Advanced multi-plane phase retrieval using graphic processing unit: augmented Lagrangian technique with sparse regularization

In our work we demonstrate a computational method of phase retrieval realized for various propagation models. The effects, arising due to the wave field propagation in an optical setup, lead to significant distortions in measurements; therefore the reconstructed wave fields are noisy and corrupted by different artifacts (e.g. blurring, "waves" on boards, etc.). These disturbances are hard to be specified, but could be suppressed by filtering. The contribution of this paper concerns application of an adaptive sparse approximation of the object phase and amplitude in order to improve imaging. This work is considered as a further development and improvement of the variational phase-retrieval algorithm originated in 1. It is shown that the sparse regularization enables a better reconstruction quality and substantial enhancement of imaging. Moreover, it is demonstrated that an essential acceleration of the algorithm can be obtained by a commodity graphic processing unit, what is crucial for processing of large images.