Athena Project-Team, Inria, Sophia-Antipolis Cedex, France.
Med Image Anal. 2012 Aug;16(6):1113-20. doi: 10.1016/j.media.2012.06.011. Epub 2012 Jul 17.
In diffusion MRI, the reconstruction of the full Ensemble Average Propagator (EAP) provides new insights in the diffusion process and the underlying microstructure. The reconstruction of the signal in the whole Q-space is still extremely challenging however. It requires very long acquisition protocols, and robust reconstruction to cope with the very low SNR at large b-values. Several reconstruction methods were proposed recently, among which the Spherical Polar Fourier (SPF) expansion, a promising basis for signal reconstruction. Yet the reconstruction in SPF is still subject to noise and discontinuity of the reconstruction. In this work, we present a method for the reconstruction of the diffusion attenuation in the whole Q-space, with a special focus on continuity and optimal regularization. We derive a modified Spherical Polar Fourier (mSPF) basis, orthonormal and compatible with SPF, for the reconstruction of a signal with continuity constraint. We also derive the expression of a Laplace regularization operator in the basis, together with a method based on generalized cross validation for the optimal choice of the parameter. Our method results in a noticeable dimension reduction as compared with SPF. Tested on synthetic and real data, the reconstruction with this method is more robust to noise and better preserves fiber directions and crossings.
在扩散磁共振成像中，全集合平均传播子（EAP）的重建为扩散过程和潜在的微观结构提供了新的见解。然而，在整个 Q 空间中重建信号仍然极具挑战性。它需要非常长的采集协议，并且需要稳健的重建来应对大 b 值时非常低的 SNR。最近提出了几种重建方法，其中包括球面极坐标傅里叶（SPF）展开，这是一种有前途的信号重建基础。然而，SPF 中的重建仍然受到噪声和重建不连续性的影响。在这项工作中，我们提出了一种用于在整个 Q 空间中重建扩散衰减的方法，特别关注连续性和最佳正则化。我们推导出了一种改进的球面极坐标傅里叶（mSPF）基，它与 SPF 正交且兼容，用于重建具有连续性约束的信号。我们还推导出了在该基中的拉普拉斯正则化算子的表达式，以及一种基于广义交叉验证的用于最优选择参数的方法。与 SPF 相比，我们的方法导致了显著的降维。在合成和真实数据上的测试表明，这种方法的重建对噪声更鲁棒，并且更好地保留了纤维方向和交叉。
