Single-frame lensless phase retrieval using learned sensor plane initialization

We report a compact lensless quantitative phase imaging approach in a minimal optical configuration. Unlike conventional iterative phase retrieval methods, the proposed single-frame phase retrieval using learned sensor-plane estimation (SF-PULSE) framework employs a convolutional neural network to estimate the phase at the sensor plane and construct an initial complex-valued wavefront consistent with the measured intensity. This initialization preconditions the inverse problem, transforming phase retrieval from a global non-convex optimization into a locally constrained refinement. As a result, the method reduces the iteration count, improves convergence stability, and mitigates twin-image artifacts without relying on sparsity constraints or multi-frame acquisition. The approach is validated through phase target reconstruction and time-resolved measurements of live cell cultures, demonstrating stable recovery of phase-derived mass and sensitivity to dynamic variations in the refractive index distribution. In 46 h long cell culture experiments with dry mass estimation, we show that SF-PULSE provides single-cell tracking precision and information for cell death path detection. This work demonstrates that phase retrieval can be achieved in a lensless configuration without interferometric optics or measurement diversity by means of learned sensor-plane initialization.