Jian Bing, Vemuri Baba C
Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA.
Inf Process Med Imaging. 2007;20:384-95. doi: 10.1007/978-3-540-73273-0_32.
In this paper, we present a novel continuous mixture of diffusion tensors model for the diffusion-weighted MR signal attenuation. The relationship between the mixing distribution and the MR signal attenuation is shown to be given by the Laplace transform defined on the space of positive definite diffusion tensors. The mixing distribution when parameterized by a mixture of Wishart distributions (MOW) is shown to possess a closed form expression for its Laplace transform, called the Rigaut-type function, which provides an alternative to the Stejskal-Tanner model for the MR signal decay. Our model naturally leads to a deconvolution formulation for multi-fiber reconstruction. This deconvolution formulation requires the solution to an ill-conditioned linear system. We present several deconvolution methods and show that the nonnegative least squares method outperforms all others in achieving accurate and sparse solutions in the presence of noise. The performance of our multi-fiber reconstruction method using the MOW model is demonstrated on both synthetic and real data along with comparisons with state-of-the-art techniques.
在本文中，我们提出了一种用于扩散加权磁共振信号衰减的新型连续扩散张量混合模型。混合分布与磁共振信号衰减之间的关系由在正定扩散张量空间上定义的拉普拉斯变换给出。当用威沙特分布混合（MOW）进行参数化时，混合分布的拉普拉斯变换具有封闭形式的表达式，称为里 Gaut 型函数，它为磁共振信号衰减提供了替代 Stejskal-Tanner 模型的方法。我们的模型自然地导致了用于多纤维重建的反卷积公式。这种反卷积公式需要求解一个病态线性系统。我们提出了几种反卷积方法，并表明非负最小二乘法在存在噪声的情况下实现准确和稀疏解方面优于所有其他方法。使用 MOW 模型的多纤维重建方法的性能在合成数据和真实数据上都得到了验证，并与现有技术进行了比较。
