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Optimal Transport Regularization of Implicit Neural Representations for Dynamic MRI Reconstruction
Blom, T.R.G. (2025) Optimal Transport Regularization of Implicit Neural Representations for Dynamic MRI Reconstruction.
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| Abstract: | The reconstruction of undersampled spatially and temporally undersampled dynamic inverse problems remains a challenge due to the trade-off between spatial and temporal resolution. Specifically, this occurs in MRI, where rapid anatomical motion and physiological changes demand high temporal fidelity, creating a trade-off between high spatial and temporal fidelity. An emerging direction in accelerated MRI reconstruction is the integration of deep learning techniques. Compared to more iterative methods like compressed sensing, deep learning methods offer improved reconstruction quality and also enable the possibility of real-time imaging. From the deep learning architectures, unsupervised learning strategies using neural networks have been proposed, as they do not require large datasets. Among these approaches, implicit neural representations (INRs) offer a strong framework by modeling data as continuous functions that map spatial and temporal coordinates to signal values. However, most existing approaches rely on positional encoding of the input coordinates, latent motion codes, and deformation networks to enhance temporal consistency in the presence of spatial undersampling. In this work, we incorporate an Optimal Transport-based regularization strategy into an implicit neural representation (INR) framework to enable higher spatiotemporal undersampling for physically plausible transitions between frames. Specifically, we incorporate temporal prior into the model through optimal transport (OT) regularization. We introduce two types of regularization: one based on the Wasserstein distance between consecutive frames and another based on a barycenter formulation. We demonstrate that both regularizers promote temporally coherent reconstructions and improve performance under high spatiotemporal subsampling rates. |
| Item Type: | Essay (Master) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics |
| Programme: | Applied Mathematics MSc (60348) |
| Link to this item: | https://purl.utwente.nl/essays/107067 |
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