## 1 Introduction
Additionally, an increasing number of related themes have undergone research [7], and low-rank matrix and sparse matrix themes aroused the study interest. Therefore, further development and application in NGV autofocusing and image fusion to aid in identifying NVG equipment availability were explored. The configuration of the mechanism comprises an NVG testing autofocusing system that includes a platform, motor, mechanism, and camera, as shown in Figure 2, as well as the multifocus problem caused by the inaccuracy between lens and NVG, as shown in Figure 3. This study adopted the  
Figure 1: Structure of image intensifier [2]. image fusion method to resolve multifocus problems. Targeting how to correctly fuse images to ensure results presenting better information representativeness compared to any single input image is also an important topic in image fusion [7]. So far, a large quantity of image fusion techniques have been proposed. Among them, wavelet transport-based image fusion is a popular subject of research [8; 9] because it can maintain precision of spectrum while increasing and improving accuracy of the space. When using wavelet decomposition, if only a few decomposition stages are used, the fused image's accuracy of space will be poorer. On the contrary, if too many decomposition stages are used, spatial similarity between the fused image and the original will be poorer [10]. Among those fusion methods, structure-aware image fusion [11] and image fusion in the discrete cosine transform (DCT) domain [12; 13] are quite classic methods and widely used in various fields [14; 15]. The following discusses wavelet-based image fusion in recent years. [PERSON] et al. [16] proposed a quantitative measure using structural dissimilarity to measure the ringing artifacts. [PERSON] and [PERSON] [17] especially focused on poor contrast and high-computational complexity issues of fusion outcomes. [PERSON] and [PERSON] [18] focused on translation-invariant a trous wavelet transform and fractal dimension using a differential box counting method. [PERSON] et al. [19] implemented image fusion methods that are combined with wavelet transform and the learning ability of artificial neural networks. In recent years, deep learning networks have also been used to execute image fusion [20; 21; 22]. In general, deep learning networks' fusion quality depend on the sample characteristics at the time of data training. Image fusion based on low-rank matrix and sparse matrix characteristics has been a popular topic in recent years. [PERSON] and [PERSON] [23] proposed a multimodal image fusion scheme, which was based on two-scale image decomposition and sparse representation. This technology mainly uses the edge information of the sparse matrix for fusion. [PERSON] et al. [24] proposed a multifocus image fusion method, mainly established in one fusion rule of sparse coefficients, which is based on the optimum theory and solved by the orthogonal matching pursuit method. [PERSON] and [PERSON] [25] proposed a novel strategy on the low frequency fusion assisted through sparse representation. [PERSON] [26] proposed a novel fusion method based on sparse representation and non-subsampled contourlet transform, and used some indicators to prove the fusion result was excellent. [PERSON] et al. [27] proposed a multifocus image fusion method through distributed compressed sensing (DCS). This method is mainly considered the high-frequency images' information. The final result was using visual and quantitative metric evaluations to analyze the results of the fusion. Among all the methods for decomposing data into low-rank matrix and sparse matrix, the most classic is robust principal component analysis (RPCA).