## 1 Introduction  
In recent years, infrared imaging systems have been greatly improved in terms of technical conditions and manufacturing processes, and they are now widely used in the fields of thermal imaging, fire detection, and aerial small target reconnaissance. The common infrared detectors are divided into infrared focal plane array detectors and infrared focal plane linear array scan detectors. Nevertheless, when the infrared detector is imaging, the response coefficient of the detector will fluctuate correspondingly under the impact of variations in the ambient temperature and the voltage of the imaging circuit, resulting in fixed pattern noise in the infrared system imaging [1, 2]. This type of noise is typically difficult to eliminate directly at the hardware level, and the most prevalent techniques for compensating for hardware faults fall into two categories: reference-based correction methods [3] and scene-based correction methods [4, 5]. The reference-based correction methods generally require the acquisition of blackbody temperature images, which are later used for the corrections performed by calibration. Common methods include single-point correction [1, 6], two-point correction [7, 8], multi-point correction [9, 10], and polynomial fit correction [11, 12]. Prior to being put into service, infrared detectors are typically adjusted using this procedure. Changes in temperature, voltage, and other environmental conditions will affect the detector response coefficients when the infrared detector is in use. Currently, if the reference-based correction method is continued, it is necessary to cease equipment use and recalibrate infrared detectors, which severely impairs the normal operation of infrared detectors. To remedy this issue, scene-based non-uniform correction methods use the textural qualities of the acquired scenes to correct the images in real time, allowing for the detector to be recalibrated without the need for the blackbody. In 2012, [PERSON] et al. [13] proposed a nonuniformity correction method for infrared focal plane array detectors based on histogram statistics. This method can correct the nonuniformity of the image by modifying the histogram of the adjacent column of the image of an infrared array. However, this algorithm requires an image histogram forward transform as well as an inverse transform, and it has a significant temporal complexity. [PERSON] et al. [14] first proposed a guided image filtering method in 2012. [PERSON] et al. [15] applied the guided filtering method to the nonuniformity correction of the infrared focal plane array detector in 2016. This method effectively removed the nonuniformity noise of the array image by constructing a one-dimensional guided filtering window and conducting twice guided filtering operations. Guided filtering needs the calculation of linear coefficients for each window, making it more time-consuming for high-resolution images. In 2018, [PERSON] et al. [16] proposed a denoising method based on multi-level wavelet transforms and guided filtering. This method corrects the nonuniformity of the array image by conducting guided filtering operations on the vertical high-frequency components of the image after the wavelet transform. After the wavelet transforms, the guided filtering only targets the high-frequency image components, which drastically reduces the temporal complexity of this method. However, the approach processes the wavelet transform in the frequency domain and tends to blur the image details. After that, [PERSON] et al. [17; 18] combined TV regularization, wavelet transform, and guided filtering to the nonuniformity correction of the focal plane array detector. Due to frequency domain denoising, all of these methods may blur visual features and produce ghost effects. In addition, the multi-frame nonuniformity correction methods [19; 20; 21; 22; 23] and nonuniformity correction methods [24; 25; 26; 27] based on a deep learning model are also applied to the field of image nonuniformity correction.