, Shuicheng Yan, Zhouchen Lin3,∗ 1 Department of Electrical and Computer Engineering, National University of Singapore 2 School of Computer Science and Technology, Huazhong University of Science and Technology 3 Key Laboratory of Machine Perception (MOE), School of EECS, Peking University [email protected], [email protected], [email protected], eleyans@n...

In this paper a new approach for speech enhancement is presented. The proposed algorithm is based on singular value decomposition (SVD) and wavelet transform. A model of contaminant noise is estimated by using SVD in the recommended method and then, using of noise estimation determines thresholding value. Needlessness of silence frame in order to estimate the noise model is an advantage of sugg...