Phase Retrieval using Untrained Neural Network Priors

Untrained deep neural networks as image priors have been recently introduced for linear inverse imaging problems such as denoising, super-resolution, inpainting and compressive sensing with promising performance gains over hand-crafted image priors such as sparsity. Moreover, unlike learned generative priors they do not require any training over large datasets. In this paper, we consider the problem of solving the non-linear inverse problem of compressive phase retrieval; this involves reconstructing a $d$-dimensional image signal from $n$ magnitude-only measurements, and $n<d$. We model images to lie in the range of an untrained deep generative network with a fixed seed. We further present two approaches for solving this problem: vanilla gradient descent and a projected gradient descent scheme and show superior empirical performance when compared to algorithms that use hand crafted priors.