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.

This paper presents a joint dehazing and denoising scheme for an image taken in hazy conditions. Conventional image dehazing methods may amplify the noise depending on the distance and density of the haze. To suppress the noise and improve the dehazing performance, an imaging model is modified by adding the process of amplifying the noise in hazy conditions. This model offers a depth-chromaticity compensation regularization for transmission map and a chromaticity-depth compensation regularization for dehazing the image. The proposed iterative image dehazing method with polarization uses these two joint regularization schemes and the relationship between transmission map and dehazed image. The transmission map and irradiance image are used to promote each other. To verify the effectiveness of the algorithm, polarizing images of different scenes in different days are collected. Different algorithms are applied to the original images. Experiment results demonstrate that the proposed scheme increases visibility in extreme weather conditions without amplifying the noise.

Recently, tensor sparsity modeling has achieved great success in the tensor completion (TC) problem. In real applications, the sparsity of a tensor can be rationally measured by low-rank tensor decomposition. However, existing methods either suffer from limited modeling power in estimating accurate rank or have difficulty in depicting hierarchical structure underlying such data ensembles. To address these issues, we propose a parametric tensor sparsity measure model, which encodes the sparsity for a general tensor by Laplacian scale mixture (LSM) modeling based on three-layer transform (TLT) for factor subspace prior with Tucker decomposition. Specifically, the sparsity of a tensor is first transformed into factor subspace, and then factor sparsity in the gradient domain is used to express the local similarity in within-mode. To further refine the sparsity, we adopt LSM by the transform learning scheme to self-adaptively depict deeper layer structured sparsity, in which the transformed sparse matrices in the sense of a statistical model can be modeled as the product of a Laplacian vector and a hidden positive scalar multiplier. We call the method as parametric tensor sparsity delivered by LSM-TLT. By a progressive transformation operator, we formulate the LSM-TLT model and use it to address the TC problem, and then the alternating direction method of multipliers-based optimization algorithm is designed to solve the problem. The experimental results on RGB images, hyperspectral images (HSIs), and videos demonstrate the proposed method outperforms state of the arts.

This paper presents a mosaic convolution-attention network (MCAN) for demosaicing spectral mosaic images captured using multispectral filter array (MSFA) imaging sensors. MSFA-based multispectral imaging systems acquire multispectral information of a scene in a single snap-shot operation. A complete multispectral image is reconstructed by demosaicing an MSFA-based spectral mosaic image. To avoid aliasing and artifacts in demosaicing, we utilize joint spatial-spectral correlation in a raw mosaic image. The proposed MCAN includes a mosaic convolution module (MCM) and a mosaic attention module (MAM). The MCM extracts features via a learning approach with a margin between splitting the periodic spectral mosaic and keeping the underlying spatial information of the raw image. Based on the strategy of position-sensitive weight sharing, MCM assigns the same weight to pixels with the same relative position in an MSFA. The MAM uses a position-sensitive feature aggregation strategy to describe the loading of mosaic patterns within the feature maps, which gradually reduces mosaic distortion through the attention mechanism. The experimental results on synthetic as well as real-world data show that the proposed scheme outperforms state-of-the-art methods in terms of spatial details and spectral fidelity.

Conventional tensor completion (TC) methods generally assume that the sparsity of tensor-valued data lies in the global subspace. The so-called global sparsity prior is measured by the tensor nuclear norm. Such assumption is not reliable in recovering low-rank (LR) tensor data, especially when considerable elements of data are missing. To mitigate this weakness, this article presents an enhanced sparsity prior model for LRTC using both local and global sparsity information in a latent LR tensor. In specific, we adopt a doubly weighted strategy for nuclear norm along each mode to characterize global sparsity prior of tensor. Different from traditional tensor-based local sparsity description, the proposed factor gradient sparsity prior in the Tucker decomposition model describes the underlying subspace local smoothness in real-world tensor objects, which simultaneously characterizes local piecewise structure over all dimensions. Moreover, there is no need to minimize the rank of a tensor for the proposed local sparsity prior. Extensive experiments on synthetic data, real-world hyperspectral images, and face modeling data demonstrate that the proposed model outperforms state-of-the-art techniques in terms of prediction capability and efficiency.

The fusion of infrared and visible images combines the information from two complementary imaging modalities for various computer vision tasks. Many existing techniques, however, fail to maintain a uniform overall style and keep salient details of individual modalities simultaneously. This paper presents an end-to-end Laplacian Pyramid Fusion Network with hierarchical guidance (HG-LPFN) that takes advantage of pixel-level saliency reservation of Laplacian Pyramid and global optimization capability of deep learning. The proposed scheme generates hierarchical saliency maps through Laplacian Pyramid decomposition and modal difference calculation. In the pyramid fusion mode, all sub-networks are connected in a bottom-up manner. The sub-network for low-frequency fusion focuses on extracting universal features to produce an opposite style while sub-networks for high-frequency fusion determine how much the details of each modality will be retained. Taking the style, details, and background into consideration, we design a set of novel loss functions to supervise both low-frequency images and full-resolution images under the guidance of saliency maps. Experimental results on public datasets demonstrate that the proposed HG-LPFN outperforms the state-of-the-art image fusion techniques.