Purpose: To develop a framework to reconstruct large-scale volumetric dynamic MRI from rapid continuous and non-gated acquisitions, with applications to pulmonary and dynamic contrast enhanced (DCE) imaging. Theory and Methods: The problem considered here requires recovering hundred-gigabytes of dynamic volumetric image data from a few gigabytes of k-space data, acquired continuously over several minutes. This reconstruction is vastly under-determined, heavily stressing computing resources as well as memory management and storage. To overcome these challenges, we leverage intrinsic three dimensional (3D) trajectories, such as 3D radial and 3D cones, with ordering that incoherently cover time and k-space over the entire acquisition. We then propose two innovations: (1) A compressed representation using multi-scale low rank matrix factorization that constrains the reconstruction problem, and reduces its memory footprint. (2) Stochastic optimization to reduce computation, improve memory locality, and minimize communications between threads and processors. We demonstrate the feasibility of the proposed method on DCE imaging acquired with a golden-angle ordered 3D cones trajectory and pulmonary imaging acquired with a bit-reversed ordered 3D radial trajectory. We compare it with soft-gated dynamic reconstruction for DCE and respiratory resolved reconstruction for pulmonary imaging. Results: The proposed technique shows transient dynamics that are not seen in gating based methods. When applied to datasets with irregular, or non-repetitive motions, the proposed method displays sharper image features. Conclusion: We demonstrated a method that can reconstruct massive 3D dynamic image series in the extreme undersampling and extreme computation setting.
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