The problem of recovering missing data of an incomplete tensor has drawn more and more attentions in the fields of pattern recognition, machine learning, data mining, computer vision, and signal processing. Researches on this problem usually share a common assumption that the original tensor is of low-rank. One of the important ways to capture the low-rank structure of the incomplete tensor is based on tensor factorization. For the traditional tensor factorization algorithms, the tensor ranks should be specified ahead, which is not reasonable in real applications. To overcome this drawback, an adaptive algorithm is first presented based on sequentially truncated higher order singular value decomposition (ST-HOSVD) for fast low-rank approximation of complete tensor, in which the tensor ranks can be obtained adaptively. Then for tensor with missing data, we use adaptive ST-HOSVD and the average operator of low-rank approximation to improve the accuracy of the fulfilled tensor. Convergence analysis of the proposed algorithm is also given in this paper. The experimental results on 14 image datasets and three video datasets show that the proposed method outperforms the state-of-the-art methods in terms of running time and the accuracy.

Microseismic monitoring data may be seriously contaminated by complex and nonstationary interference noises produced by mechanical vibration, which significantly impact the data quality and subsequent data-processing procedure. One challenge in microseismic data processing is separating weak seismic signals from varying noisy data. To address this issue, we proposed an ambient-noise-assisted multivariate empirical mode decomposition (ANA-MEMD) method for adaptively suppressing noise in low signal-to-noise (S/N) microseismic data. In the proposed method, a new multi-channel record is produced by combining the noisy microseismic signal with preceding ambient noises. The multi-channel record is then decomposed using multivariate empirical mode decomposition (MEMD) into multivariate intrinsic mode functions (MIMFs). Then, the MIMFs corresponding to the main ambient noises can be identified by calculating and sorting energy percentage in descending order. Finally, the IMFs associated with strong interference noise, high-frequency and low-frequency noise are filtered out and suppressed by the energy percentage and frequency range. We investigate the feasibility and reliability of the proposed method using both synthetic data and field data. The results demonstrate that the proposed method can mitigate the mode mixing problem and clarify the main noise contributors by adding additional ambient-noise-assisted channels, hence separating the microseismic signal and ambient noise effectively and enhancing the S/Ns of microseismic signals.

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As an important tool of multiway/tensor data analysis tool, Tucker decomposition has been applied widely in various fields. But traditional sequential Tucker algorithms have been outdated because tensor data is growing rapidly in term of size. To address this problem, in this article, we focus on parallel Tucker decomposition of dense tensors on distributed-memory systems. The proposed method uses hierarchical SVD to accelerate the SVD step in traditional sequential algorithms, which usually takes up most computation time. The data distribution strategy is designed to follow the implementation of hierarchical SVD. We also find that compared with the state-of-the-art method, the proposed method has lower communication cost in large-scale parallel cases under the assumption of the α-β model.