基于统计物理正向建模和近端优化方法的MR弹性成像刚度图像有限元重建
Finite Element Reconstruction Of Stiffness Images In MR Elastography Using Statistical Physical Forward Modeling And Proximal Optimization Methods
摘要：
组织特性的定量表征，称为弹性成像，可以被视为解决不适定的逆问题。磁共振弹性成像（MRE）中的有限元方法（FEM）基于求解约束优化问题，该问题由物理正演模型和正则化子组成，分别作为数据保真度项和先验项。在现有的弹性正演模型中，由简谐运动平衡方程产生的物理定律表明了MRE测量数据与未知弹性分布之间的确定性关系，这导致在存在噪声的情况下弹性分布估计较差且不稳定。为此，我们提出了一个有效的统计方法，物理正演模型的改进，制定它作为线性代数表示相对于未知的弹性分布，并将分析噪声模型。为了解决随后的总变差正则化优化任务，我们受益于一个固定点计划，涉及近端梯度方法。不同信噪比条件下的弹性重建仿真结果验证了该方法的有效性。
英文摘要：
Quantitative characterization of tissue properties, known as elasticity imaging, can be cast as solving an ill-posed inverse problem. The finite element methods (FEMs) in magnetic resonance elastography (MRE) imaging are based on solving a constrained optimization problem consisting of a physical forward model and a regularizer as the data-fidelity term and the prior term, respectively. In existing formulation for the elasticity forward model, physical laws that arise from equilibrium equation of harmonic motion, indicate a deterministic relationship between MRE-measured data and unknown elasticity distribution which leads to the poor and unstable elasticity distribution estimation in the presence of noise. Toward this end, we propose an efficient statistical methodology for physical forward model refinement by formulating it as linear algebraic representation with respect to the unknown elasticity distribution and incorporating an analytical noise model. To solve the subsequent total variation regularized optimization task, we benefit from a fixed-point scheme involving proximal gradient methods. Simulation results of elasticity reconstruction in various SNR conditions verify the effectiveness of the proposed approach.
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