  This paper puts forth a novel bi-linear modeling framework for data recovery
via manifold-learning and sparse-approximation arguments and considers its
application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain
MR image is viewed as a point that lies onto or close to a smooth manifold, and
landmark points are identified to describe the point cloud concisely. To
facilitate computations, a dimensionality reduction module generates
low-dimensional/compressed renditions of the landmark points. Recovery of the
high-fidelity MRI data is realized by solving a non-convex minimization task
for the linear decompression operator and those affine combinations of landmark
points which locally approximate the latent manifold geometry. An algorithm
with guaranteed convergence to stationary solutions of the non-convex
minimization task is also provided. The aforementioned framework exploits the
underlying spatio-temporal patterns and geometry of the acquired data without
any prior training on external data or information. Extensive numerical results
on simulated as well as real cardiac-cine and perfusion MRI data illustrate
noteworthy improvements of the advocated machine-learning framework over
state-of-the-art reconstruction techniques.
