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Magnetic resonance imaging is a versatile diagnostic tool with numerous clinical applications. However, despite advances towards higher resolutions, it cannot resolve images on a cellular level. To nevertheless probe tissue microstructure, multidimensional correlation imaging emerges as a promising method. It takes advantage of the fact that each tissue compartment has a unique signal. Usually, these multi-compartmental characteristics are averaged over a macroscopic voxel. In contrast, correlation imaging aims to probe the true, heterogeneous nature of tissue. Based on image series acquired with varying inversion time T I and echo time T E, multiparametric spectra of T1 and T2 relaxation times in every voxel can be reconstructed, revealing sub-voxel tissue classes. However, even with impractically long acquisition times spent on dense sampling of the image (3D) and T IT E-space (2D), the inverse problem of retrieving these components from measured signal curves remains highly ill-conditioned and requires expensive regularized approaches. We formulate multiparametric correlation imaging as a classification problem and propose a flexible physics informed deep learning framework comprising a multilayer perceptron. This way, we efficiently reconstruct voxel-wise T1-T2-spectra with increased robustness to noise and undersampling in the T I-T E-space compared to state-of-the-art regression. Our results show feasibility of further acceleration of the acquisition by a factor of 4. After training on synthetic data that is not constraint by pre-defined tissue classes and independent of annotated data, we test our method on in-vivo brain data, revealing sub-voxel compartments in white and gray matter. This allows us to quantify tissue microstructure and will potentially lead to novel biomarkers.
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