In this letter, based on tensor modeling, we propose a novel panchromatic (Pan)-guided tensor low-rank (PGTLR) model for multispectral image (MSI) sharpening, which aims to fuse the low resolution (LR) MSI and Pan image to output the high resolution (HR) MSI. On one hand, we novelly exploit the tensor low-fibered-rank prior of HR MSI to model its global three-dimensional spatial-spectral correlations, which is constructed as the tensor nuclear norm (TNN) prior term. On the other hand, we further novelly exploit the Pan-guided tensor low-fibered-rank prior to model the spatial link between HR MSI and Pan, which is constructed as the novel Pan-guided TNN prior term. Furthermore, the proposed PGTLR model is optimized by an efficient alternative algorithm. Moreover, the experimental results on reduced-scale and full-scale datasets quantitatively and visually validate the superiority of PGTLR.

In this article, we propose a novel, unified, and effective hyperspectral image (HSI) destriping and denoising method with gradient subspace-regularized HSI and stripe-coupled nonconvex tensor low-rank priors (GSHSNTLRs). First, by exploiting the mode-3 low-rank properties of the gradients of HSI (i.e., the spatial horizontal gradient, spatial vertical gradient, and spectral gradient of HSI) along the spectral dimension, we apply the mode-3 low-rank decomposition of the gradients of HSI to obtain their representation coefficient tensors (RCTs), and further study the tensor low-tubal-rank properties of the RCTs in the gradient subspace. Thus, we propose the unified gradient subspace-regularized log tensor nuclear norm (LogTNN)-based nonconvex tensor low-rank prior term of the RCTs. Moreover, by fully considering the structural speciality of stripe noise, which has strong tensor low-tubal-rank property, we particularly study the HSI-guided tensor low-rank modeling for the stripe noise by exploring the tensor low-tubal-rank property of HSI plus stripe and propose the unified HSI and stripe-coupled LogTNN-based nonconvex tensor low-rank prior term of HSI and stripe simultaneously. Subsequently, the proposed GSHSNTLR model is solved by using the alternating direction method of multipliers (ADMMs). Finally, lots of experimental results and analysis fully demonstrate the destriping and denoising performance and superiority of GSHSNTLR.

This paper proposes a new hyperspectral image (HSI) denoising and destriping method via gradient tensor subspace low-rank learning and along-across stripe directional constraints (GTSL2A2SDC) under the unified framework of tensor representation modeling. On one hand, for the modeling of stripe noise, based on the inherently directional and structural attributes of the stripe noise, we mainly investigate the mode-1 gradient tensor of stripe along the stripe direction which holds the preferable “zero plane” constraint as well as the mode-2 gradient tensor of stripe across the stripe direction which holds the preferable tensor low-fibered-rank attribute along the mode-3 spectral dimension. Therefore, we novelly propose the unified along-across stripe directional gradient tensor constraints for the stripe noise, which can simultaneously characterize the directional and structural attributes of the stripe noise. On the other hand, for the modeling of HSI, based on the preferably spectral low-rankness attributes of the multi-mode gradient tensors of HSI, namely, mode-1 gradient tensor, mode-2 gradient tensor and mode-3 gradient tensor, we further utilize the spectral low-rank factorization of the gradient tensors of HSI to get the corresponding representation tensors, and particularly investigate the nonlocal self-similarities-based low-rankness of the representation tensors under the gradient tensor-based subspace low-rank learning framework. Moreover, we optimize the proposed GTSL2A2SDC model via an efficiently alternative and iterative algorithm. Lastly, extensive experiments comprehensively validate the denoising and destriping capacity and superiority of GTSL2A2SDC.

In this paper, we propose an effective multi-mode structural nonconvex tensor low rank (M2SNTLR) regularized hyperspectral image (HSI) destriping and denoising method in a unified framework of tensor representation. Firstly, we exploit and model the tensor low-tubal-rank properties of the HSI and its spectral gradient along spectral mode simultaneously via the tensor tubal rank functions. Secondly, based on the speciality and directionality of stripe noise, we particularly exploit and model the tensor low-tubal-rank properties of stripe noise and its unidirectional vertical gradient along spatial vertical mode simultaneously via also the tensor tubal rank functions. Thirdly, by using the log tensor nuclear norm (logTNN)-based nonconvex surrogate on those tensor tubal rank functions for a closer approximation, we thus propose the logTNN-based multi-mode structural nonconvex tensor low rank priors of HSI and stripe noise. Furthermore, we solve the proposed M2SNTLR model via the alternating direction method of multipliers. At last, extensive experiments validate that the proposed M2SNTLR method performs better denoising results than various low rank-based HSI denoising methods.

