Deslauriers-Gauthier Samuel, Marziliano Pina
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.
Annu Int Conf IEEE Eng Med Biol Soc. 2012;2012:2294-7. doi: 10.1109/EMBC.2012.6346421.
In this paper, we investigate the reconstruction of a signal defined as the sum of K orientations from samples taken with a kernel defined on the 3D rotation group. A potential application is the recovery of fiber orientations in diffusion magnetic resonance imaging. We propose an exact reconstruction algorithm based on the finite rate of innovation theory that makes use of the spherical harmonics representation of the signal. The number of measurements needed for perfect recovery, which may be as low as 3K, depends only on the number of orientations and the bandwidth of the kernel used. Furthermore, the angular resolution of our method does not depend on the number of available measurements. We illustrate the performance of the algorithm using several simulations.
在本文中，我们研究了一个信号的重建问题，该信号被定义为从在三维旋转群上定义的核所采集的样本中K个方向的总和。一个潜在的应用是在扩散磁共振成像中恢复纤维方向。我们基于有限创新率理论提出了一种精确的重建算法，该算法利用了信号的球谐表示。完美恢复所需的测量次数可能低至3K，仅取决于方向的数量和所使用核的带宽。此外，我们方法的角分辨率不依赖于可用测量的数量。我们通过几个模拟来说明该算法的性能。
