We propose a novel numerical approach to separate multiple tissue compartments in image voxels and to estimate quantitatively their nuclear magnetic resonance (NMR) properties and mixture fractions, given magnetic resonance fingerprinting (MRF) measurements. The number of tissues, their types or quantitative properties are not a-priori known, but the image is assumed to be composed of sparse compartments with linearly mixed Bloch magnetisation responses within voxels. Fine-grid discretisation of the multi-dimensional NMR properties creates large and highly coherent MRF dictionaries that can challenge scalability and precision of the numerical methods for (discrete) sparse approximation. To overcome these issues, we propose an off-the-grid approach equipped with an extended notion of the sparse group lasso regularisation for sparse approximation using continuous (non-discretised) Bloch response models. Further, the nonlinear and non-analytical Bloch responses are approximated by a neural network, enabling efficient back-propagation of the gradients through the proposed algorithm. Tested on simulated and in-vivo healthy brain MRF data, we demonstrate effectiveness of the proposed scheme compared to the baseline multicompartment MRF methods.

中文翻译：

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跨网格磁共振指纹识别的离网方法

我们提出了一种新颖的数值方法来分离图像体素中的多个组织隔室，并在给出磁共振指纹图谱（MRF）测量的情况下，定量估计其核磁共振（NMR）特性和混合物分数。组织的数量，其类型或定量特性尚不清楚，但假定图像由稀疏隔室组成，在体素内线性混合的Bloch磁化响应线性混合。多维NMR属性的细网格离散化创建了大型且高度相关的MRF词典，这可能会挑战（离散）稀疏近似数值方法的可伸缩性和精度。为了克服这些问题，我们提出了一种网格化方法，该方法配备了使用连续（非离散）Bloch响应模型进行稀疏近似的稀疏组套索正则化的扩展概念。此外，通过神经网络对非线性和非分析性Bloch响应进行近似，从而可以通过提出的算法对梯度进行有效的反向传播。通过对模拟和体内健康大脑MRF数据的测试，我们证明了与基线多室MRF方法相比，该方案的有效性。