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Deep neural networks as image priors have been recently introduced forproblems such as denoising, super-resolution and inpainting with promisingperformance gains over hand-crafted image priors such as sparsity and low-rank.Unlike learned generative priors they do not require any training over largedatasets. However, few theoretical guarantees exist in the scope of usinguntrained neural network priors for inverse imaging problems. We explore newapplications and theory for untrained neural network priors. Specifically, weconsider the problem of solving linear inverse problems, such as compressivesensing, as well as non-linear problems, such as compressive phase retrieval.We model images to lie in the range of an untrained deep generative networkwith a fixed seed. We further present a projected gradient descent scheme thatcan be used for both compressive sensing and phase retrieval and providerigorous theoretical guarantees for its convergence. We also show boththeoretically as well as empirically that with deep network priors, one canachieve better compression rates for the same image quality compared to handcrafted priors.

Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors