## 1 Introduction  
With advancements in infrared technology, infrared polarization imaging has found growing applications in various domains, such as industrial inspection [1; 2; 3], medical diagnosis [4; 5; 6], and astronomical remote sensing [7; 8; 9]. This technology facilitates the augmentation of information acquired through infrared imaging and enables further exploration of post-image processing algorithms. The infrared focal plane polarization detector has garnered significant interest as the central component of infrared polarization imaging. It consists of multiple groups of micro-linear polarization units and infrared detectors [10]. The micro-linear polarization units are arranged in an ordered structure on the surface of the infrared detector, with each group containing four pixels. Each group records four different necessary intensity response values [11]. However, this design structure decreases the spatial resolution of the infrared focal plane polarization imaging system, resulting in a significant impact on the measurement accuracy of polarization information. To address the issue of limited sampling by the detector and the inability to obtain a full-resolution polarization image, super-resolution reconstruction of the polarization image is necessary. This involves utilizing an effective reconstruction algorithm to enhance image details and clarity, compensating for the loss of resolution caused by the system structure. Super-resolution reconstruction techniques can be categorized based on their implementation methods into interpolation methods [12; 13; 14; 15; 16], reconstruction methods [17; 18; 19], and learning methods [20; 21; 22; 23; 24; 25; 26; 27; 28]. The interpolation methods include bilinear and bicubic interpolation methods [12], which were the initial algorithms utilized for super-resolution tasks. Subsequently, new algorithms were proposed, such as gradient-based interpolation [13], Newton polynomial-based interpolation (NP) [14], Edge-Aware Residual Interpolation (EARI) [15], and polarization image demosaicking using Polarization Channel Difference Prior (PCDP) [16], which leverage image geometric information and channel correlation. These interpolation techniques offer the advantage of quick reconstruction and effective edge preservation. However, since the degradation information of the actual pixel is not always accurately known, the models employed are not fixed. The primary objective of super-resolution algorithms in reconstruction methods is to reverse-engineer the imaging process of an image. This involves establishing an observation model that links the low-resolution image with the high-resolution image. To solve the model, image-specific prior knowledge is introduced, either at a local or global level. As an example, [PERSON] et al. combined the 3D block-matching algorithm with the concept of non-local filtering and introduced the Block-matching 3D Projectile On Convex Sets (BPOCS) algorithm [17]. [PERSON] et al. proposed the Frequency domain Phase-based Projection On Convex Sets (FPPOCS) algorithm, which combines the Wiener filter with the phase spectrum features of high-resolution images [18]. Similarly, in our previous work, we utilized principal component analysis and soft threshold denoising, using micro-scanning to capture sub-pixel micro-displacement frame sequences without altering the optical system's structure. We proposed the Micro-scanning Polarization Projection On Convex Sets (MPOCS) algorithm, designed specifically for infrared focal plane polarization detection systems [19]. The primary focus of the reconstruction method's super-resolution algorithm is the degradation process of the image. It aims to narrow down the range of potential solutions using an observational model, thereby ultimately improving the preservation of the image's geometry. However, due to the complex degradation factors encountered during the imaging process, artificial modeling cannot fully establish this process comprehensively.