  Multi-focus noisy image fusion represents an important task in the field of
image fusion which generates a single, clear and focused image from all source
images. In this paper, we propose a novel multi-focus noisy image fusion method
based on low-rank representation (LRR) which is a powerful tool in
representation learning. A multi-scale transform framework is adopted in which
source images are decomposed into low frequency and high frequency
coefficients, respectively. For low frequency coefficients, the fused low
frequency coefficients are determined by a spatial frequency strategy, while
the high frequency coefficients are fused by the LRR-based fusion strategy.
Finally, the fused image is reconstructed by inverse multi-scale transforms
with fused coefficients. Experimental results demonstrate that the proposed
algorithm offers state-of-the-art performance even when the source images
contain noise. The Code of our fusion method is available at
https://github.com/hli1221/imagefusion_noisy_lrr
