Transmission matrix (TM) allows light control through complex media, such as multimode fibers (MMFs), gaining great attention in areas, such as biophotonics, over the past decade. Efforts have been taken to retrieve a complex-valued TM directly from intensity measurements with several representative phase-retrieval algorithms, which still see limitations of slow or suboptimum recovery, especially under noisy environments. Here, we propose a modified nonconvex optimization approach. Through numerical evaluations, it shows that the optimum focusing efficiency is approached with less running time or sampling ratio. The comparative tests under different signal-to-noise levels further indicate its improved robustness. Experimentally, the superior focusing performance of our algorithm is collectively validated by single- and multispot focusing; especially with a sampling ratio of 8, it achieves a 93.6% efficiency of the gold-standard holography method. Based on the recovered TM, image transmission through an MMF is realized with high fidelity. Due to parallel operation and GPU acceleration, our nonconvex approach retrieves a 8685 × 1024 TM (sampling ratio is 8) with 42.3 s on average on a regular computer. The proposed method provides optimum efficiency and fast execution for TM retrieval that avoids the need for an external reference beam, which will facilitate applications of deep-tissue optical imaging, manipulation, and treatment.

We demonstrate a deep-learning-based fiber imaging system that can transfer real-time artifact-free cell images through a meter-long Anderson localizing optical fiber. The cell samples are illuminated by an incoherent LED light source. A deep convolutional neural network is applied to the image reconstruction process. The network training uses data generated by a setup with straight fiber at room temperature (～20 ° C) but can be utilized directly for high-fidelity reconstruction of cell images that are transported through fiber with a few degrees bend or fiber with segments heated up to 50°C. In addition, cell images located several millimeters away from the bare fiber end can be transported and recovered successfully without the assistance of distal optics. We provide evidence that the trained neural network is able to transfer its learning to recover images of cells featuring very different morphologies and classes that are never “seen” during the training process.