Sajda Paul, Du Shuyan, Brown Truman R, Stoyanova Radka, Shungu Dikoma C, Mao Xiangling, Parra Lucas C
Laboratory of Intelligent Imaging and Neural Computing, Department of Biomedical Engineering, Columbia University, 351 Engineering Terrace Building, Mail Code 8904, 1210 Amsterdam Ave., New York, NY 10027, USA.
IEEE Trans Med Imaging. 2004 Dec;23(12):1453-65. doi: 10.1109/TMI.2004.834626.
We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.
我们提出了一种从人脑磁共振（MR）化学位移成像（CSI）中盲目恢复成分源光谱的算法。我们将该算法称为约束非负矩阵分解（cNMF），它不强制独立性或稀疏性，而是仅要求源矩阵和混合矩阵为非负。它基于非负矩阵分解（NMF）算法，对其进行扩展以包括对恢复光谱幅度正值性的约束。即使在存在噪声导致大量观测幅度为负的情况下，这种约束也能使物理上有意义的光谱得以恢复。我们使用³¹P体积脑数据演示并表征了该算法的性能，并将结果与两种不同的盲源分离方法进行比较：贝叶斯光谱分解（BSD）和非负稀疏编码（NNSC）。然后，我们将cNMF算法纳入分层分解框架，表明在从粗到细的处理层次结构下，它可用于恢复组织特异性光谱。我们在¹H脑数据上演示了分层过程，并得出结论，该算法的计算效率使其非常适合用于诊断检查。
