## 1 Introduction  
There is abundant information about brightness and color in real natural scenes, and the dynamic range is very wide. Therefore, high dynamic range (HDR) images, which can truly represent natural scenes, are widely used in digital photography, aerospace, satellite meteorology, medical treatment, and military industries [1; 2; 3]. The HDR imaging technology can be divided into two categories. The first is the hardware-based method [4; 5], which utilizes HDR devices to capture real natural scenes. However, these devices are too expensive to be popular with the public. The second uses software-based technology to obtain HDR images [6]. The notion of this category is that real natural scenes can be captured with a stack of low dynamic range (LDR) images with different exposures, and an HDR image can be obtained by using the camera response function [7; 8]. Then, tone mapping technology [9; 10; 11] is used to reduce the dynamic range of the HDR image for display on the common device. However, the quality of the reconstructed HDR image depends heavily on the related exposure settings (e.g., exposure time and exposure value), which are often unknown to the user. Therefore, software-based HDR imaging technology through multi-exposure fusion [12; 13; 14] has attracted increasing amounts of attention. This technology can directly obtain greater information and produce a more perceptually appealing composite LDR image, reflecting natural scenes more closely. Furthermore, the result of a multi-exposure fusion can be directly presented on the LDR displays. In recent years, many scholars have performed in-depth studies on multi-exposure fusion. [PERSON] et al. [15] proposed a multi-exposure fusion method based on weight maps, the factors of which are comprised of three quality measures (i.e., contrast, saturation, and exposure quality at the pixel level). Moreover, the multi-resolution approach, based on Laplacian pyramids, was also applied to pursue better human visual perception. However, this method placed too much emphasis on contrast. Thus, the details of brighter and darker regions were lost in the fused image. [PERSON] et al. [16] evaluated the exposure quality of pixels in the source images via illumination estimation filtering and then realized multi-exposure image fusion. [PERSON] et al. [17] achieved the multi-exposure fused image with gradient information, which can effectively preserve texture details. [PERSON] et al. [18] decomposed a number of multi-exposure source images into a detailed layer, containing small-scale details, and a base layer, containing large-scale intensity variations. Then, they used spatial consistency to fuse the basic and detailed layers. [PERSON] et al. [19] proposed a multi-exposure fusion method, based on an improved pyramid, to preserve detail information. [PERSON] et al. [12] introduced a dense scale invariant feature transform (SIFT) descriptor into image fusion to extract local details from multi-exposure source images. [PERSON] et al. [13] proposed a multi-exposure fusion method, based on an effective structural path decomposition approach, which took account of the local and global characteristics of the source images and obtained better fused image quality. [PERSON] et al. [20] proposed an unsupervised deep learning framework for multi-exposure fusion (MEF), utilizing a no-reference quality metric as the loss function, which obtained excellent fusion results. On the basis of [PERSON] et al. [13], [PERSON] et al. [14] then proposed a multi-exposure fusion method by optimizing the color multi-exposure fusion structural similarity (MEF-SSIMc) index. However, the above fused methods did not consider that there were halo artifacts in the multi-exposure fused image. These halo artifacts always occur in the region of sharp local brightness changes, severely reducing the perceptual appeal.