Image transmission through multimode fiber (MMF) is now widely used in medical imaging, biological tissue detection, communication technology, and other fields. In multimode fiber imaging, the light pulse carrying the spatial information of the object enters the multimode fiber, and thousands of transmission modes excited in the fiber form encoded spatial information. Due to the complex mechanisms of interference, coupling, self-phase modulation, and group velocity dispersion among the fiber modes, the exit end of the fiber eventually forms a speckle image. With the development of optical modulators and computational optics, the advantages of deep learning methods in image reconstruction have become increasingly prominent. The high operational efficiency and strong resistance to fiber disturbances have pushed MMF image transmission into practical applications. Most existing studies use the MNIST handwritten digit set (28×28 resolution) for both training and testing, which is insufficient to train the generalization ability of network models. This reliance on limited data reduces the practical performance of the models. To enhance the practical application of multimode fiber imaging, we propose a hybrid model——TMnn (Transmission Matrix and Neural Network), based on complex value operations and a neural network that incorporates the physical processes of multimode fiber light field modulation. The model is applied to train and verify different natural scene image datasets, and the results show that the model training speed is significantly improved while maintaining the quality of image reconstruction. At the same time, the generalization ability of the neural network is also enhanced in the image restoration task.

Combining the physical mechanisms of optical fiber and neural networks, we propose a multimode optical fiber speckle reconstruction algorithm, TMnn, based on complex value operations, which is trained on a natural scene image dataset. According to the response relationship between the input and output optical fields of multimode fiber, the inverse transmission matrix of the fiber is fitted using an iterative algorithm. The reconstruction optimization is then performed through a convolutional neural network to complete the speckle image reconstruction. The model is mainly divided into two modules. The first is the reconstruction module, which constructs the complex value deep neural network to fit the transmission matrix and initially reconstructs the images. The network consists of an input layer, complex convolution layers, complex batch normalization layers, and complex dense connection layers. The second part is the optimization module, which optimizes the initially reconstructed image by constructing a 3×3 convolutional neural network. The initial reconstructed image is taken as input, and the image features are extracted deeply. Image details are then reconstructed through the convolution layer, pooling layer, and fully connected layer in sequence.

By comparing with traditional neural networks (SCNN, DCNN), CANN (Complex Artificial Neural Network), and USINET, we confirm the advantages of the model in terms of reconstruction effect and training speed. In terms of model training, we make a comparison with CANN on the ImageNet dataset. Compared with CANN, the SSIM index shows a significant improvement, and the number of iterations is reduced by 200. However, the addition of two complex convolution layers increases the number of parameters, which has a certain effect on the training time cost. We also compare the model with USINET, and the training information is shown in Table 2. The results show that the average SSIM index of this algorithm improved by about 0.5%, and the training time is reduced by 6.46 hours. The TMnn model outperforms USINET in the first 4 hours of training and tends to converge after about 6 hours of training, with the SSIM value stabilizing at around 0.8. This indicates that the model constructed in this paper does not compromise training speed or model performance despite the complex operations.

We integrate the physical mechanism of optical fiber transmission with deep learning technology to construct a deep neural network based on complex-valued operations, which achieves high-quality reconstruction with an SSIM index above 0.7. Through the reconstruction of various datasets, the validity and generalization of the model are demonstrated. By comparing it with traditional neural networks, fully connected complex networks, and USINET, the advantages of the model are confirmed in terms of reconstruction quality and training speed. However, the network still has limitations in reconstructing more complex, detailed images. The network structure and model parameters for feature extraction need optimization to better capture detailed features and further enhance the quality of natural scene image reconstruction.