# Super-Resolution Reconstruction of an Array Lidar Range Profile
## 1 Introduction
However, these methods face challenges in scenarios with limited data availability. Additionally, deep learning models often require retraining or fine-tuning to maintain a high performance across different datasets or application contexts, which increases the complexity of their application. The internal mechanisms of deep learning models are also complex, typically regarded as a \"black box,\" which can pose challenges in applications that demand result transparency and interpretability. The imaging system used in this paper cannot obtain high-resolution images due to the limitations of the detection array, and in the application fields of precision guidance and urban security, it is difficult to ensure that there is a more complete target sample library during the process of super-resolution reconstruction of the target range profile by using a neural network method. Therefore, it is particularly important to propose an image super-resolution reconstruction technique that does not rely on sample learning. Model-based methods do not require large amounts of training data, which provides a significant advantage in scenarios with limited data availability. Since they are based on well-defined physical and mathematical models, these methods exhibit good generalization capabilities across different scenarios without the need for retraining or fine-tuning for various datasets or application contexts. Additionally, model-based methods typically offer a superior interpretability and transparency, as their mechanisms and results can be understood and analyzed through physical and mathematical principles. Reconstructionmodel-based methods incorporate the a priori knowledge of the image as constraints into the image super-resolution reconstruction process. This class of methods is able to utilize image a priori knowledge to infer high-resolution image detail information for better preservation of image details, and can combine different a priori knowledge and constraints for image reconstruction with high flexibility and scalability. The projection onto convex sets (POCS) super-resolution reconstruction method belongs to a type of reconstruction modeling method that is able to add the a priori information of the low-resolution image sequences to the reconstruction process and then reconstructs a higher-quality high-resolution image by correcting the projection of the interpolated high-resolution reference image [14]. However, this method has the problems of non-unique solution and low convergence stability, which leads to the presence of artifacts at the edge of the image, and for this reason, some scholars have carried out improvement research. [PERSON] et al. [15] introduced Gaussian gradient map theory for neighborhood consistency information measurement, introduced the gradient information of the image as a convex set constraint, and adaptively selected the iteration step size for pixels with different gradients, which improved the original POCS with a poor retention of edge effects but that lacked the ability to process image detail quality. [PERSON] et al. [16] performed edge detection on the initial high-resolution frame to be reconstructed and then applied the improved point spread function (PSF) to the detected edge pixels, so that the horizontal and vertical coefficients of the PSF corresponding to the pixels at the edges were set to different weights according to the change in the edge slope. The proposed method took into account the specificity of the reconstruction of the edge parts of the image, so that the edge of the reconstructed high-resolution image was well maintained. [PERSON] et al. [17] considered the difference between the target region and the background of the image to introduce an adaptive correction threshold and adjusted the size of the correction threshold by utilizing the statistical properties of the edge strength obtained by the Scharr operator, so that the recovered high-resolution sub-millimeter-wave image was close to the real image. [PERSON] [18] et al.