Learning to synthesize: robust phase retrieval at low photon counts

The quality of inverse problem solutions obtained through deep learning is limited by the nature of the priors learned from examples presented during the training phase. Particularly in the case of quantitative phase retrieval, spatial frequencies that are underrepresented in the training database, most often at the high band, tend to be suppressed in the reconstruction. Ad hoc solutions have been proposed, such as pre-amplifying the high spatial frequencies in the examples; however, while that strategy improves the resolution, it also leads to high-frequency artefacts, as well as low-frequency distortions in the reconstructions. Here, we present a new approach that learns separately how to handle the two frequency bands, low and high, and learns how to synthesize these two bands into full-band reconstructions. We show that this “learning to synthesize” (LS) method yields phase reconstructions of high spatial resolution and without artefacts and that it is resilient to high-noise conditions, e.g., in the case of very low photon flux. In addition to the problem of quantitative phase retrieval, the LS method is applicable, in principle, to any inverse problem where the forward operator treats different frequency bands unevenly, i.e., is ill-posed. A computational approach that avoids artifacts when extracting data about the phase of light from noisy intensity signals can improve imaging of transparent objects including cells. Mo Deng from the Massachusetts Institute of Technology, United States, and colleagues have developed a procedure that separates raw intensity signals into high-frequency and low-frequency spectral channels. Then deep neural network algorithms, trained to operate in these two frequency bands, retrieve the phase information. A final algorithm recombines the two channels into a new phase image. The team’s experiments revealed that this method avoids the tendency of recent automatic phase extraction programs to over-represent low frequency signals, a quirk that reduces image resolution. The new reconstruction scheme is especially adept at handling noisy signal inputs, such as low light conditions.