Image fusion can integrate the complementary information of multiple images. However, when the images to be fused are damaged, the existing fusion methods cannot recover the lost information. Matrix completion, on the other hand, can be used to recover the missing information of the image. Therefore, the step-by-step operation of image fusion and completion can fuse the damaged images, but it will cause artifact propagation. In view of this, we develop a unified framework for image fusion and completion. Within this framework, we first assume that the image is superimposed by low-rank and sparse components. To obtain the separation of different components to fuse and restore them separately, we propose a low-rank and sparse dictionary learning model. Specifically, we impose low-rank and sparse constraints on low-rank dictionary and sparse component respectively to improve the discrimination of learned dictionaries and introduce the condition constraints of low-rank and sparse components to promote the separation of different components. Furthermore, we integrate the low-rank characteristic of the image into the decomposition model. Based on this design, the lost information can be recovered with the decomposition of the image without using any additional algorithm. Finally, the maximum $l_1$-norm fusion scheme is adopted to merge the coding coefficients of different components. The proposed method can achieve image fusion and completion simultaneously in the unified framework. Experimental results show that this method can well preserve the brightness and details of images, and is superior to the compared methods according to the performance evaluation.

图像融合可以融合多幅图像的互补信息。然而，当待融合图像损坏时，现有的融合方法无法恢复丢失的信息。另一方面，矩阵补全可用于恢复图像的缺失信息。因此，图像融合和补全的分步操作可以对损坏的图像进行融合，但会造成伪影传播。鉴于此，我们开发了统一的图像融合和补全框架。在这个框架内，我们首先假设图像由低秩和稀疏分量叠加。为了获得不同组件的分离以分别融合和恢复它们，我们提出了一种低秩稀疏字典学习模型。具体来说，我们分别对低秩字典和稀疏分量施加低秩约束和稀疏约束，以提高学习字典的辨别力，并引入低秩和稀疏分量的条件约束，以促进不同分量的分离。此外，我们将图像的低秩特征整合到分解模型中。基于这种设计，可以通过对图像的分解来恢复丢失的信息，而无需使用任何额外的算法。最后，最大 丢失的信息可以通过图像的分解来恢复，而无需使用任何额外的算法。最后，最大 丢失的信息可以通过图像的分解来恢复，而无需使用任何额外的算法。最后，最大${升}_1$采用-范数融合方案合并不同分量的编码系数。所提出的方法可以在统一的框架内同时实现图像融合和补全。实验结果表明，该方法能够很好地保留图像的亮度和细节，在性能评价方面优于对比方法。