## 1 Introduction  
With the rapid growth of the world economy, non-renewable resources such as oil, natural gas, and coal are constantly consumed, and the problem of the energy crisis has become more and more obvious [1]. To seek the way of sustainable development, nuclear power plants have become a hotspot of people's attention in many countries. At present, nuclear power plants have become one of the most important components of modern energy [2, 3]. Nuclear safety is the lifeline for the healthy development of nuclear power, which directly affects people's normal life, production, and social activities. Especially after the Three Mile Island nuclear power plant leakage accident in the United States in 1979, the Chernobyl nuclear power plant accident in the former Soviet Union in 1986, and the Fukushima nuclear power plant accident in Japan in 2011, the public has paid great attention to the safety of nuclear power plants [4, 5, 6]. The nuclear fuel element is the core component of a reactor. The nuclear fuel pellet located in the cladding releases energy through nuclear fission. The interaction between the pellet and the cladding will affect the safety of the fuel element. If the pellet is damaged, the debris will enter the gap between the pellet and the cladding, which may cause close contact between the pellet and the cladding to form a hotspot. The hotspot will result in the local temperature of the cladding being too high and the rupturing of the cladding, which can lead to nuclear leakage. Therefore, the safety inspection is one of the important means to ensure the safe operation of nuclear power plants. Nondestructive testing technology has the advantages of being nondestructive and rapid and reflecting the overall structure information of the tested samples [7]. In recent years, with the development of electronics and information science, X-ray and neutron imaging technologies have become more and more mature. Advanced detection imaging equipment and image processing software have been developed and applied continuously and can realize three-dimensional tomography and visualization of the tested samples [8; 9]. However, the spent nuclear fuel element is a strong emitter of X-rays and gamma rays, and it is impossible to analyze the irradiated object by X-ray computed tomography (CT). Neutron CT is useful for nondestructive testing of spent nuclear fuel elements due to the suitable neutron attenuation properties of uranium [10]. When scanning in the range of 180 or 360\({}^{\circ}\), if the detected object is sampled by a high-density projection, the traditional filtered back-projection (FBP) algorithm will be used to reconstruct high-quality images. When the number of projections does not satisfy the complete sampling condition required by [PERSON]'s sampling theorem for reconstruction, it is called sparse-view CT reconstruction [11]. The iterative reconstruction algorithm is mainly used for image reconstruction of sparse-view projections, such as iterative filtered back-projection algorithm, algebra reconstruction technique (ART) [12], simultaneous iterative reconstruction technique (SIRT) [13], and simultaneous algebraic reconstruction technique (SART) [14]. With the development of compressed sensing theory, algebraic iterative reconstruction theory based on total variation (TV) has great potential in the reconstruction of sparse-view projections [15; 16]. [PERSON] proposed an ROF denoising model for the image total variation, which used the total variation as a regular constraint for image denoising so that the edge and detail information of the image could be well preserved while the noise is reduced [17]. [PERSON] et al. proposed TV-POCS and ASD-POCS algorithms, which have played a good role in the aspect of sparse-view reconstruction [18; 19]. Several methods based on TV and its variants, including edge-preserving TV [20], anisotropic TV [21; 22], weighted TV [23; 24], and directional TV [25], were proposed to improve the performance of the algorithm.