  There remains an important need for the development of image reconstruction
methods that can produce diagnostically useful images from undersampled
measurements. In magnetic resonance imaging (MRI), for example, such methods
can facilitate reductions in data-acquisition times. Deep learning-based
methods hold potential for learning object priors or constraints that can serve
to mitigate the effects of data-incompleteness on image reconstruction. One
line of emerging research involves formulating an optimization-based
reconstruction method in the latent space of a generative deep neural network.
However, when generative adversarial networks (GANs) are employed, such methods
can result in image reconstruction errors if the sought-after solution does not
reside within the range of the GAN. To circumvent this problem, in this work, a
framework for reconstructing images from incomplete measurements is proposed
that is formulated in the latent space of invertible neural network-based
generative models. A novel regularization strategy is introduced that takes
advantage of the multiscale architecture of certain invertible neural networks,
which can result in improved reconstruction performance over classical methods
in terms of traditional metrics. The proposed method is investigated for
reconstructing images from undersampled MRI data. The method is shown to
achieve comparable performance to a state-of-the-art generative model-based
reconstruction method while benefiting from a deterministic reconstruction
procedure and easier control over regularization parameters.
