A Sequentially Truncated Higher Order Singular Value Decomposition-Based Algorithm for Tensor Completion

Abstract

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.

ORTP: A Video SAR Imaging Algorithm Based on Low-Tubal-Rank Tensor Recovery

“…• experiments on real video data: In real video dataset, we choose an NBA basketball video of size 144×256×40 (source: YouTube, as used in [49]), with a non-stationary panning camera moving from left to right horizontally following the running players. The proposed ORTP algorithm is compared with 1) low-tubal-rank recovery algorithms including AM, TNM, NM, CO, NO, MM, and 2) low-rank tensor recover algorithms using other rank definitions including high order singular value decomposition (HOSVD) in [37], H-Tucker (HT) algorithm in [38], TT algorithm in [39], Tucker format by Riemannian optimization (RO) in [58] and Bayesian minimum meansquared error estimate framework (BME) in [59]. • experiments on real video SAR data: an analysis of the performance of the proposed ORTP algorithm compared with the existing video SAR imaging algorithms and various low-rank tensor recovery algorithms on real video SAR data.…”

HOSVD-Based Algorithm for Weighted Tensor Completion

“…In this section, we test our weighted HOSVD algorithm for tensor completion on three videos, see [ 50 ]. The dataset is the tennis-serve data from an Olympic Sports Dataset [ 51 ].…”

“…The three videos are color video. In our simulation, we use the same setup as the one in [ 50 ], and choose 30 frames evenly from each video. For each frame, the size is scaled to , so each video is transformed into a 4-D tensor data of size .…”

“…In this work, the following the pre-existing reference databases have been used for our evaluations: tennis-seve dataset ([ 50 , 51 ]) and candel video data ([ 52 ]).They are publicly available at: (accessed date 10 May 2021); (accessed date 10 May 2021).…”

Tensor Completion through Total Variationwith Initialization from Weighted HOSVD

“…2) Data: In this part, we have tested our algorithm on three video data, see [14]. The video data are tennisserve data from an Olympic Sports Dataset.…”