Domain adaptation tries to adapt a model trained from a source domain to a different but related target domain. Currently, prevailing methods for domain adaptation rely on either instance reweighting or feature transformation. Unfortunately, instance reweighting has difficulty in estimating the sample weights as the dimension increases, whereas feature transformation sometimes fails to make the transformed source and target distributions similar when the cross-domain discrepancy is large. In order to overcome the shortcomings of both methodologies, in this article, we model the unsupervised domain adaptation problem under the generalized covariate shift assumption and adapt the source distribution to the target distribution in a subspace by applying a distribution adaptation function. Accordingly, we propose two frameworks: Bregman-divergence-embedded structural risk minimization (BSRM) and joint structural risk minimization (JSRM). In the proposed frameworks, the subspace distribution adaptation function and the target prediction model are jointly learned. Under certain instantiations, convex optimization problems are derived from both frameworks. Experimental results on the synthetic and real-world text and image data sets show that the proposed methods outperform the state-of-the-art domain adaptation techniques with statistical significance.

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.

Multichannel image completion with mixture noise is a challenging problem in the fields of machine learning, computer vision, image processing, and data mining. Traditional image completion models are not appropriate to deal with this problem directly since their reconstruction priors may mismatch corruption priors. To address this issue, we propose a novel nonlocal self-similarity-based weighted tensor low-rank decomposition (NSWTLD) model that can achieve global optimization and local enhancement. In the proposed model, based on the corruption priors and the reconstruction priors, a pixel weighting strategy is given to characterize the joint effects of missing data, the Gaussian noise, and the impulse noise. To discover and utilize the accurate nonlocal self-similarity information to enhance the restoration quality of the details, the traditional nonlocal learning framework is optimized by employing improved index determination of patch group and handling strip noise caused by patch overlapping. In addition, an efficient and convergent algorithm is presented to solve the NSWTLD model. Comprehensive experiments are conducted on four types of multichannel images under various corruption scenarios. The results demonstrate the efficiency and effectiveness of the proposed model.

Hyperspectral image mixed denoising is a challenging task in the fields of remote sensing, environmental monitoring, mineral exploration, etc. A crucial difficulty is to acquire clean restoration from hyperspectral image (HSI) that encounters Gaussian noise, impulse noise, strip noise and deadlines. In the previous works, combining global information and nonlocal information is a popular way to learn the comprehensive characteristics of the clean HSI. However, the advantages of 2D spatial structure similarity and spectral low-rankness may not be fully exploited at the same time in global prior learning. The iterative update between global restoration and nonlocal restoration may cause high time consumption and certain loss of information. To address these issues, we propose a three-stage mixed denoising model based on novel hybrid low-rank tensor approximation and global-guided-nonlocal prior mechanism (HLTA-GN). Firstly, to learn a good global prior, hybrid low-rank tensor approximation incorporated with a useful nonconvex tensor rank estimation is presented to balance 2D spatial similarity and spectral low-rankness. Secondly, to learn a high-quality nonlocal prior, global-guided-nonlocal prior mechanism is proposed to help nonlocal restoration suppress the residual noise. At the same time, a regularized sequential low-rank tensor approximation is proposed to enhance the robustness to noisy patch groups. Thirdly, a weighted fusion on global prior and nonlocal prior helps to further balance global denoising and patch processing. An efficient learning algorithm is provided to solve HLTA-GN. Abundant experiments are conducted on various HSIs with several scenarios. The experimental results demonstrate the superiority of HLTA-GN.