In this letter, based on the tensor representation modeling, we propose a novel and strict tensor-based pansharpening model via double nonconvex tensor low-tubal-rank (DNTLTR) priors for the fusion of low resolution multispectral (LRMS) and panchromatic (Pan) images to produce the high resolution MS (HRMS) images. By modeling the MS image as a third-order tensor for better modeling its spatial-spectral structural correlations, we particularly exploit the tensor low-tubal-rank properties of HRMS as well as the difference of HRMS and Pan at the same time, and then propose a novel unified log tensor nuclear norm-based double nonconvex tensor low-tubal-rank prior term. Moreover, for the spectral preservation of LRMS image, we also impose the spatial degradation-based spectral fidelity constraint between HRMS and LRMS. Then, we apply the alternating direction method of multiplier to optimize the proposed DNTLTR model. Finally, we show both the reduced-scale and full-scale fusion experiments to validate the effectiveness of DNTLTR visually and quantitatively.

In this letter, we propose a patchwise temporal-spatial feature aggregation (PTFA) network for object detection in satellite video. First, the feature extractor processes the key frame (KF) along with its support frames to ensure comprehensive spatial coverage of potential objects. Subsequently, we model the semantic similarities among instance-level proposals to exploring robust interaction between temporally adjacent support frames and KF. Furthermore, due to the extremely small size of objects in satellite video, we crop the input frames to different patches by the fixed criterion. Then, the temporal-spatial feature aggregation (TSFA) operations are performed on instance-level RoI features, which attains more nuanced and comprehensive descriptors from the explicit high-resolution temporal-spatial features. The patch features are reconstructed to the original one for complementing more valid feature responses. Finally, we compare our PTFA network with many recent works on the SAT-MTB dataset. Extensive experiments demonstrate that our method achieves the state-of-the-art performance than various static image and video object detection (VID) approaches.

In this article, we propose a novel adaptive spatial structure-aware and spectral gradient structure tensor-guided model (AS3GSTM) for pansharpening, which realizes the process of fusing the low-resolution multispectral (LRMS) image and the paired panchromatic (Pan) image to output the high-resolution multispectral (HRMS) image. Specifically, based on the basic spectral fidelity term between HRMS and LRMS obtained from the spatial degradation model for spectral fidelity, we also enforce the radiometric ratio-guided high-frequency detail fidelity term between HRMS, LRMS, and Pan for high-frequency detail fidelity. Moreover, considering that the HRMS image and the Pan image actually not only have strong spatial structure similarities, but also differ from each other, we further propose a novel Pan-guided adaptive spatial structure-aware prior term for the HRMS image to guide the fusion process. Besides, we particularly exploit the structure tensor of the spectral gradient of HRMS for simultaneously spectral-spatial prior modeling, and propose a novel spectral gradient-guided structure tensor total variation prior term for the HRMS image. Subsequently, we design an efficiently alternating algorithm to optimize the proposed AS3GSTM model. Finally, lots of fusion experiments comprehensively validate the superiority of AS3GSTM.

In this paper, we propose a new method for simultaneous hyperspectral image (HSI) destriping and denoising with spectral low-rank and tensor nuclear norm under the tensor framework. Specifically, the tensor nuclear norm is used to model the tensor low-rank property of stripe. Moreover, the nuclear norm is used to model the low-rank property of spectral gradient of HSI. Then, the ADMM algorithm is used to effectively solve the proposed model. Experimental results on simulated HSI dataset and real HSI dataset verify the superiority of the proposed method.

Pansharpening, which is also known as the fusion of low resolution multispectral (LRMS) and panchromatic (PAN) images, refers to producing a high resolution multispectral (HRMS) image by preserving the spectral detail from the LRMS image while extracting the spatial detail from the PAN image. In this article, we revisit and novelly reinterpret the multi-resolution analysis (MRA)-based pansharpening framework as the fusion framework of “spectral detail + spatial detail" and can obtain two alternative formulations of spectral detail and spatial detail respectively, and hence propose a novel variational pansharpening method with MRA-inspired spatial and spectral details preserved model. Firstly, the spatial degradation relationship between HRMS and LRMS is imposed as the spectral fidelity term. Secondly, based on the new reinterpretation of “spectral detail + spatial detail" of MRA fusion framework, we propose to use the structure tensor to model the spatial detail image, and propose a new structure tensor total variation (STV)-guided spatial detail preserved prior term. Moreover, to model the spectral detail image, we propose to impose the spectral detail preserved constraint between the two alternative formulations of spectral detail as the MRA-inspired spectral detail preserved prior term. Then, we optimize the proposed model via the alternating direction method of multipliers (ADMM). Furthermore, variously experimental results on the reduced-scale and full-scale datasets validate the superiority of proposed method.

