# Infrared Dim and Small Target Detection Based on the Improved Tensor Nuclear Norm
## 1 Introduction  
The dim and small target detection algorithm is widely used in the military for guidance, e.g., regarding anti-missiles and early warning operations. It is also widely used in civilian fields, such as medical cancer detection, astronomical observations, and space debris monitoring. At present, target points with no fixed texture or shape features in an image, an SNR below 5 dm, and a target scale size between 2 \(\times\) 2 and 9 \(\times\) 9 are known as dim and small targets [1]. Because of the above characteristics of dim and small targets, in the detection process, the algorithm has difficulty distinguishing the noise and clutter in the background of the infrared image from the target, giving the final detection results a high false alarm rate. Therefore, further research on dim and small target detection algorithms is of great importance. In recent years, domestic and foreign scholars have conducted a series of studies on dim and small target detection algorithms; these can be divided into three main types: those based on traditional spatiotemporal filtering, those based on neural networks, and those based on the low rank and sparse theory. Representative algorithms of traditional filtering methods are top-hat filtering [2, 3], two-dimensional least mean square filtering [4, 5], and anisotropic diffusion filtering [6, 7]. The top-hat algorithm is mainly used to obtain the target image by opening and closing the original image through the structural element. Many scholars have made a series of improvements to the structural elements to achievegood results. [PERSON] [2] used different information from the target and neighborhood to build two related structural elements to improve top-hat filtering. [PERSON] [3] suppressed the background information in the image with the help of adaptive ring structure elements and enhanced the target signal by local entropy. The top-hat algorithm can effectively suppress the effect of impulse noise on the detection effect in the process of target detection, but this type of algorithm causes the loss of the target signal contour when the opening and closing operations are performed by the structural elements. The two-dimensional least mean square filtering algorithm mainly uses information from the image neighborhood range to obtain the prediction value; it then traverses the whole image to obtain the prediction image by adaptively updating the prediction value through the error between the prediction value and the real value. Finally, it generates a target image showing the difference between the original image and the prediction image. [PERSON] [4] employed pairs of neighborhood information in four directions to obtain the predicted values. [PERSON] [5] used the master view method on this basis and took the domain information in eight directions to predict the central image element information. This method avoids the influence of TDMLS anisotropy on the detection results and improves the detection effect, but this type of algorithm has difficulty making accurate predictions about non-smooth backgrounds, resulting in an unsatisfactory detection effect. The anisotropic filtering algorithm uses the difference in gradients between the target image element and the background image in each direction to model the background through a diffusion function. [PERSON] [6] improved the diffusion function based on the traditional anisotropic filtering algorithm and combined it with the idea of high-order energy accumulation, leading to an increase in the target point energy. Based on further improvement of the diffusion function, [PERSON] [7] established a new search pipe diameter weight function; the combination of the anisotropy algorithm and pipe filtering algorithm was shown to achieve a better detection effect in the case of a large background span, but in a large edge contour area block, the background of the gradient difference in each direction has a small difference, so the detection effect is not ideal.