## 1 Introduction  
With the proposal of the concept of the Internet of Things and the continuous promotion of the construction of the smart grid, the use of infrared diagnosis technology for real-time monitoring and fault diagnosis of power equipment can effectively improve the operation reliability of the power grid [1; 2; 3]. However, there is a wide range of electrical equipment in the power grid, and the large-scale deployment of expensive traditional high-resolution infrared sensors will cause enterprises to incur unbearable costs [4; 5]. Therefore, how to use low-cost, low-resolution infrared sensors to achieve the effect of high-resolution infrared sensors is the key to promote the application of infrared diagnosis technology in the Internet of Things power system [6]. The main purpose of super resolution (SR) imaging technology is to overcome the limitations of low-cost and low-precision image acquisition devices. Through single- frame or multi-frame low resolution (LR) image input, it is necessary to complete image reconstruction according to different prior knowledge, obtain high resolution (HR) images, and recover high-frequency information lost in the process of image acquisition [7]. According to the number of LR images inputted during reconstruction, super-resolution can be divided into single-frame and multi-frame image super-resolution. Among these, multi-frame image super-resolution methods include the interpolation method [8; 9], iterative back projection method [10], maximum likelihood estimation method [11], sparse coding method [12] and learning-based method [13; 14]. The super-resolution method of multiple images uses complementary information contained in different images to improve the resolution by registering multiple images obtained at similar time positions in the same scene. The single-frame super-resolution method only uses a single image in a scene, which is more difficult. For the specific objective of infrared imaging of electrical equipment, the focus of super-resolution image reconstruction is not only clear structure and easy recognition, but also accurate response to equipment temperature. Multi-image super-resolution can easily cause the reflection of the reconstructed image to the temperature to lose accuracy, because the input low-resolution infrared images do not strictly come at the same time. This problem is particularly serious in the case of rapid change in equipment temperature, which is more concerning in the power industry. Therefore, the super-resolution method based on a single image can ensure accuracy of reconstruction. The super-resolution methods based on a single image are mainly divided into three categories: interpolation-based, reconstruction-based and learning-based super-resolution methods. Among them, the super-resolution method based on interpolation is the simplest, but due to its inherent smoothing benefits, it is easy to lose details and blur the edges of the reconstructed image. Researchers have put forward various improvement measures for this problem [15; 16; 17]. The super-resolution method based on reconstruction [11; 18; 19] completes the inverse iterative solution, based on the image degradation model, by introducing a priori knowledge as the limiting condition. Reference [18] proposed a super-resolution algorithm based on nonlocal information. [PERSON] et al. [19] calculated the blur kernel and high-resolution image at the same time. In the process of alternating iteration, a normalized sparsity measure is adopted, which is a generalized integral of relative total variation. It is used to represent the heavy tailed a priori characteristics of the image. For the accurate processing of a local image, [PERSON] et al. [11] adopted local structure self-similarity in the natural image to put forward the notion of turning kernel regression total variational, which is supplemented by the non-local total variational regular term to complete the establishment of the SR model.