Novel image and patch manifold models that can exploit the non-linear and non-local redundancies in a dynamic dataset will be introduced. Specifically, the collection of images/patches in the dataset is assumed to be on a smooth manifold. I will introduce novel iterative algorithms to exploit the structure of the data. The use of these algorithms enables implicit motion compensation and motion resolution, and hence is a good alternative to current strategies that perform these operations explicity.
Several model based reconstruction algorithms, which model dynamic MRI datasets as a linear combination of basis functions, have been introduced in the last several years with great success. However, these methods have limited ability in exploiting the non-linear and non-local dependencies in several MR imaging applications, including free breathing and ungated dynamic MRI. In this talk, I will introduce image and patch manifold models that can exploit these redundancies. Specifically, the collection of images/patches in the dataset is assumed to be on a smooth manifold. I will introduce novel iterative algorithms to exploit the structure of the data. The use of these algorithms enables implicit motion compensation and motion resolution, and hence is a good alternative to current strategies that perform these operations explicity.
Topics.
1. Introduction to Manifold models
2. Patch manifold models
3. Image manifold models
4. Fast algorithms
5. Validation.
S. Poddar, M.Jacob, Dynamic MRI using Smoothness Regularization on Manifolds (SToRM), IEEE Transactions on Medical Imaging, vol 35, no 4, April 2016.
Y. Mohsin, S.G Lingala, E. DiBella, M.Jacob, Accelerated dynamic MRI Using Patch Regularization for Implicit motion CompEnsation (PRICE), Magnetic Resonance in Medicine, in press.
Y. Mohsin, G. Ongie, M. Jacob, Iterative shrinkage algorithm for patch smoothness regularized medical image recovery, IEEE Trans. Medical Imaging, 34(12), pp 2417-28, 2015.
Z. Yang, M. Jacob,"Nonlocal regularization of inverse problems: a unified variational framework", IEEE Trans. Image Processing, pp: 3192-203, vol.22(8), Aug 2013.
S.Poddar, X.Bi, D.Wang, M.Jacob, A Calibration-less approach to free-breathing ungated cardiac MRI, Proc. ISMRM 2017, Honolulu, USA.
S. Poddar, M. Jacob, Low rank recovery with manifold smoothness prior: theory and application to accelerated MRI, IEEE ISBI, New York City, USA, 2015.