Optical Diffractive Neural Networks for Matrix Completion

Matrix completion plays a crucial role in the field of communications when transmission paths are obstructed. In this study, we propose a method for matrix completion based on the principles of optical diffractive networks. This method jointly trains an electronic neural network encoder and an all-optical diffractive neural network decoder using deep learning. After training, the encoder module can transmit information through obstructed paths, while the decoder can perform decoding at the speed of light through passive optical diffraction propagation. The system exhibits robustness to the size and shape of obstructions. We validated the feasibility of this method using the MNIST dataset.