Most pansharpening methods refer to the fusion of the original low-resolution multispectral (MS) and high-resolution panchromatic images (PAN) acquired simultaneously over the same area. Due to its good robustness, multiresolution analysis (MRA) has become one of the important categories of pansharpening methods. However, when only MS and PAN images acquired at different times can be provided, the fusion results from current MRA methods are often not ideal due to the failure to effectively analyze multitemporal misalignments between MS and PAN images from different times. To solve this issue, MRA pansharpening based on variation factor for MS and PAN images from different times is proposed. The multi-resolution analysis pansharpening based on dual-scale regression model is first established, and the variation factor is then introduced to effectively analyze the multitemporal misalignments by using alternating direction method of multipliers (ADMM), yielding the final fusion results. Experiments with synthetic and real datasets show that the proposed method exhibits significant performance improvement compared to the traditional pansharpening methods, as well as the state-of-the-art MRA methods. Visual comparisons demonstrate that the variation factor introduces encouraging improvements in the compensation of multi-temporal misalignments in ground objects and advances pansharpening applications for MS and PAN images acquired at different times.

To get the high resolution multi-spectral (HRMS) images by the fusion of low resolution multi-spectral (LRMS) and panchromatic (PAN) images, an effectively pansharpening model with spatial Hessian non-convex sparse and spectral gradient low rank priors (PSHNSSGLR) is proposed in this paper. In particularly, from the statistical aspect of view, the spatial Hessian hyper-Laplacian non-convex sparse prior is developed to model the spatial Hessian consistency between HRMS and PAN. More importantly, it is recently the first work for pansharpening modeling with the spatial Hessian hyper-Laplacian non-convex sparse prior. Meanwhile, the spectral gradient low rank prior on HRMS is further developed for spectral feature preservation. Then, the alternating direction method of multipliers (ADMM) approach is applied for optimizing the proposed PSHNSSGLR model. Afterwards, many fusion experiments demonstrate the capability and superiority of PSHNSSGLR.

This paper proposed a new pansharpening model with spatial hyper- Laplacian and spectral sparse constraints (PSHSS), which finally generated the high resolution multispectral (HR MS) images. Based on the panchromatic (PAN) and low resolution multispectral (LR MS) images, an enhanced PAN image was first constructed. To-gether with the local spectral consistency constraint, then the pro-posed PSHSS model particularly exploited the spatial gradient hyper-Laplacian sparse constraint between enhanced PAN and HR MS for spatial prior modeling, and the spectral gradient sparse constraint of HR MS for spectral prior modeling. Then, the proposed PSHSS model was optimized under the alternating direction method of multipliers (ADMM) framework. Finally, the fusion experiment demonstrated the superiority of PSHSS method.

This letter proposed a spatial and spectral anisotropic tensor total variation (SSATTV) driven adaptive pansharpening model for the fusion of low-resolution (LR) multispectral (MS) and panchromatic (Pan) images to the high-resolution (HR) MS images. Except for the local spectral consistency constraint-based fidelity term between HR and LR MS used for spectral preservation, the proposed model reformulated the adaptive linear constraint-based fidelity term between Pan and HR MS with the tensor-representation modeling, and particularly proposed a SSATTV prior term which imposed the spatial anisotropic TV prior between HR MS and Pan for spatial gradient feature preservation, and the spectral TV sparsity prior on HR MS for further spectral feature preservation. Furthermore, the proposed model was efficiently solved via the alternating direction method of multipliers (ADMM) scheme. Specifically, the experiments validated the superiority of proposed SSATTV method.

