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
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