在基于奇异值分解的磁共振波谱参数估计中运用先验知识——以三磷酸腺苷为例。

Using prior knowledge in SVD-based parameter estimation for magnetic resonance spectroscopy--the ATP example.

作者信息

Stoica Petre, Selén Yngve, Sandgren Niclas, Van Huffel Sabine

机构信息

Systems and Control Division, Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden.

出版信息

IEEE Trans Biomed Eng. 2004 Sep;51(9):1568-78. doi: 10.1109/TBME.2004.828031.

DOI:10.1109/TBME.2004.828031

PMID:15376505

Abstract

We introduce the knowledge-based singular value decomposition (KNOB-SVD) method for exploiting prior knowledge in magnetic resonance (MR) spectroscopy based on the SVD of the data matrix. More specifically, we assume that the MR data are well modeled by the superposition of a given number of exponentially damped sinusoidal components and that the dampings alphakappa, frequencies omegakappa, and complex amplitudes rhokappa of some components satisfy the following relations: alphakappa = alpha (alpha = unknown), omegakappa = omega + (kappa- 1)delta (omega = unknown, delta = known), and rhokappa = Ckapparho (rho = unknown, ckappa = known real constants). The adenosine triphosphate (ATP) complex, which has one triple peak and two double peaks whose dampings, frequencies, and amplitudes may in some cases be known to satisfy the above type of relations, is used as a vehicle for describing our SVD-based method throughout the paper. By means of numerical examples, we show that our method provides more accurate parameter estimates than a commonly used general-purpose SVD-based method and a previously suggested prior knowledge-based SVD method.

摘要

我们介绍了基于知识的奇异值分解（KNOB-SVD）方法，用于在基于数据矩阵奇异值分解的磁共振（MR）波谱中利用先验知识。更具体地说，我们假设MR数据可以通过给定数量的指数衰减正弦分量的叠加得到很好的建模，并且某些分量的衰减系数ακ、频率ωκ和复振幅ρκ满足以下关系：ακ = α（α为未知），ωκ = ω + (κ - 1)δ（ω为未知，δ为已知），以及ρκ = Cκρ（ρ为未知，Cκ为已知实常数）。三磷酸腺苷（ATP）复合物有一个三重峰和两个双峰，在某些情况下其衰减、频率和振幅可能已知满足上述类型的关系，本文将其用作描述我们基于奇异值分解方法的载体。通过数值示例，我们表明我们的方法比常用的基于奇异值分解的通用方法和先前提出的基于先验知识的奇异值分解方法能提供更准确的参数估计。