In this paper, a mode decomposition (MD) method for degenerated modes has been studied. Convolution neural network (CNN) has been applied for image training and predicting the mode coefficients. Four-fold degenerated $LP_{11}$ series has been the target to be decomposed. Multiple images are regarded as an input to decompose the degenerate modes. Total of seven different images, including the full original near-field image, and images after linear polarizers of four directions (0$^\circ$, 45$^\circ$, 90$^\circ$, and 135$^\circ$), and images after two circular polarizers (right-handed and left-handed) has been considered for training, validation, and test. The output label of the model has been chosen as the real and imaginary components of the mode coefficient, and the loss function has been selected to be the root-mean-square (RMS) of the labels. The RMS and mean-absolute-error (MAE) of the label, intensity, phase, and field correlation between the actual and predicted values have been selected to be the metrics to evaluate the CNN model. The CNN model has been trained with 100,000 three-dimensional images with depths of three, four, and seven. The performance of the trained model was evaluated via 10,000 test samples with four sets of images - images after three linear polarizers (0$^\circ$, 45$^\circ$, 90$^\circ$) and image after right-handed circular polarizer - showed 0.0634 of label RMS, 0.0292 of intensity RMS, 0.1867 rad of phase MAE, and 0.9978 of average field correlation. The performance of 4 image sets showed at least 50.68\% of performance enhancement compared to models considering only images after linear polarizers.

翻译：在本文中,已经研究了一种对退化模式进行模式分解(MD)的方法。 在图像培训和预测模式系数时,已经应用了进式神经网络(CNN) 。 四倍降价$LP11}系列已经是拆解的目标。 多种图像被视为解析变形模式的一种投入。 总共7种不同的图像, 包括全原始近地图像, 以及四个方向的线性极化后图像( 0 $circ$, 45 $circ$, 90 circ$, 135$circ 美元), 两次循环极化后图像( 右倾右手和左手) 。 模型的输出标记被选为模式系数的真和假组成部分。 总共7种最低方向的离子( RMS) 0. 018 平面图像的RMS 和平面的平面图案 。 已经用经过培训的 4 IMRIS 模型的3 和预测性能被选为 100000 。