Solving Bilinear Inverse Problems using Deep Generative Priors

02/12/2018
by   Muhammad Asim, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset