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.

Most pansharpening methods refer to the fusion of the original low-resolution multispectral (MS) and high-resolution panchromatic (PAN) images 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 MRA 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 the 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 multitemporal misalignments in ground objects and advances pansharpening applications for MS and PAN images acquired at different times.

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.

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.

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.

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.