In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product) [14] . Induced by the t-product, we first rigorously deduce the tensor spectral norm, tensor nuclear norm, and tensor average rank, and show that the tensor nuclear norm is the convex envelope of the tensor average rank within the unit ball of the tensor spectral norm. These definitions, their relationships and properties are consistent with matrix cases. Equipped with the new tensor nuclear norm, we then solve the TRPCA problem by solving a convex program and provide the theoretical guarantee for the exact recovery. Our TRPCA model and recovery guarantee include matrix RPCA as a special case. Numerical experiments verify our results, and the applications to image recovery and background modeling problems demonstrate the effectiveness of our method.

Camera shake or target movement often leads to undesired blur effects in videos captured by a hand-held camera. Despite significant efforts having been devoted to video-deblur research, two major challenges remain: (1) how to model the spatio-temporal characteristics across both the spatial domain (i.e., image plane) and the temporal domain (i.e., neighboring frames) and (2) how to restore sharp image details with respect to the conventionally adopted metric of pixel-wise errors. In this paper, to address the first challenge, we propose a deblurring network (DBLRNet) for spatial-temporal learning by applying a 3D convolution to both the spatial and temporal domains. Our DBLRNet is able to capture jointly spatial and temporal information encoded in neighboring frames, which directly contributes to the improved video deblur performance. To tackle the second challenge, we leverage the developed DBLRNet as a generator in the generative adversarial network (GAN) architecture and employ a content loss in addition to an adversarial loss for efficient adversarial training. The developed network, which we name as deblurring GAN, is tested on two standard benchmarks and achieves the state-of-the-art performance.

While features of different scales are perceptually important to visual inputs, existing vision transformers do not yet take advantage of them explicitly. To this end, we first propose a cross-scale vision transformer, CrossFormer. It introduces a cross-scale embedding layer (CEL) and a long-short distance attention (LSDA). On the one hand, CEL blends each token with multiple patches of different scales, providing the self-attention module itself with cross-scale features. On the other hand, LSDA splits the self-attention module into a short-distance one and a long-distance counterpart, which not only reduces the computational burden but also keeps both small-scale and large-scale features in the tokens. Moreover, through experiments on CrossFormer, we observe another two issues that affect vision transformers’ performance, i.e., the enlarging self-attention maps and amplitude explosion. Thus, we further propose a progressive group size (PGS) paradigm and an amplitude cooling layer (ACL) to alleviate the two issues, respectively. The CrossFormer incorporating with PGS and ACL is called CrossFormer++. Extensive experiments show that CrossFormer++ outperforms the other vision transformers on image classification, object detection, instance segmentation, and semantic segmentation tasks.

Human motion prediction aims to generate future motions based on the observed human motions. Witnessing the success of Recurrent Neural Networks (RNN) in modeling sequential data, recent works utilize RNNs to model human-skeleton motions on the observed motion sequence and predict future human motions. However, these methods disregard the existence of the spatial coherence among joints and the temporal evolution among skeletons, which reflects the crucial characteristics of human motions in spatiotemporal space. To this end, we propose a novel Skeleton-Joint Co-Attention Recurrent Neural Networks (SC-RNN) to capture the spatial coherence among joints, and the temporal evolution among skeletons simultaneously on a skeleton-joint co-attention feature map in spatiotemporal space. First, a skeleton-joint feature map is constructed as the representation of the observed motion sequence. Second, we design a new Skeleton-Joint Co-Attention (SCA) mechanism to dynamically learn a skeleton-joint co-attention feature map of this skeleton-joint feature map, which can refine the useful observed motion information to predict one future motion. Third, a variant of GRU embedded with SCA collaboratively models the human-skeleton motion and human-joint motion in spatiotemporal space by regarding the skeleton-joint co-attention feature map as the motion context. Experimental results of human motion prediction demonstrate that the proposed method outperforms the competing methods.