  In this work, we propose an iterative reconstruction scheme (ALONE - Adaptive
Learning Of NEtworks) for 2D radial cine MRI based on ground truth-free
unsupervised learning of shallow convolutional neural networks. The network is
trained to approximate patches of the current estimate of the solution during
the reconstruction. By imposing a shallow network topology and constraining the
$L_2$-norm of the learned filters, the network's representation power is
limited in order not to be able to recover noise. Therefore, the network can be
interpreted to perform a low dimensional approximation of the patches for
stabilizing the inversion process. We compare the proposed reconstruction
scheme to two ground truth-free reconstruction methods, namely a well known
Total Variation (TV) minimization and an unsupervised adaptive Dictionary
Learning (DIC) method. The proposed method outperforms both methods with
respect to all reported quantitative measures. Further, in contrast to DIC,
where the sparse approximation of the patches involves the solution of a
complex optimization problem, ALONE only requires a forward pass of all patches
through the shallow network and therefore significantly accelerates the
reconstruction.
