  We introduce a novel generative smoothness regularization on manifolds
(SToRM) model for the recovery of dynamic image data from highly undersampled
measurements. The proposed generative framework represents the image time
series as a smooth non-linear function of low-dimensional latent vectors that
capture the cardiac and respiratory phases. The non-linear function is
represented using a deep convolutional neural network (CNN). Unlike the popular
CNN approaches that require extensive fully-sampled training data that is not
available in this setting, the parameters of the CNN generator as well as the
latent vectors are jointly estimated from the undersampled measurements using
stochastic gradient descent. We penalize the norm of the gradient of the
generator to encourage the learning of a smooth surface/manifold, while
temporal gradients of the latent vectors are penalized to encourage the time
series to be smooth. The main benefits of the proposed scheme are (a) the quite
significant reduction in memory demand compared to the analysis based SToRM
model, and (b) the spatial regularization brought in by the CNN model. We also
introduce efficient progressive approaches to minimize the computational
complexity of the algorithm.
