Existing methods for tensor completion (TC) have limited ability for characterizing low-rank (LR) structures. To depict the complex hierarchical knowledge with implicit sparsity attributes hidden in a tensor, we propose a new multilayer sparsity-based tensor decomposition (MLSTD) for the low-rank tensor completion (LRTC). The method encodes the structured sparsity of a tensor by the multiple-layer representation. Specifically, we use the CANDECOMP/PARAFAC (CP) model to decompose a tensor into an ensemble of the sum of rank-1 tensors, and the number of rank-1 components is easily interpreted as the first-layer sparsity measure. Presumably, the factor matrices are smooth since local piecewise property exists in within-mode correlation. In subspace, the local smoothness can be regarded as the second-layer sparsity. To describe the refined structures of factor/subspace sparsity, we introduce a new sparsity insight of subspace smoothness: a self-adaptive low-rank matrix factorization (LRMF) scheme, called the third-layer sparsity. By the progressive description of the sparsity structure, we formulate an MLSTD model and embed it into the LRTC problem. Then, an effective alternating direction method of multipliers (ADMM) algorithm is designed for the MLSTD minimization problem. Various experiments in RGB images, hyperspectral images (HSIs), and videos substantiate that the proposed LRTC methods are superior to state-of-the-art methods.

Sparse subspace clustering (SSC) has emerged as an effective approach for the automatic analysis of hyperspectral images (HSI). Traditional SSC-based approaches employ the input HSI data as a dictionary of atoms, in terms of which all the data samples are linearly represented. This leads to highly redundant dictionaries of huge size, and the computational complexity of the resulting optimization problems becomes prohibitive for large-scale data. In this article, we propose a scalable subspace clustering method, which integrates the learning of a concise dictionary and robust subspace representation in a unified model. This reduces significantly the size of the involved optimization problems. We introduce a new adaptive spatial regularization for the representation coefficients, which incorporates spatial information of HSI and improves the robustness of the model to noise. We derive an effective solver based on alternating minimization and alternating direction method of multipliers (ADMMs) to solve the resulting optimization problem. Experimental results on four representative hyperspectral images show the effectiveness of the proposed method and excellent clustering performance relative to the state of the art.

Band selection (BS) reduces effectively the spectral dimension of a hyperspectral image (HSI) by selecting relatively few representative bands, which allows efficient processing in subsequent tasks. Existing unsupervised BS methods based on subspace clustering are built on matrix-based models, where each band is reshaped as a vector. They encode the correlation of data only in the spectral mode (dimension) and neglect strong correlations between different modes, i.e., spatial modes and spectral mode. Another issue is that the subspace representation of bands is performed in the raw data space, where the dimension is often excessively high, resulting in a less efficient and less robust performance. To address these issues, in this article, we propose a tensor-based subspace clustering model for hyperspectral BS. Our model is developed on the well-known Tucker decomposition. The three factor matrices and a core tensor in our model encode jointly the multimode correlations of HSI, avoiding effectively to destroy the tensor structure and information loss. In addition, we propose well-motivated heterogeneous regularizations (HRs) on the factor matrices by taking into account the important local and global properties of HSI along three dimensions, which facilitates the learning of the intrinsic cluster structure of bands in the low-dimensional subspaces. Instead of learning the correlations of bands in the original domain, a common way for the matrix-based models, our model learns naturally the band correlations in a low-dimensional latent feature space, which is derived by the projections of two factor matrices associated with spatial dimensions, leading to a computationally efficient model. More importantly, the latent feature space is learned in a unified framework. We also develop an efficient algorithm to solve the resulting model. Experimental results on benchmark datasets demonstrate that our model yields improved performance compared to the state-of-the-art.

Band selection, which removes irrelevant bands from hyperspectral images (HSIs) and keeps essential spectral information contained in a relatively few bands, allows huge savings in data storage, computation time, and imaging hardware. In this article, we propose a novel structural subspace clustering (STSC) method for hyperspectral band selection, which leverages the self-representation property of data and structural prior information to learn the cluster structure of bands. Particularly, we propose a general clustering model where the coarse coefficients matrix derived from a self-representation model is decomposed as a combination of a desirable coefficients matrix and a sparse matrix. This strategy adaptively adjusts the coarse coefficients matrix to learn the intrinsic data structure in low-dimensional subspaces. To guide this learning process, we introduce a structural regularization approach which makes use of the prior information about local and global properties of spectral bands. Moreover, we incorporate also prior knowledge about the dictionary, which demonstrates to yield a better clustering performance. We develop an adaptive method to estimate the number of selected bands by analyzing eigenvalue gaps of Laplacian matrix. To solve the resulting model, an efficient algorithm based on alternating direction method of multipliers (ADMMs) is developed. Extensive experiments on benchmark HSIs show that our method outperforms the state-of-the-art band selection methods.

Clustering algorithms play an essential and unique role in classification tasks, especially when annotated data are unavailable or very scarce. Current clustering approaches in remote sensing are mostly designed for a single data source, such as hyperspectral image (HSI), while, nowadays, multisensor data are being routinely acquired. In this article, we propose a multiview subspace clustering model that exploits effectively the rich information from multiple features extracted either from a single data source (HSI) or from multiple sources that we call generically multiviews of the same scene. An important novelty of our approach is that it integrates local and nonlocal spatial information from each view in a unified framework. Our model learns a common intrinsic cluster structure from view-specific subspace representations by a new decomposition-based scheme. In addition, we develop innovative manifold-based spatial regularization as a hybrid hypergraph, which merges local and nonlocal spatial context and improves, thereby, the learning of view-specific structures. We develop an efficient algorithm to solve the resulting optimization problem. Extensive experiments on real data sets demonstrate the superior clustering performance over the state of the art.

Sparse subspace clustering (SSC), as an effective subspace clustering technique, has been widely applied in the remote sensing community, demonstrating a superior performance over the traditional methods such as k-means. In this paper, we propose a unified framework for hyperspectral image (HSI) clustering, which incorporates spatial information and label information in an SSC model, aiming at generating a more precise similarity matrix. The spatial information is included through a joint sparsity constraint on the coefficient matrix of each local region. Pixels within a local region are encouraged to select a common set of samples in the subspace-sparse representation, which greatly promotes the connectivity of the similarity matrix. We incorporate the available label information effectively within the same framework, by zeroing the entries of the sparse coefficient matrix, which correspond to the data points from different classes. An optimization algorithm is derived based on the alternating direction method of multipliers for the resulting model. Experimental results on real HSIs demonstrate a superior performance over the related state-of-the-art methods.