  Deep learning based fusion methods have been achieving promising performance
in image fusion tasks. This is attributed to the network architecture that
plays a very important role in the fusion process. However, in general, it is
hard to specify a good fusion architecture, and consequently, the design of
fusion networks is still a black art, rather than science. To address this
problem, we formulate the fusion task mathematically, and establish a
connection between its optimal solution and the network architecture that can
implement it. This approach leads to a novel method proposed in the paper of
constructing a lightweight fusion network. It avoids the time-consuming
empirical network design by a trial-and-test strategy. In particular we adopt a
learnable representation approach to the fusion task, in which the construction
of the fusion network architecture is guided by the optimisation algorithm
producing the learnable model. The low-rank representation (LRR) objective is
the foundation of our learnable model. The matrix multiplications, which are at
the heart of the solution are transformed into convolutional operations, and
the iterative process of optimisation is replaced by a special feed-forward
network. Based on this novel network architecture, an end-to-end lightweight
fusion network is constructed to fuse infrared and visible light images. Its
successful training is facilitated by a detail-to-semantic information loss
function proposed to preserve the image details and to enhance the salient
features of the source images. Our experiments show that the proposed fusion
network exhibits better fusion performance than the state-of-the-art fusion
methods on public datasets. Interestingly, our network requires a fewer
training parameters than other existing methods. The codes are available at
https://github.com/hli1221/imagefusion-LRRNet