The feature learning methods based on convolutional neural networks (CNNs) have produced tremendous achievements in high-resolution (HR) synthetic aperture radar (SAR) image classification. However, the inherent speckle noise could weaken the effectiveness of the convolutional feature statistics. To effectively characterize the features of SAR land-covers under speckle noise, we propose a subspace wavelet encoding network (SWENet) trainable end-to-end and based on an encoder–decoder architecture for modeling the robust feature statistics in individual feature subspaces. We introduce a subspace encoder block at the end of the encoder stage and divide the entire feature space into a set of subspaces; the second-order statistics of all subspaces are concatenated. Then, the wavelet pooling block, suppressing the noise and keeping the structures of learned features well, decomposes the features into low-frequency (storing the basic object structures) and high-frequency components by Haar wavelet layer (HWL), and this block reconstructs the processed components using inverse IHWL during the upsampling stage. Especially, the wavelet pooling block is defined in each subspace for powerful feature learning. Experimental results on a TerraSAR-X image classification dataset suggest that our proposed SWENet yields a performance boost over its competitors.

Pansharpening is to generate a high resolution multispectral (HRMS) image by preserving the spectral information from a low resolution multispectral (LRMS) image and the spatial content from a panchromatic (PAN) image. This article proposes a unified pansharpening method with structure tensor driven spatial consistency and deep plug and play priors. First, the spectral fidelity constraint between HRMS and LRMS is imposed for preserving spectral information. Second, the structure tensor is applied to characterize the spatial geometric information of HRMS and PAN images, thus the structure tensor driven spatial consistency prior between HRMS and PAN is particularly exploited for preserving spatial content. Moreover, by generalizing the convolution neural network (CNN) fusion method into a unified variational framework, a novel CNN-based deep plug and play prior between the HRMS and CNN-based fused MS images is also proposed to generate more image characteristics for further preserving spectral information and spatial content. Besides, the proposed model is solved by the alternating direction method of multipliers (ADMM) algorithm. Finally, extensive experiments on both reduced and full resolution by comparing with various representative approaches exhibit the excellent performance of the proposed method.

This article proposed a nonconvex variational model for pansharpening with spatial and spectral gradient difference-induced nonconvex sparsity priors (PSSGDNSP), which can fuse the panchromatic (Pan) and low-resolution (LR) multispectral (MS) images to generate the high-resolution (HR) MS image. More particularly, the proposed PSSGDNSP model exploits the spatial gradient difference-induced nonconvex$l_{1/2}$sparsity prior between HR MS and Pan, and the spectral gradient difference-induced nonconvex$l_{1/2}$sparsity prior between HR and LR MS. Consequently, our proposed PSSGDNSP model well preserves both the spatial and spectral information. In fact, our proposed band-coupled model treats the MS image like a third-order tensor so that the intrinsic band correlation of the MS image can be fully kept. Moreover, we solve our proposed PSSGDNSP model by applying the alternating direction method of multipliers (ADMM) method. Finally, the experiments fully validate the superiority and performance of our proposed PSSGDNSP method.

As an important, challenging, and difficult problem in image processing, multiplicative noise removal (MNR) has attracted great attention. To this end, many variational methods have been effectively proposed in the past few decades. Among these variational methods, total variation (TV) and its higher‐order extensions are very effective, where the former can preserve sharp edges but cause some undesirable staircase effects and the latter can better reduce the staircase effects but sometimes smooth the image details. To overcome the drawbacks while taking full use of their merits, the authors propose a novel hybrid higher‐order TV regularisation model for MNR, in which the novelty of the proposed model consists of combining the image prior information of first‐order and second‐order derivatives to propose a novel higher‐order regulariser, named as hybrid higher‐order TV (HHTV). More specifically, a more preferable equivalent formulation of HHTV is derived. Then, they use the derived equivalent formulation to design an efficient alternating iterative algorithm to solve the proposed model. Finally, the experimental results demonstrate that the proposed HHTV method outperforms several state‐of‐the‐art methods in terms of image quality and convergence speed.

Limited and expensive availability of labeled training samples resulted in the development of methods defining the hyperspectral classification task in the form of data augmentation based supervised learning. However, most of the methods just implicitly utilize the spectral-spatial information in the isotropic neighborhood, instead of explicitly indicating the anisotropic or steering neighborhood system. In this paper, we apply steering stencils for estimating the local directional homogenous regions and exploiting more valuable spectral-spatial contexts. By using a best steering stencil matching method, we propose a data augmentation and refining method to improve the performance of any spectral-spatial classifier with limited labeled samples. Experiments show that the proposed method is very effective for many spectral-spatial classifiers.

Pansharpening aims to produce a higher resolution multi-spectral (HRMS) image by fusing the spectral information in lower resolution multispectral (LRMS) image and the spatial information in corresponding high resolution panchromatic (PAN) image. In this work, we propose a multi-scale densely deep learning based pansharpening method. Following an end-to-end learning architecture, the proposed deep neural network contains three modules: 1) a parallel multi-scale convolutional layer is used to extract multiscale features of PAN image; 2) a global identity branch structure is adopted to preserve spectral structures; and 3) a dense learning block is integrated to improve the spectral-spatial expressive power. Compared with other state-of-the-art methods, experimental results obtained with our proposed method achieve high pansharpening quality in visualization and quantification.

