Probing shallower: perceptual loss trained Phase Extraction Neural Network (PLT-PhENN) for artifact-free reconstruction at low photon budget

Abstract

Deep neural networks (DNNs) are efficient solvers for ill-posed problems and have been shown to outperform classical optimization techniques in several computational imaging problems. In supervised mode, DNNs are trained by minimizing a measure of the difference between their actual output and their desired output; the choice of measure, referred to as "loss function," severely impacts performance and generalization ability. In a recent paper [A. Goy et al., Phys. Rev. Lett. 121(24), 243902 (2018)], we showed that DNNs trained with the negative Pearson correlation coefficient (NPCC) as the loss function are particularly fit for photon-starved phase-retrieval problems, though the reconstructions are manifestly deficient at high spatial frequencies. In this paper, we show that reconstructions by DNNs trained with default feature loss (defined at VGG layer ReLU-22) contain more fine details; however, grid-like artifacts appear and are enhanced as photon counts become very low. Two additional key findings related to these artifacts are presented here. First, the frequency signature of the artifacts depends on the VGG's inner layer that perceptual loss is defined upon, halving with each MaxPooling2D layer deeper in the VGG. Second, VGG ReLU-12 outperforms all other layers as the defining layer for the perceptual loss.