Class-Specific Blind Deconvolutional Phase Retrieval Under a Generative Prior
This addresses a specific inverse problem in imaging modalities, offering an incremental improvement with generative priors for applications like X-ray crystallography.
The paper tackles the ill-posed problem of recovering two signals from phaseless convolution measurements, common in imaging like Fourier ptychography, by using alternating gradient descent with deep generative priors, achieving quality image reconstruction and robustness to noise in realistic measurement models.
In this paper, we consider the highly ill-posed problem of jointly recovering two real-valued signals from the phaseless measurements of their circular convolution. The problem arises in various imaging modalities such as Fourier ptychography, X-ray crystallography, and in visible light communication. We propose to solve this inverse problem using alternating gradient descent algorithm under two pretrained deep generative networks as priors; one is trained on sharp images and the other on blur kernels. The proposed recovery algorithm strives to find a sharp image and a blur kernel in the range of the respective pre-generators that \textit{best} explain the forward measurement model. In doing so, we are able to reconstruct quality image estimates. Moreover, the numerics show that the proposed approach performs well on the challenging measurement models that reflect the physically realizable imaging systems and is also robust to noise