点击次数：

论文类型：期刊论文

发表时间：2015-05-01

发表刊物：INVERSE PROBLEMS AND IMAGING

收录刊物：SCIE、ESI高被引论文、Scopus

卷号：9

期号：2

页面范围：601-624

ISSN号：1930-8337

关键字：Higher-order tensor; low-rank matrix completion; low-rank tensor completion; alternating least squares; non-convex optimization

摘要：Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data reconstruction, and so on. We propose a new model to recover a low-rank tensor by simultaneously performing low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An alternating minimization algorithm is applied to solve the model, along with two adaptive rank-adjusting strategies when the exact rank is not known.
   Phase transition plots reveal that our algorithm can recover a variety of synthetic low-rank tensors from significantly fewer samples than the compared methods, which include a matrix completion method applied to tensor recovery and two state-of-the-art tensor completion methods. Further tests on real-world data show similar advantages. Although our model is non-convex, our algorithm performs consistently throughout the tests and gives better results than the compared methods, some of which are based on convex models. In addition, subsequence convergence of our algorithm can be established in the sense that any limit point of the iterates satisfies the KKT condtions.