As one of the most popular kinds of the component substitution (CS)‐based pansharpening methods, the intensity‐hue‐saturation (IHS) method can produce the pan‐sharpened images with high spatial quality while causing some spectral distortion, mainly owing to it cannot estimate an accurate intensity image in the IHS space. To solve this issue in the IHS method, in this study, the authors propose a new pansharpening method with gradient transferring in the generalised IHS transform space, which aims at estimating a more accurate intensity image. More specifically, the novelty of the proposed method consists of building a novel variational gradient transferring model to transfer the spatial gradient information of the panchromatic image into the new intensity image as well as preserve the local spectral information from the low resolution multispectral image. Finally, they compare the proposed method with some CS methods using the Pleiades, QuickBird, and GeoEye‐1 satellite datasets from both the subjective and objective aspects. Specifically, the experimental results show that the proposed method yields better pansharpening results than the other methods in terms of higher spatial and spectral qualities.

Generally, the traditional semi-supervised extreme learning machine (S2-ELM) method cannot fully exploit the limited label information in hyperspectral image (HSI) classification. In this paper, we propose a discriminative S2-ELM method, called pixel-pairwise constrained S2-ELM (P2S2- ELM) method. Both the manifold regularization to leverage unlabeled data and the pixel-pairwise constraint between the labeled pixels are incorporated into a unified minimizing framework, thus the proposed P2S2-ELM method is able to learn a more effective and discriminative projection. Experimental results on several real hyperspectral data sets exhibit its efficiency and superiority to the counterparts, when only a small number of labeled samples are available.

In this paper, we propose a new variational pan-sharpening method with Hessian nuclear norm induced spatial consistency, which aims to fuse a low resolution (LR) multispectral (MS) image and a high resolution (HR) panchromatic (Pan) image into an HR MS image. In addition to using the fidelity based local spectral consistency term for preserving the spectral information, we particularly exploit the Hessian feature consistence between the HR MS image and Pan image, and propose a new Hessian nuclear norm induced spatial consistency term for preserving the spatial information. Then, the proposed model is solved by an efficient algorithm under the FISTA framework. Finally, the experimental results demonstrate that the proposed method outperforms various pan-sharpening methods in terms of higher spectral and spatial qualities.

In this study, a novel normal curvature‐induced variational model which involves a higher‐order regulariser based on the normal curvature prior information of image surface is proposed for image restoration. Furthermore, the authors derive a preferably equivalent formulation for the proposed normal curvature‐induced higher‐order regulariser. Then, they design an efficient algorithm to solve the proposed model by using the famous alternating direction method of multipliers technique. Finally, they assess the performance of the proposed method on both natural images and biomedical cell images by comparing it with the famous fast total variation (TV) method, fractional‐order TV method and Hessian‐nuclear‐norm regularisation method. Specifically, the proposed method can achieve better and more balanced results in terms of peak‐signal‐to‐noise ratio, convergence rate and restoration quality.

Pan-sharpening refers to the fusion of a low-resolution (LR) multispectral (MS) image and a high-resolution (HR) panchromatic (PAN) image to obtain an HR MS image (i.e., pan-sharpened MS image). From the point of view of variational complementary data fusion, it becomes an optimization problem with geometry and spectral preserving constraints. In this paper, a novel unified optimizing pan-sharpening model is proposed by integrating a data-generative fidelity term and a compound prior term, which incorporates both spatial fractional-order geometry and spectral-spatial low-rank priors. Specifically, the proposed model consists of three important ingredients: 1) data-generative fidelity term, which models the degradation relationship between the LR and HR MS images to enforce the geometry and spectral preserving constraints; 2) fractional-order total variation-based spatial fractional-order geometry prior term, which especially exploits the spatial fractional-order gradient feature consistence between the PAN and pan-sharpened MS images to transfer the spatial structure information of the PAN image into the pan-sharpened MS image; and 3) weighted nuclear norm-based spectral-spatial low-rank prior term, which exploits the nonlocal patches-based low-rank structural sparsity simultaneously in the pan-sharpened MS image and the LR MS image for further preserving image spatial structures and spectral information. Thus, the main novelty behind the proposed model is an optimizing mechanism by fully taking advantage of the spatial details and texture expressive power of the spatial fractional-order geometry prior as well as the spectral-spatial correlation preserving capacity of the low-rank prior. Finally, the proposed model can be implemented in an alternating direction method of multipliers framework, and thus, an efficient algorithm is presented. To verify the validity, the new proposed method is systematically compared with some state-of-the-art techniques using the Pleiades, GeoEye-1, QuickBird, and WorldView2 satellite data sets in the subjective, objective, and efficiency aspects. The results show that the proposed method performs better than the compared methods in terms of higher spatial and spectral qualities.

