# Super-Resolution Reconstruction of an Array Lidar Range Profile
## 1 Introduction
improved the original POCS by constructing reference frames using energy successive degradation and motion estimation using the Vandewalle alignment method to determine the exact position of the low-scoring image in the high-scoring grid, which can effectively improve the image clarity and increase detail information. Fractional calculus and fractional processes, with applications in control systems and image processing, are a hot topic. Many computational fractional intelligence systems and stability analysis and image processing applications have been proposed [19]. [PERSON] [20] proposed a new image enhancement algorithm using the combination of rough set and the particle swarm optimization (PSO) algorithm to distinguish the smooth area and edge and texture areas of the image and, according to the results of image segmentation, an adaptive fractional differential filter was used to enhance the image. [PERSON] et al. [21] proposed an image enhancement algorithm based on a rough set and fractional order differentiator. By combining the rough set theory with a Gaussian mixture model, a new image segmentation algorithm with higher immunity was obtained. [PERSON] et al. [22] designed an infrared (IR) and visible (VIS) image fusion algorithm for the injection of the IR objects into the VIS background in a perceptual manner. It ensures that the fused image has both the rich background information of the VIS image and the salient features of the IR image. Aiming at the problem that the range profiles formed by the current array lidar have low resolution and contain few target details and little edge information, and inspired by the above literature, a POCS super-resolution reconstruction method combining the LK optical flow method and the Gaussian pyramid is proposed in this paper. Considering the distance mutation of the target at the edge background, the gradient constraint is introduced under the data consistency constraint to enrich the edge information of the reconstructed image; finally, projection iteration correction is performed on the reference high-resolution range profile to achieve the improvement in the resolution of the range profile while retaining more detailed edge information of the target. The main contributions of this paper are as follows:  
1. The LK optical flow method is introduced into the traditional POCS super-resolution reconstruction method, which combines the Gaussian pyramid with multi-scale correction of the estimation vector to improve the motion estimation accuracy and effectively enhance the reconstructed image detail information. 2. Considering the sudden change in the target's distance at the edge background, the gradient constraint is introduced on top of the data consistency constraint, which enhances the reconstruction ability of the target edge. The rest of this paper is structured as follows: In Section 2, we discuss the details of the proposed method and provide the theoretical analysis. In Section 3, we conduct experimental tests based on the redwood-3 dscan dataset and APD array lidar data and present the experimental results. In Section 4, we present the conclusion and discussion of our work.