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Hyperspectral and multispectral image fusion aims to fuse a low-spatial-resolution hyperspectral image (HSI) and a high-spatial-resolution multispectral image to form a high-spatial-resolution HSI. Motivated by the success of model- and deep learning-based approaches, we propose a novel patch-aware deep fusion approach for HSI by unfolding a subspace-based optimization model, where moderate-sized patches are used in both training and test phases. The goal of this approach is to make full use of the information of patch under subspace representation, restrict the scale and enhance the interpretability of the deep network, thereby improving the fusion. First, a subspace-based fusion model was built with two regularization terms to localize pixels and extract texture. Then, the subspace-based fusion model was solved by the alternating direction method of multipliers algorithm, and the model was divided into one fidelity-based problem and two regularization-based problems. Finally, a structured deep fusion network was proposed by unfolding all steps of the algorithm as network layers. Specifically, the fidelity-based problem was solved by a gradient descent algorithm and implemented by a network. The two regularization-based problems were described by proximal operators and learnt by two u-shaped architectures. Moreover, an aggregation fusion technique was proposed to improve the performance by averaging the fused images in all iterations and aggregating the overlapping patches in the test phase. Experimental results, conducted on both synthetic and real datasets, demonstrated the effectiveness of the proposed approach.

Fusing a low-resolution hyperspectral (LRHS) image and a high-resolution multispectral (HRMS) image to generate a high-resolution hyperspectral (HRHS) image has grown a significant and attractive application in remote sensing fields. Recently, the popularization of deep learning has injected more possibilities into the fusion work. However, there still exists a difficulty that is how to make the best of the acquired LRHS and HRMS images. In this article, we present a twice optimizing net with matrix decomposition to fulfill the fusion task, which can be roughly divided into three stages: pre-optimization, deep prior learning, post-optimization. Specifically, we first transform this fusion problem into a spectral optimization problem and a spatial optimization problem with the help of matrix decomposition. These two optimization problems can be handled sequentially by solving a linear equation, respectively, and then we can obtain the initial HRHS image by multiplying the two solutions. Next, we establish the mapping between the initial image and the reference image through an end-to-end deep residual network based on local and nonlocal connectivity. In order to get better performance, we have customized a loss function specifically for the fusion task as well. Finally, we return the predicted result again to the optimization procedure to get the final fusion image. After the evaluation on three simulated datasets and one real dataset, it illustrates that the proposed method outperforms many state-of-the-art ones.