Sparse aperture optical systems consist of multiple sub-apertures. By optimizing the array structure and performing image restoration, the information obtained about the target object can be comparable to that of an equivalent single-aperture optical system, effectively addressing problems caused by increasing aperture size. However, since the light-transmitting area of a sparse aperture system is smaller than that of its single-aperture counterpart, it results in the loss of intermediate-frequency information, leading to issues such as blurred texture details and reduced image contrast. To address these problems, we combine polarization imaging with sparse aperture imaging.

In this paper, we propose a polarization image fusion method for sparse aperture optical systems. This process mainly includes the following steps: First, a Golay 3 polarization sparse aperture imaging system is built to capture polarization images at four different polarization angles. Second, these images are preprocessed to calculate the degree of linear polarization and the angle of polarization. Then, the polarization sparse aperture fusion network (PSAFNet) is used to fuse the polarization intensity image, the degree of linear polarization, and the polarization angle, integrating the polarization information into the intensity image and producing a more information-rich result. Next, intermediate-frequency regions of the full-aperture image, sparse-aperture image, and fused image are extracted. The Canny operator is applied to extract intermediate-frequency edges to compare the richness of intermediate-frequency information. Information entropy, standard deviation, and the multi-scale structural similarity index (MS-SSIM) are also used to evaluate PSAFNet and other fusion methods.

The proposed PSAFNet method effectively alleviates the decline in intermediate-frequency information caused by the sparse aperture structure. In an indoor scene (Fig. 8), compared with the sparse aperture image, the fused image shows increases of 26.2%, 21.0%, and 27.0% in edge density, information entropy, and the number of connected regions, respectively (Fig. 9). In an outdoor scene (Fig. 12), the fused image shows corresponding improvements of 32.9%, 23.6%, and 16.6% (Fig. 13). Compared with other fusion methods, the proposed method performs better in indoor scenes (Fig. 10), with higher information entropy, standard deviation, and MS-SSIM (Table 1). The MS-SSIM of PSAFNet is close to 1, indicating higher similarity to the single-aperture image in contrast and structure, with lower image distortion. Compared with the sparse aperture image, the information entropy increases by 10.10%, and the standard deviation increases by 63.49%. In outdoor scenes (Fig. 14), the proposed method also surpasses other fusion methods, with information entropy increasing by 3.55% and standard deviation by 30.35% (Table 2).

We propose a polarization image fusion method, PSAFNet, for sparse aperture optical systems based on a deep learning network. The method extracts texture features from the polarization intensity image and the degree of linear polarization, as well as semantic features from the polarization intensity and polarization angle using an encoder. The fusion module uses spatial and channel attention mechanisms to enhance image details and preserve semantic information. In addition, edge features are extracted and fused with attention-enhanced features to further strengthen edge representation. Finally, combined deconvolution is used in the decoder to generate the fused image. To validate the performance of the method, polarization images are collected using the Golay 3 sparse aperture imaging system. Experimental results show that the algorithm achieves stable and optimal results in preserving texture detail and the overall image structure. Compared with sparse aperture images, the fused image contains more intermediate-frequency information, clearer contours, and richer texture details. The introduction of polarization information effectively addresses problems such as image smoothing and weakened textures due to intermediate-frequency loss. Compared with traditional fusion methods such as wavelet transform and PFNet, this method more effectively enhances texture details and contrast in sparse aperture.