Deep Sparse Tensor Filtering Network for Synthetic Aperture Radar Images Classification

Multilayer Sparsity-Based Tensor Decomposition for Low-Rank Tensor Completion

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.

Accurate Tensor Completion via Adaptive Low-Rank Representation

Low-rank representation-based approaches that assume low-rank tensors and exploit their low-rank structure with appropriate prior models have underpinned much of the recent progress in tensor completion. However, real tensor data only approximately comply with the low-rank requirement in most cases, viz., the tensor consists of low-rank (e.g., principle part) as well as non-low-rank (e.g., details) structures, which limit the completion accuracy of these approaches. To address this problem, we propose an adaptive low-rank representation model for tensor completion that represents low-rank and non-low-rank structures of a latent tensor separately in a Bayesian framework. Specifically, we reformulate the CANDECOMP/PARAFAC (CP) tensor rank and develop a sparsity-induced prior for the low-rank structure that can be used to determine tensor rank automatically. Then, the non-low-rank structure is modeled using a mixture of Gaussians prior that is shown to be sufficiently flexible and powerful to inform the completion process for a variety of real tensor data. With these two priors, we develop a Bayesian minimum mean-squared error estimate framework for inference. The developed framework can capture the important distinctions between low-rank and non-low-rank structures, thereby enabling more accurate model, and ultimately, completion. For various applications, compared with the state-of-the-art methods, the proposed model yields more accurate completion results.

Skip-Connected Covariance Network for Remote Sensing Scene Classification

This paper proposes a novel end-to-end learning model, called skip-connected covariance (SCCov) network, for remote sensing scene classification (RSSC). The innovative contribution of this paper is to embed two novel modules into the traditional convolutional neural network (CNN) model, i.e., skip connections and covariance pooling. The advantages of newly developed SCCov are twofold. First, by means of the skip connections, the multi-resolution feature maps produced by the CNN are combined together, which provides important benefits to address the presence of large-scale variance in RSSC data sets. Second, by using covariance pooling, we can fully exploit the second-order information contained in such multi-resolution feature maps. This allows the CNN to achieve more representative feature learning when dealing with RSSC problems. Experimental results, conducted using three large-scale benchmark data sets, demonstrate that our newly proposed SCCov network exhibits very competitive or superior classification performance when compared with the current state-of-the-art RSSC techniques, using a much lower amount of parameters. Specifically, our SCCov only needs 10% of the parameters used by its counterparts.

Learning a Low Tensor-Train Rank Representation for Hyperspectral Image Super-Resolution

Hyperspectral images (HSIs) with high spectral resolution only have the low spatial resolution. On the contrary, multispectral images (MSIs) with much lower spectral resolution can be obtained with higher spatial resolution. Therefore, fusing the high-spatial-resolution MSI (HR-MSI) with low-spatial-resolution HSI of the same scene has become the very popular HSI super-resolution scheme. In this paper, a novel low tensor-train (TT) rank (LTTR)-based HSI super-resolution method is proposed, where an LTTR prior is designed to learn the correlations among the spatial, spectral, and nonlocal modes of the nonlocal similar high-spatial-resolution HSI (HR-HSI) cubes. First, we cluster the HR-MSI cubes as many groups based on their similarities, and the HR-HSI cubes are also clustered according to the learned cluster structure in the HR-MSI cubes. The HR-HSI cubes in each group are much similar to each other and can constitute a 4-D tensor, whose four modes are highly correlated. Therefore, we impose the LTTR constraint on these 4-D tensors, which can effectively learn the correlations among the spatial, spectral, and nonlocal modes because of the well-balanced matricization scheme of TT rank. We formulate the super-resolution problem as TT rank regularized optimization problem, which is solved via the scheme of alternating direction method of multipliers. Experiments on HSI data sets indicate the effectiveness of the LTTR-based method.