基于坐标变换的四相涡旋光束轻量化识别方案

Four-Phase Vortex Beam Lightweight Identification Scheme Based on Coordinate Transformation

摘要: 针对不同旋转角度的四相涡旋光束图像识别任务，文章提出了一种结合极坐标变换与Kolmogorov-Arnold网络(KANs)的高效识别方法。传统卷积神经网络(Convolutional Neural Network, CNN)识别方法通常依赖于高维数据的直接处理，不仅计算复杂度高，而且对旋转不变性特征的提取效果有限。而本文方法首先通过极坐标变换，将笛卡尔坐标系下的二维光强分布图像映射为极坐标系下的一维特征序列。这种转换不仅有效保留了光束的旋转对称性和角度特征，同时显著降低了数据维度，从而减少了后续计算的复杂性。在此基础上，设计并构建了Kolmogorov-Arnold网络模型(KANs)，充分利用其强大的特征提取和分类能力，对经过极坐标变换的一维序列进行学习与分类。实验结果显示，该方法在面对不同旋转角度类别的图像数据集中，表现出卓越的识别性能，识别准确率高达99.6%。同时，相较于传统方法，本方法显著降低了时间复杂度和空间复杂度，提升了识别效率。本文提出的极坐标变换与KANs结合的识别框架为涡旋光束的快速、高效识别提供了一种创新性解决方案，为光场信息的智能处理和应用拓展奠定了基础。

Abstract: For the task of image recognition of four-phase vortex beams with different rotation angles, this paper proposes an efficient recognition method combining polar coordinate transformation and Kolmogorov-Arnold networks (KANs). The traditional convolutional neural network (CNN) recognition method usually relies on the direct processing of high-dimensional data, which not only has high computational complexity, but also has a limited effect on the extraction of rotational invariant features. In contrast, the method in this paper first maps the two-dimensional light intensity distribution image in a Cartesian coordinate system to a one-dimensional feature sequence in a polar coordinate system through polar coordinate transformation. This transformation not only effectively preserves the rotational symmetry and angular features of the light beams, but also significantly reduces the data dimensions, which in turn reduces the complexity of the subsequent calculations. On this basis, Kolmogorov-Arnold network models (KANs) are designed and constructed to make full use of their powerful feature extraction and classification capabilities to learn and classify the one-dimensional sequences transformed by polar coordinates. Experimental results show that the method exhibits excellent recognition performance in the face of image datasets with different rotation angle categories, with recognition accuracy as high as 99.6%. Meanwhile, compared with the traditional method, this method significantly reduces the time complexity and space complexity and improves the recognition efficiency. The recognition framework combining polar coordinate transforms and KANs proposed in this paper provides an innovative solution for the fast and efficient recognition of vortex beams and lays the foundation for the intelligent processing and application expansion of light field information.