  Among the representation learning, the low-rank representation (LRR) is one
of the hot research topics in many fields, especially in image processing and
pattern recognition. Although LRR can capture the global structure, the ability
of local structure preservation is limited because LRR lacks dictionary
learning. In this paper, we propose a novel multi-focus image fusion method
based on dictionary learning and LRR to get a better performance in both global
and local structure. Firstly, the source images are divided into several
patches by sliding window technique. Then, the patches are classified according
to the Histogram of Oriented Gradient (HOG) features. And the sub-dictionaries
of each class are learned by K-singular value decomposition (K-SVD) algorithm.
Secondly, a global dictionary is constructed by combining these
sub-dictionaries. Then, we use the global dictionary in LRR to obtain the LRR
coefficients vector for each patch. Finally, the l_1-norm and choose-max fuse
strategy for each coefficients vector is adopted to reconstruct fused image
from the fused LRR coefficients and the global dictionary. Experimental results
demonstrate that the proposed method can obtain state-of-the-art performance in
both qualitative and quantitative evaluations compared with serval classical
methods and novel methods.The Code of our fusion method is available at
https://github.com/hli1221/imagefusion_dllrr
