## 1 Introduction  
High-resolution and nondestructive subcellular imaging instruments ensure that observing the activities of cells accessible is always on demand in biology development. In the 1990s, the introduction of an atomic force microscope (AFM) [1] provided a high-resolution and non-destructive measurement tool at macroscopic levels [2], which is a powerful platform for biological samples, from single molecules to living cells, to be visualized and manipulated [3]. As a near-field microscope, AFM has high resolution in the near field, but it is difficult to detect the inner structures [4]. Atomic force acoustic microscope (AFAM) is a nanoscale microscope that provides ultra-high-resolution images of the sample without destroying the intracellular structures [5]. It is developed by combining AFM with an ultrasound imaging module. The ultrasound transducer produces a single frequency acoustic wave under the cell, and the vibration of the probe is detected by the spot optical tracking system. As the outputs of AFAM, morphology images and acoustic images provide different information: morphology image provides the topography features of the cell by detecting the adhesive between probe and cell, i.e., the AFM image, while the acoustic image shows the phase of the acoustic waves at the same position, which reflects all contributions in the path to make the acoustic signal shift in the phase. In recent years, AFAM is applied for medical and biological research. For example, the observation of liver cells [6]. AFAM is applied to analyze small cells nowadays. The cells are so thin that signal shift is slight because of the thickness. Hence, the acoustic image only reflects the subcellular structure of the cell. Since the acoustic and morphology image provides completely different types of information, it will be beneficial for studying the cells' structure if we combine them together. Image fusion is an important research topic in many related areas such as computer vision, remote sensing, robotics, and medical imaging etc. [7]. It is designed to combine multiple source images into a fused image that contains more information than individual source images. Image fusion is widely used in multi-mode image processing, such as visible and infrared images, computed tomography, and magnetic resonance images, and PET-CT images. Strategies for image fusion vary for different fusion tasks. Multi-scale transform (MST) is one of the most popular tools applied in image fusion tasks and has been fully studied. It divides the image into a low-frequency map, which shows a smoothed overall characteristic of the image, and a series of high-frequency maps, which contain the edge details of the image. The commonly used MST methods are the Laplacian pyramid (LP) [8] and nonsubsampled contourlet transform (NSCT) [9]. NSCT is an improved version of contourlet with good fusion results. Unfortunately, its computational efficiency is low. Fusion strategies based on MSTs can be further developed by using an effective way for low-frequency and high-frequency maps fusion to acquire high fusion quality. [PERSON] [10] proposes an image fusion framework based on MSTs and sparse representation (SR) [11], which performs well for the fusion of multi-modality images but needs complex computation. In addition to MST-based methods, deep learning for image fusion has attracted a lot of interest. In recent years, generative adversarial networks (GANs) [12] have been proven to provide more details than the traditional Convolutional Neural Networks (CNNs) in image generation. [PERSON] [13] introduced an end-to-end fusion method based on FusionGAN, avoiding manually designing fusion models in traditional methods. However, the network's loss function is still manual designed and the method only works well in visible and infrared images fusion [13].