Union of Surfaces Model for Data Living on Manifolds

Current cardiac MR imaging exams are long (> 1hr) and require the subject to hold their breath several times. These long scans are often challenging for several patient populations (e.g. obese subjects and patients with compromised pulmonary function). Our main goal is to develop a short 3-D free-breathing & un-gated cardiac imaging protocol to evaluate cardiac structure, function, perfusion, and fibrosis in obese subjects in a short scan time.

We model the time profiles as points living on a manifold. We introduce a union of surfaces model to represent such signals efficiently. We rely on a non-linear lifting or mapping of the data, which will transform the union of surfaces representation to the well-know union of subspaces model. Relying on this connection, we introduce sampling theorems and fast algorithms for the recovery of signals with extensive non-linear structure.