Robust sparse representation based multi-focus image fusion with dictionary construction and local spatial consistency

Abstract Recently, sparse representation-based (SR) methods have been presented for the fusion of multi-focus images. However, most of them independently consider the local information from each image patch during sparse coding and fusion, giving rise to the spatial artifacts on the fused image. In order to overcome this issue, we present a novel multi-focus image fusion method by jointly considering information from each local image patch as well as its spatial contextual information during the sparse coding and fusion in this paper. Specifically, we employ a robust sparse representation (LR_RSR, for short) model with a Laplacian regularization term on the sparse error matrix in the sparse coding phase, ensuring the local consistency among the spatially-adjacent image patches. In the subsequent fusion process, we define a focus measure to determine the focused and de-focused regions in the multi-focus images by collaboratively employing information from each local image patch as well as those from its 8-connected spatial neighbors. As a result of that, the proposed method is likely to introduce fewer spatial artifacts to the fused image. Moreover, an over-complete dictionary with small atoms that maintains good representation capability, rather than using the input data themselves, is constructed for the LR_RSR model during sparse coding. By doing that, the computational complexity of the proposed fusion method is greatly reduced, while the fusion performance is not degraded and can be even slightly improved. Experimental results demonstrate the validity of the proposed method, and more importantly, it turns out that our LR-RSR algorithm is more computationally efficient than most of the traditional SR-based fusion methods.