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.

Dynamical machine learning volumetric reconstruction of objects’ interiors from limited angular views

Limited-angle tomography of an interior volume is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al. Proc. Natl. Acad. Sci. 116, 19848–19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in the angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as a better fit to regularize the reconstructions. We devised a Recurrent Neural Network (RNN) architecture with a novel Separable-Convolution Gated Recurrent Unit (SC-GRU) as the fundamental building block. Through a comprehensive comparison of several quantitative metrics, we show that the dynamic method is suitable for a generic interior-volumetric reconstruction under a limited-angle scheme. We show that this approach accurately reconstructs volume interiors under two conditions: weak scattering, when the Radon transform approximation is applicable and the forward operator well defined;and strong scattering, which is nonlinear with respect to the 3D refractive index distribution and includes uncertainty in the forward operator.

Imaging in focusing Kerr media using reverse propagation [Invited]

We present imaging experiments in focusing Kerr media using digital holography and digital reverse propagation(DRP)of the wave.For moderate power,the nonlinear DRP algorithm can be used to improve the quality of images over the linear DRP.We discuss the limits of the method at high power,the role of small-scale filaments,and the problem of time-dependent self-phase modulation.