# Hybrid Multimodal Medical Image Fusion Method Based on LatLRR and ED-D\({}^{2}\)GAN
## 1 Introduction  
Common medical images, such as Computed Tomography (CT) images, have high spatial resolution and can provide accurate anatomical information of lesions for the clinical diagnosis of patients [1]. However, due to the low resolution of soft tissue, CT images have certain limitations in qualitative diagnosis [2]. Positron Emission Tomography (PET) images are highly sensitive for the early diagnosis of tumors, but due to the low spatial resolution of the images, accurate anatomical structure information of the lesion cannot be provided by these images [3]. In the face of complex diseases, medical images with a single mode cannot provide sufficient auxiliary information for clinicians to refer to, while the fused images can simultaneously present effective information of images with different modes, which can improve the identification ability of the lesion area. It has an important clinical application value in early diagnosis, clinical staging, localization of lesion areas, formulation of diagnosis and treatment plans, and evaluations of the curative effect of tumors. So far, a large number of image fusion methods has been proposed by relevant researchers, mainly including the methods based on multi-scale decomposition, and the methods based on sparse representation, deep learning, and hybrid models. Among them, the image fusion methods based on multi-scale decomposition [4] firstly decomposed the source images into different low-frequency sub-bands and high-frequency sub-bands. Then,specific fusion rules are used to synthesize each sub-band of the fused image. Finally, the fusion result is reconstructed by the corresponding inverse transform [5]. [PERSON] et al. [6] proposed a multi-modal medical image fusion method in non-subsampled shearlet transform (NSST) domains for the Internet of Medical Things. The source images were decomposed into low-frequency and high-frequency component by the decomposition method based on NSST. In the low-frequency component, weighted fusion based on significance features is performed by using Multi local extrema (MLE) and co-occurrence filter. The fusion method based on fuzzy is used in the high-frequency component. Such methods can effectively obtain the detail information of the source images, but these methods need to manually design complex fusion rules. The number of the decomposition layers and the design of fusion rules will directly affect the quality of the final fused images. Compared with the methods based on multi-scale decomposition, sparse representation methods [7] under the condition of sharing the same set of sparse coefficients of the high-frequency and low-frequency images, through the use of sliding windows from the source images into multiple overlapping blocks, which can reduce the visual artifacts of the fused images and improve the robustness of registration error. [PERSON] et al. [8] proposed a method for multi-modal medical image denoising and fusion tasks based on sparse representation, in which group sparse representation can provide satisfactory fusion results with fewer artifacts through strong robustness. However, these methods are very time-consuming and dictionary learning is complex. In recent years, deep learning models have been widely used in the field of image segmentation [9], image analysis [10], image detection [11], image fusion [12], and image classification [13] through good feature extraction and representation capabilities. In the field of image fusion, [PERSON] et al. [14] firstly introduced the Convolutional Neural Network (CNN) into the multi-focus image fusion field. By learning the CNN model, it can effectively avoid the problem where traditional methods need to design complex fusion rules, but this method only uses the results of the last layer of the network model. FusionGAN [15] proposed by [PERSON] et al.