  The projected gradient descent (PGD) method has shown to be effective in
recovering compressed signals described in a data-driven way by a generative
model, i.e., a generator which has learned the data distribution. Further
reconstruction improvements for such inverse problems can be achieved by
conditioning the generator on the measurement. The boundary equilibrium
generative adversarial network (BEGAN) implements an equilibrium based loss
function and an auto-encoding discriminator to better balance the performance
of the generator and the discriminator. In this work we investigate a
network-based projected gradient descent (NPGD) algorithm for
measurement-conditional generative models to solve the inverse problem much
faster than regular PGD. We combine the NPGD with conditional GAN/BEGAN to
evaluate their effectiveness in solving compressed sensing type problems. Our
experiments on the MNIST and CelebA datasets show that the combination of
measurement conditional model with NPGD works well in recovering the compressed
signal while achieving similar or in some cases even better performance along
with a much faster reconstruction. The achieved reconstruction speed-up in our
experiments is up to 140-175.
