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Tensor completion is a fundamental tool to estimate unknown information from observed data, which is widely used in many areas, including image and video recovery, traffic data completion and the multi-input multi-output problems in information theory. Based on Tucker decomposition, this paper proposes a new algorithm to complete tensors with missing data. In decomposition-based tensor completion methods, underestimation or overestimation of tensor ranks can lead to inaccurate results. To tackle this problem, we design an alternative iterating method that breaks the original problem into several matrix completion subproblems and adaptively adjusts the multilinear rank of the model during optimization procedures. Through numerical experiments on synthetic data and authentic images, we show that the proposed method can effectively estimate the tensor ranks and predict the missing entries. [ABSTRACT FROM AUTHOR]

Tensor completion is a fundamental tool to estimate unknown information from observed data, which is widely used in many areas, including image and video recovery, traffic data completion and the multi-input multi-output problems in information theory. Based on Tucker decomposition, this paper proposes a new algorithm to complete tensors with missing data. In decomposition-based tensor completion methods, underestimation or overestimation of tensor ranks can lead to inaccurate results. To tackle this problem, we design an alternative iterating method that breaks the original problem into several matrix completion subproblems and adaptively adjusts the multilinear rank of the model during optimization procedures. Through numerical experiments on synthetic data and authentic images, we show that the proposed method can effectively estimate the tensor ranks and predict the missing entries.

In this paper, channel estimation for multiuser massive MIMO system is addressed for the scenario, where the number of scatterers is small compared to the base station antennas and single antenna users in the cell. If the number of scatterers is limited, then the corresponding angle of arrivals are finite. Moreover, if all the users share the same angle of arrivals, then the correlation among the channel vector increases. Thus, the high-dimensional channel is approximated to the low-rank matrix. This rank minimization problem is formulated as the weighted nuclear norm problem and is estimated using iterative weighted singular value thresholding (IWSVT) algorithm. To increase the convergence rate, fast IWSVT algorithm is proposed and the performance is measured based on mean square error and uplink and downlink achievable sum-rate. The simulation study shows that the proposed weighted nuclear norm minimization method with fast IWSVT algorithm performs better than the conventional least square and the nuclear norm minimization method for various finite scatterers in different signal-to-noise ratio levels. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we give a lower bound guaranteeing exact matrix completion via singular value thresholding (SVT) algorithm. The analysis shows that when the parameter in SVT algorithm is beyond some finite scalar, one can recover some unknown low-rank matrices exactly with high probability by solving a strictly convex optimization problem. Furthermore, we give an explicit expression for such a finite scalar. This result in the paper not only has theoretical interests, but also guides us to choose suitable parameters in the SVT algorithm. [Copyright &y& Elsevier]