# Multi-Focus Image Fusion Based on Decision Map and Sparse Representation
## 1 Introduction
Finally, these coefficients are merged according to the maximum selection fusion rule to reconstruct the fused image [18]. On this basis, the authors used the synchronous orthogonal matching tracking sparse coding algorithm (SOMP) in the multi-focus image fusion process, which can cause different images that need to be fused to use the same atom for sparse representation to improve the algorithm performance and fusion efficiency [19]. Furthermore, [PERSON] et al. combined sparse representation theory with other fusion algorithms for multi-focus image fusion. However, the algorithm has a large amount of sparse decomposition calculation and a high time requirement [20]. Subsequently, [PERSON] et al. attempted to combine MST with the sparse representation model. The proposed fusion structure overcomes the original defects and can be applied to the fusion processing of multiple multi-focus images. However, the algorithm still failed to effectively reduce the computational complexity, and there were still difficulties in practical applications [21]. They also applied the adaptive sparse representation model to image denoising [22]. In [23], the SR model with dictionary learning was used in multi-focus image fusion. A large number of experiments have shown that the fusion methods based on sparse representation are better than the multiscale transformation methods. Nevertheless, as with most existing methods, existing fusion methods based on sparse representation also have potential degradation problems, such as blocking artifacts, artificial edges, and ringing effects. Finally, the image fusion methods are mainly realized by artificial neural networks. Among them, the pulse-coupled neural network (PCNN) is a cat neural cortex-based biological neural network proposed by [PERSON] et al. [25], which is widely used in various image processing fields, including image fusion. Researchers have developed PCNN-based multi-focus image fusion methods in the multiscale transform domain [26; 27; 28] or directly in the spatial domain [29]. The most significant advantage of the PCNN-based fusion method is that its information processing model can simulate the human visual system so that a fusion image conforming to human visual characteristics can be obtained. However, the fusion performance of the PCNN model is often affected by its large number of free parameters, which makes it less stable. In addition, [PERSON] et al. proposed a multi-focus image fusion method based on a deep convolutional neural network (CNN) [30]. It uses a high-quality image patch training deep convolutional neural network and its fuzzy version to encode the mapping, which can jointly generate activity level measurement and fusion rules and overcome some difficulties faced by certain existing fusion methods. Based on the analysis and research of existing multi-focus image fusion methods, we propose a new multi-focus image fusion method based on decision map and sparse representation (DMSR), which can not only satisfy the requirements of the visual effect and fusion performance but also make the algorithm robust and adaptive. In our framework, the advantages of fusion methods based on the decision map and sparse representation are combined. Considering that the human visual system does not require much detail in identifying the focused and defocused area of the source images, we generated a sparsity graph using low-scale images of the source images. In the existing multi-focus image fusion methods based on the decision map, each pixel is strictly defined as focused or defocused, which inevitably leads to erroneous judgment in the decision map. In particular, the pixels of the uncertain region are difficult to determine simply as focus or defocus. In order to avoid this defect, we analyzed the sparseness of the corresponding points in the sparsity graph and divided each pixel into three categories--focused, defocused, and uncertain--to generate the initial decision map.