  In this work we address the problem of real-time dynamic medical MRI and X
Ray CT image reconstruction from parsimonious samples Fourier frequency space
for MRI and sinogram tomographic projections for CT. Today the de facto
standard for such reconstruction is compressed sensing. CS produces high
quality images (with minimal perceptual loss, but such reconstructions are time
consuming, requiring solving a complex optimization problem. In this work we
propose to learn the reconstruction from training samples using an autoencoder.
Our work is based on the universal function approximation capacity of neural
networks. The training time for the autoencoder is large, but is offline and
hence does not affect performance during operation. During testing or
operation, our method requires only a few matrix vector products and hence is
significantly faster than CS based methods. In fact, it is fast enough for
real-time reconstruction the images are reconstructed as fast as they are
acquired with only slight degradation of image quality. However, in order to
make the autoencoder suitable for our problem, we depart from the standard
Euclidean norm cost function of autoencoders and use a robust l1-norm instead.
The ensuing problem is solved using the Split Bregman method.
