# Multi-Focus Image Fusion Based on Decision Map and Sparse Representation
## 1 Introduction  
Multi-focus image fusion is a method of combining multiple images with different focal points into a composite image in which all objects are completely focused. The composite image will be more suitable for visual perception, making it easier for humans to further complete image processing tasks. Multi-focus image fusion technology has been widely used in digital photography, computer vision, military reconnaissance, and other fields [1]. With the maturity and improvement of image fusion technology, miscellaneous image fusion methods have emerged in the past few years. As many new fusion algorithms have been proposed recently, we feel inclined to divide the current fusion methods into four categories: multiscale transform (MST) methods, spatial domain methods, sparse representation (SR) methods, and neural network methods. Among the existing transform domain image fusion methods, MST is widely used [2]. A variety of multiscale transforms have been proposed and applied to image fusion. These include the Laplacian pyramid (LP), discrete wavelet transform (DWT) [3; 4], dual-tree complex wavelet transform (DTCWT) [5], and discrete cosine harmonic wavelet transform (DCHWT) [6]. The multiscale geometric analysis tools developed in recent years have higher directional sensitivity than wavelets, such as shearlet transform [7], curvelet transform (CVT) [8], nonsubsampled contourlet transform (NST) [9], and so on. All of these transform domain fusion methods have a similar \"decomposition-fusion-reconstruction\" framework. First, the source images are decomposed into a multiscale transform domain to obtain transform coefficients, and the transform coefficients are then fused based on a certain fusion rule. Finally, the fusion coefficients are inversely transformed to reconstruct the fused image. The inchoate spatial domain fusion methods average source images pixel-by-pixel, which usually causes unsatisfactory results, such as blurry details and low-grade contrast. In order to overcome these drawbacks, some block-based [10; 11] and region-based methods [12; 13] have been proposed in recent years. The core principle is to select image blocks or regions from source images on the basis of some focus measure metrics [14], such as gradient energy, spatial frequency, image variance, etc. The block-based image fusion methods have a simple process of segmentation and calculation, but the segmentation size directly affects the discrimination of the image block clarity, which easily produces a \"block effect\". The image fusion methods based on region segmentation are modified. According to the characteristics of image focus information distribution, sophisticated segmentation algorithms are used to split the images to be fused, which can determine the position of the focus region accurately and improve the quality of image fusion. Nevertheless, due to the complexity of the segmentation algorithm used, the efficiency of fusion methods is not high in practical applications. In the last few years, some state-of-the-art algorithms have been presented, such as guided filtering (GF) [15], image matting (IM) [16], and the bilateral filter [17]. To some extent, these methods can not only extract the focused area from the source images more accurately but also maintain consistency with the image source. The essence of the sparse representation model is a more compact representation of important information in natural signals with a handful of elements. In view of the efficient representation of the sparse representation model, the model is diffusely used in target tracking, face recognition, and image denoising. Numerous multi-focus image fusion methods based on sparse representation have also been proposed [18; 19; 20; 21; 22; 23; 24]. For instance, [PERSON] and [PERSON] first applied SR to multi-focus image fusion. The method uses the smooth window technique to divide the images to be fused into several image blocks and solves the sparse coefficients using the L1 norm.