The ubiquitous information from multiple-view data, as well as the complementary information among different views, is usually beneficial for various tasks, for example, clustering, classification, denoising, and so on. Multiview subspace clustering is based on the fact that multiview data are generated from a latent subspace. To recover the underlying subspace structure, a successful approach adopted recently has been sparse and/or low-rank subspace clustering. Despite the fact that existing subspace clustering approaches may numerically handle multiview data, by exploring all possible pairwise correlation within views, high-order statistics that can only be captured by simultaneously utilizing all views are often overlooked. As a consequence, the clustering performance of the multiview data is compromised. To address this issue, in this paper, a novel multiview clustering method is proposed by using t-product in the third-order tensor space. First, we propose a novel tensor construction method to organize multiview tensorial data, to which the tensor-tensor product can be applied. Second, based on the circular convolution operation, multiview data can be effectively represented by a t-linear combination with sparse and low-rank penalty using “self-expressiveness.” Our extensive experimental results on face, object, digital image, and text data demonstrate that the proposed method outperforms the state-of-the-art methods for a range of criteria.

Blind source separation (BSS) in time-frequency (TF) domain is a versatile framework to recover sources from the recorded mixture signals in a reverberant environment. In general, a two-stage strategy is one of the popular BSS frameworks for the underdetermined BSS case (the number of mixtures is less than the number of sources), which is a tough problem due to the mixing matrix is not invertible. In this paper, we propose a new two-stage scheme combining density-based clustering and sparse reconstruction to estimate mixing matrix and sources, respectively. At the first stage, we transform the mixing matrix estimation as an eigenvector clustering problem based on a particular local dominant assumption. The eigenvectors are first exploited from the rank-one structure of local covariance matrices of mixture TF vectors. These eigenvectors are then clustered and adjusted to give estimated mixing matrix by cooperating density-based clustering and weight clustering. At the second stage, we transform the source reconstruction as a ℓp norm (0>p ≤ 1) minimization by an iterative Lagrange multiplier method. With a proper initialization, the obtained solution is a global minimum for any p in (0,1] with convergence guarantee. The proposed approach is demonstrated to be superior to the state-of-the-art baseline methods in various underdetermined experiments.

In this letter, the application of super-resolution (SR) techniques to GaoFen(GF)-4, which is the most advanced geostationary-orbit earth observing satellite in China, remote sensing images is investigated and tested. One of the shortcomings of the geostationary-orbit-based earth observing satellite is the limitation of spatial resolution. However, human beings never stop pursuing higher resolution in images. This is the first experiment of applying SR to a sequence of low-resolution (LR) images captured by GF-4 within a short time period. One of the barriers for applying SR to remote sensing images is the large time gaps between those LR image acquisition, because the reflection characteristic of the ground may change within the time period when those LR images were captured. However, GF-4 has the unique advantage of capturing a sequence of LR images of the same region in minutes, i.e., working as a staring camera from the point view of SR. The reconstructed high-resolution images of some regions in Beijing and Hainan are shown and evaluated in this letter. This letter demonstrates that the application of SR to geostationary-orbit-based earth observation data is feasible and valuable, and it has the potential to be applied to the images acquired by all other geostationary-orbit-based earth observing systems.