Dataset Information

Extrinsic local regression on manifold-valued data.

ABSTRACT: We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach.

SUBMITTER: Lin L

PROVIDER: S-EPMC5722259 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Publications

Extrinsic local regression on manifold-valued data.

Lin Lizhen L St Thomas Brian B Zhu Hongtu H Dunson David B DB

Journal of the American Statistical Association 20160720 519

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting b ...[more]

PMID: 29225385

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Project description:Despite the proliferation of deep learning techniques for accelerated MRI acquisition and enhanced image reconstruction, the construction of large and diverse MRI datasets continues to pose a barrier to effective clinical translation of these technologies. One major challenge is in collecting the MRI raw data (required for image reconstruction) from clinical scanning, as only magnitude images are typically saved and used for clinical assessment and diagnosis. The image phase and multi-channel RF coil information are not retained when magnitude-only images are saved in clinical imaging archives. Additionally, preprocessing used for data in clinical imaging can lead to biased results. While several groups have begun concerted efforts to collect large amounts of MRI raw data, current databases are limited in the diversity of anatomy, pathology, annotations, and acquisition types they contain. To address this, we present a method for synthesizing realistic MR data from magnitude-only data, allowing for the use of diverse data from clinical imaging archives in advanced MRI reconstruction development. Our method uses a conditional GAN-based framework to generate synthetic phase images from input magnitude images. We then applied ESPIRiT to derive RF coil sensitivity maps from fully sampled real data to generate multi-coil data. The synthetic data generation method was evaluated by comparing image reconstruction results from training Variational Networks either with real data or synthetic data. We demonstrate that the Variational Network trained on synthetic MRI data from our method, consisting of GAN-derived synthetic phase and multi-coil information, outperformed Variational Networks trained on data with synthetic phase generated using current state-of-the-art methods. Additionally, we demonstrate that the Variational Networks trained with synthetic k-space data from our method perform comparably to image reconstruction networks trained on undersampled real k-space data.

Dataset Information

Extrinsic local regression on manifold-valued data.

Publications

Extrinsic local regression on manifold-valued data.

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