Solving Bilinear Inverse Problems using Deep Generative Priors
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This paper proposes a new framework to handle the bilinear inverse problems (BIPs): recover w, and x from the measurements of the form y = A(w,x), where A is a bilinear operator. The recovery problem of the unknowns w, and x can be formulated as a non-convex program. A general strategy is proposed to turn the ill-posed BIP to a relatively well-conditioned BIP by imposing a structural assumption that w, and x are members of some classes W, and X, respectively, that are parameterized by unknown latent low-dimensional features. We learn functions mapping from the hidden feature space to the ambient space for each class using generative models. The resulting reduced search space of the solution enables a simple alternating gradient descent scheme to yield promising result in solving the non-convex BIP. To demonstrate the performance of our algorithm, we choose an important BIP; namely, blind image deblurring as a motivating application. We show through extensive experiments that this technique shows promising results in deblurring images of real datasets and is also robust to noise perturbations.
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