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.
Keywords: Image reconstruction; compressive sensing; generative neural networks; invertible neural networks.