  Deep Neural Network (DNN)-based image reconstruction, despite many successes,
often exhibits uneven fidelity between high and low spatial frequency bands. In
this paper we propose the Learning Synthesis by DNN (LS-DNN) approach where two
DNNs process the low and high spatial frequencies, respectively, and, improving
over [30], the two DNNs are trained separately and a third DNN combines them
into an image with high fidelity at all bands. We demonstrate LS-DNN in two
canonical inverse problems: super-resolution (SR) in diffraction-limited
imaging (DLI), and quantitative phase retrieval (QPR). Our results also show
comparable or improved performance over perceptual-loss based SR [21], and can
be generalized to a wider range of image recovery problems.
