Untrained network regularized by total variation in single-shot lensless holography

The optical complex-amplitude (CA) distribution of an object contains rich information, providing insights into the object’s optical characteristics such as retardation and absorption. Coaxial lensless holography (CLH) using a learning-based approach offers promise for retrieving CA maps with advantages such as compact setup and single-shot acquisition, while suffers from the laborious and time-consuming acquisition of datasets and labels required for network training. To address this challenge, we propose an untrained neural network with Lp-norm total variation regularization (LTVR-net) by integrating physical model into the learning process. The LTVR-net effectively suppresses twin-image and artifact noises in reconstructing CA images, outperforming traditional methods on quantitative metrics. Besides, the CA retrieval results at different imaging distances consistently exhibit excellent performance, indicating that LTVR-net possesses a distance-resolution-balanced characteristic. This feature holds promise for expanding the application scope of CLH, allowing for more versatile and flexible configurations in various scenarios. Furthermore, the experimental results on biological tissue demonstrate the ability of LTVR-net to reveal fine structures with clear boundaries, highlighting its superiority in biological imaging. These results collectively prove that LTVR-net is an untrained, single-shot, and distance-robust approach capable of achieving high-quality CA retrieval.