高阶张量能够以其简单的多项式形式表示多叶函数, 被广泛应用于纤维方向分布估计中.但随着高阶张量阶数的增加, 现有方法存在难以稳定重构纤维方向和角度分辨率低等缺陷.引入非负约束条件是目前提高稳定性的常用方法,该方法也仅能保证低于6阶时纤维方向的稳定估计. 针对以上问题,文章在高阶张量拟合模型基础上引入球面反卷积模型,并提出了一种自适应非负约束迭代算法进行纤维方向分布估计.该算法以高阶张量为基函数拟合纤维扩散分布, 沿纤维方向调整非负约束,并自适应训练调整矩阵参数.为了验证本算法的有效性,通过仿真数据与实际临床数据在同等条件下与现有CT-FOD, CSD算法进行角度分辨率,角度误差以及纤维重建对比实验.结果表明,文章所提出的方法在角度分辨率和稳定性方面优于现有的两种方法.

Higher order tensor has been widely used in the estimation of fiber orientation distribution for its simple polynomial form and its ability to model multi-lobed spherical functions. However, existing methods are unable to reconstruct fiber orientation stably, whose angular resolution is dissatisfied. Introducing non-negative constraint is the common method to improve accuracy, but it can only guarantee estimation of fiber orientation stably when the order is less than 6. We introduce spherical deconvolution algorithm to higher order tensor algorithm and present an adaptively non-negative iterative constraint to estimate the fiber orientation distribution. This algorithm applies basis function which based on higher order tensor to fit fiber diffusion distribution, adjusts non-negative constraint through fiber orientations and trains the parameters of adjustive matrix daptively. In order to test the effectiveness of the proposed algorithm, we do angular resolution, angle error and fiber reconstruction experiments which compared with CT-FOD and CSD algorithms in the same condition with synthetic data and real data. The contrastive results demonstrated that our algorithm improves fiber direction identification accuracy and the stability.