Pansharpening refers to the fusion of a low spatial-resolution multispectral image with a high spatial-resolution panchromatic image. In this paper, we propose a novel low-rank tensor completion (LRTC)-based framework with some regularizers for multispectral image pansharpening, called LRTCFPan. The tensor completion technique is commonly used for image recovery, but it cannot directly perform the pansharpening or, more generally, the super-resolution problem because of the formulation gap. Different from previous variational methods, we first formulate a pioneering image super-resolution (ISR) degradation model, which equivalently removes the downsampling operator and transforms the tensor completion framework. Under such a framework, the original pansharpening problem is realized by the LRTC-based technique with some deblurring regularizers. From the perspective of regularizer, we further explore a local-similarity-based dynamic detail mapping (DDM) term to more accurately capture the spatial content of the panchromatic image. Moreover, the low-tubal-rank property of multispectral images is investigated, and the low-tubal-rank prior is introduced for better completion and global characterization. To solve the proposed LRTCFPan model, we develop an alternating direction method of multipliers (ADMM)-based algorithm. Comprehensive experiments at reduced-resolution (i.e., simulated) and full-resolution (i.e., real) data exhibit that the LRTCFPan method significantly outperforms other state-of-the-art pansharpening methods. The code is publicly available at: https://github.com/zhongchengwu/code_LRTCFPan .

Pansharpening refers to a spatio-spectral fusion of a lower spatial resolution multispectral (MS) image with a high spatial resolution panchromatic image, aiming at obtaining an image with a corresponding high resolution both in the domains. In this article, we propose a generic fusion framework that is able to weightedly combine variational optimization (VO) with deep learning (DL) for the task of pansharpening, where these crucial weights directly determining the relative contribution of DL to each pixel are estimated adaptively. This framework can benefit from both VO and DL approaches, e.g., the good modeling explanation and data generalization of a VO approach with the high accuracy of a DL technique thanks to massive data training. The proposed method can be divided into three parts: 1) for the VO modeling, a general details injection term inspired by the classical multiresolution analysis is proposed as a spatial fidelity term and a spectral fidelity employing the MS sensor’s modulation transfer functions is also incorporated; 2) for the DL injection, a weighted regularization term is designed to introduce deep learning into the variational model; and 3) the final convex optimization problem is efficiently solved by the designed alternating direction method of multipliers. Extensive experiments both at reduced and full-resolution demonstrate that the proposed method outperforms recent state-of-the-art pansharpening methods, especially showing a higher accuracy and a significant generalization ability.

Pansharpening is related to the fusion of a low spatial resolution multispectral (MS) image retaining an abundant spectral content and a high spatial resolution panchromatic (PAN) image to obtain a product with both the abundant spectral content of the former and the high spatial resolution of the latter. Many previous studies are only focused on the global or local relationship between the PAN image and the corresponding high-resolution multispectral (HRMS) image. However, we found that the relationship between PAN and HRMS images in the gradient domain can be better explored through the image context. In this article, we propose context-aware details injection fidelity (CDIF) with adaptive coefficients estimation, which can fully explore the complicated relationship between the PAN image and the HRMS image in the gradient domain. More specifically, we apply a clustering method to divide the pixels of an image into different context-based regions. Afterward, the adaptive coefficients are estimated by using a regression-based method for each region. The CDIF is effective in extracting the main features from the two inputs to be fused. In addition, we integrate the CDIF with a conventional fidelity term and a total variation regularization to formulate a novel variational pansharpening model that is solved by designing an algorithm based on the alternating direction method of multiplier (ADMM) framework. Qualitative and quantitative assessments on different datasets support the effectiveness and robustness of the proposed method. The code is available at https://github.com/liangjiandeng/CDIF .

Pansharpening is a very debated spatio-spectral fusion problem. It refers to the fusion of a high spatial resolution panchromatic (PAN) image with a lower spatial but higher spectral resolution multispectral (LRMS) image in order to obtain an image with high resolution in both the domains. In this paper, we propose a novel variational optimization-based (VO) approach to address this issue incorporating the outcome of a deep convolutional neural network (DCNN). This solution can take advantages of both the paradigms. On one hand, higher performance can be expected introducing machine learning methods based on the training by examples philosophy into VO approaches. On other hand, the combination of VO techniques with DCNNs can aid the generalization ability of these latter. In particular, we formulate a l2-based proximal deep injection term to evaluate the distance between the DCNN outcome and the desired high spatial resolution multispectral image. This represents the regularization term for our VO model. Furthermore, a new data fitting term measuring the spatial fidelity is proposed. Finally, the proposed convex VO problem is efficiently solved by exploiting the framework of the alternating direction method of multipliers, thus guaranteeing the convergence of the algorithm. Extensive experiments both on simulated and real datasets demonstrate that the proposed approach can outperform state-of-the-art spatio-spectral fusion methods, even showing a significant generalization ability.

Pansharpening (which stands for panchromatic sharpening) involves the fusion between a multispectral (MS) image with a higher spectral content than a fine spatial resolution panchromatic (PAN) image to generate a high spatial resolution multispectral (HRMS) image. A widely-used concept is the construction of the relationship between PAN and HRMS images by designing pixel-based coefficients. Previous pixel-based methods compute the coefficients pixel-by-pixel while suffering from inaccuracies in some areas leading to spatial distortion. However, we found that the coefficients inherit the spatial properties of the HRMS image, e.g., the local smoothness and nonlocal self-similarity, and the spatial correlation between the coefficients and the HRMS image can increase the accuracy of the estimation process. In this article, we propose a novel spatial fidelity with nonlocal regression (SFNLR) to describe the relationship between PAN and HRMS images. Unlike from the pixel-based perspective, the SFNLR can jointly utilize the local smoothness and nonlocal self-similarity of the coefficients for preserving spatial information. Besides, the SFNLR is integrated with a widely-used spectral fidelity to formulate a new variational model for the pansharpening problem. An effective algorithm based on the alternating direction method of multiplier (ADMM) framework is designed to solve the proposed model. Qualitative and quantitative assessments on reduced and full resolution datasets from different satellites demonstrate that the proposed approach outperforms several state-of-the-art methods. The code is available at: https://github.com/Jin-liangXiao/SFNLR.

The purpose of panchromatic sharpening, i.e., pansharpening, is to fuse a low spatial resolution multispectral (LRMS) image with a high spatial resolution panchromatic (PAN) image, aiming to obtain a high spatial resolution multispectral (HRMS) image. Pansharpening models based on variational optimization consist of a spectral fidelity term, a spatial fidelity term, and a regularization term. Most of the methods assume that the existing PAN image and the homologous HRMS image satisfy the global or local linear relationship, which could be far from the real case, thus causing sub-optimal performance. Inspired by the nonlinear mapping ability of machine learning (ML) techniques, we propose a novel spatial fidelity term with learnable nonlinear mapping (LNM-SF), which trains an implicit functional operator via a specifically designed convolutional neural network (CNN) and efficiently constructs the nonlinear relationship between the known PAN and the latent HRMS images. Relying upon the above description of the spatial fidelity term, a new variational model with a learnable nonlinear mapping in the spatial fidelity term for pansharpening, named LNM-PS, is simply integrated by the conventional spectral fidelity term into the proposed LNM-SF. To effectively solve the resulting optimization problem, we develop an alternating direction method of multipliers (ADMM)-based algorithm with the fast iterative shrinkage-thresholding algorithm (FISTA) as inner solver. Extensive numerical experiments on different datasets, assessing the performance both at reduced-resolution and full-resolution, show the superiority of the proposed LNM-PS method. The code is available at https://github.com/liangjiandeng/-LNM-PS.