In this paper, we propose a new fractional order variational method for pan-sharpening, which aims to obtain a high resolution multi-spectral (MS) image from a low resolution MS image and a high resolution panchromatic (PAN) image. On one hand, we use the data generative constraint for preserving the spectral information. More specifically, on the other hand, we exploit the fractional order gradient feature consistence between the high resolution MS image and PAN image for preserving the spatial information. Based on these assumptions, a new fractional order variational model is proposed and an efficient algorithm is designed to solve the proposed model. Experimental results show that the proposed method outperforms various well-known pan-sharpening methods in terms of higher spatial and spectral qualities.

In this paper, we propose a new spatial-Hessian-feature-guided variational model for pan-sharpening, which aims at obtaining a pan-sharpened multispectral (MS) image with both high spatial and spectral resolutions from a low-resolution MS image and a high-resolution panchromatic (PAN) image. First, we assume that the low-resolution MS image corresponds to the blurred and downsampled version of the high-resolution pan-sharpened MS image. Since the pan-sharpened MS image and the PAN image are two images of the same scene, the pan-sharpened MS image shares similar geometric correspondence with the PAN image. To this end, the geometric correspondence between the PAN image and the pan-sharpened MS image is learnt as spatial position consistency by interest point detection. Second, a new vectorial Hessian Frobenius norm term based on the image spatial Hessian feature is presented to constrain the special correspondence between the PAN image and the pan-sharpened MS image, as well as the intracorrelations among different bands of the pan-sharpened MS image. Based on these assumptions, a novel variational model is proposed for pan-sharpening. Accordingly, an efficient algorithm for the proposed model is designed under the operator splitting framework. Finally, the results on both simulated data and real data demonstrate the effectiveness of the proposed method in producing pan-sharpened results with high spectral quality and high spatial quality.

This paper proposed a novel method for face hallucination based on a neighbor embedding technique. Traditional neighbor embedding approaches often offer counterintuitive results because consistency between high resolution images and low resolution images cannot be preserved without taking the intrinsic features of the image patches into account. In order to reinforce the consistency, on the one hand, we exploit the singular-values-unique (SVU) features inspired by singular values decomposition (SVD) successfully applied in image processing. On the other hand, we introduced the Histograms of Oriented Gradients (HOG) features to characterize the local geometric structure of the image patches to alleviate the effects of noise. At last, the learning space is extended to a coupled feature space that combines the SVU and HOG features. Simulation experiments show that this proposed approach could provide competitive results in simulation experiments in subjective and objective quality.

In this paper, we present a new variational method for pan-sharpening, which aims to obtain a high resolution multi-spectral (MS) image from a low resolution MS image and a high resolution panchromatic (PAN) image. Firstly, we assume that the desired high resolution MS image after down-sampling should be close to the low resolution MS image. More specifically, the intensity maps of PAN image and high resolution MS image bands are treated as three-dimensional (3D) differential surfaces. Then, we constrain that the surfaces of PAN image and high resolution MS image band should have the same bending directions at each point in 3D space. Based on these assumptions, a variational model is proposed and an efficient algorithm is designed to solve this variational model. Experimental results demonstrate that the proposed method outperforms various pan-sharpening methods in terms of both excellent spatial and spectral qualities.

A novel pansharpening method is proposed for creating a fused image of high spatial and spectral resolutions through merging a panchromatic (PAN) image with a multispectral (MS) image. To replace the patch pairs sampled from the images directly as the dictionary pairs, a joint learning model is proposed to learn a pair of compact dictionaries. Meanwhile, instead of restricting the coding coefficients of low resolution (LR) MS and high resolution (HR) MS image patches to be equal, ridge regression model is employed to describe their relation. Then, the fused MS image is calculated by combining the mapped sparse coefficients and the dictionary for the HR MS image. By comparing with some well-known methods in terms of several universal quality evaluation indexes, the simulated experimental results demonstrate the superiority of our method.