## 1 Introduction
The underlying principle of learning methods involves establishing correspondence between low-resolution and high-resolution images, utilizing the complementary information within similar blocks to preserve signal characteristics. In 2018, [PERSON] et al. introduced the Polarization Demosaicing Convolutional Neural Network (PDCNN) [20] to address the challenge of polarization super resolution, which lacked a specialized network for focal plane polarizing images. Subsequently, to mitigate accumulated errors caused by formula computation steps, [PERSON] et al. proposed an end-to-end fully convolutional neural network, FORK-NET [21]. This network takes the focal plane image as input and generates output intensity, polarization degree, and polarization angle images. An objective evaluation index indicated the superior performance of FORK-NET compared to PDCNN. Consequently, researchers explored alternative network models, such as the Multi-Scale Adaptive Weighted Network (MSAWN) [22], Deep Compressed Sensing (DCS) [23], and the sparsely polarimetric image demosaicing model (Sparse-PDM) [24]. These networks primarily target visible light polarization and necessitate extensive training data, typically sourced from Sony IMX250 series visible light polarization cameras. Articles [24; 25] describe the publicly available dataset created by these researchers. The advantage of deep learning methods lies in their ability to achieve excellent reconstruction effects. Nevertheless, these methods also possess certain drawbacks that limit their suitability for specific tasks. Super-resolution performance becomes heavily reliant on computational power and data volume, limiting their deployment in computationally constrained and data-limited environments. Furthermore, the lack of clear interpretation in the structural units is evident. Conversely, shallow learning methods derived from traditional machine learning algorithms offer advantages such as adaptability to small datasets, relatively lower computational costs, and interpretability. In this paper, we propose an infrared polarization super-resolution reconstruction model based on sparse representation. Our model optimizes the Stokes vector images, eliminating the need for mechanical reconstruction of a multi-channel polarization image. To enhance efficiency and accuracy, we construct three over-complete sets of Stokes vector image dictionaries. These dictionaries streamline the calculation process of the polarization degree and polarization angle while minimizing the potential for error. Furthermore, we introduce a reconstruction method based on our model. This method utilizes the proposed model to initially reconstruct the low-resolution image in blocks. The image is then divided by the weight coefficients of the overlaps, and the details are refined using the Iterative Back Projection (IBP) technique to achieve high-resolution reconstruction results. To build the dictionary, we designed a near-real-time short-wave infrared time-sharing polarization system prototype, leveraging our previous error analysis work [29]. This prototype enabled us to acquire the necessary dataset for simulation experiments. Additionally, we established a short-wave infrared focal plane polarization system for capturing real data. The experimental results demonstrate the superiority of our proposed method in both objective and subjective evaluation indexes. The rest of this paper is organized as follows: Section 2 introduces the reconstruction model and algorithm, including the establishment of an over-complete dictionary set, noise analysis, and the iterative solution method. Section 3 presents the simulation and real experiment results, provides the objective evaluation index, and explains the subjective index. The anti-noise performance of the proposed algorithm is analyzed, and the running time of the algorithm is provided. Next, we discuss the results and introduce future research directions.