Phase retrieval methods for lensless digital holographic microscopy and their robustness to data errors

In this work, we numerically compare accuracy and robustness of five popular phase retrieval approaches for lensless digital holographic microscopy. In our analysis we consider three single-frame approaches: (1) seminal Gabor method, (2) optimization-based method exploiting data fidelity and object priors, and (3) UTIRnet as a representative of deep learning methods. We also analyze two multi-frame approaches: (4) conventional Gerchberg-Saxton (GS) algorithm and (5) recently proposed optimization-based algorithm called defocus-interdependence conjugate gradient method (DI-CG). In our numerical study we focus on robustness of the phase retrieval algorithms to disturbances in the captured data with a distinction between the influence of high and low-frequency intensity errors. Our study shows that although single-frame algorithms fail to recover slowly varying phase features, they offer excellent resistance to external disturbances. Contrary, more refined multiple-frame approaches are generally more accurate but suffer from increased sensitivity to data errors, which, to some extent, can be mitigated with a regularization technique.