基于范数优化的并行磁共振成像算法

PMRI reconstruction algorithms based on norm optimization

研究了并行磁共振成像图像重建的范数优化问题.首先,通过分析目前常用的2种并行磁共振成像重建算法——GRAPPA算法和SENSE算法,归纳出它们在重建过程中所用的动态数学模型,描述成形如矩阵方程Ax=b的形式;然后,将范数优化引入到重建算法中的建模及模型参数估计中,通过采用不同矩阵范数意义下的目标函数,即在不同的范数空间中重建图像,提高优化的自由度和算法设计的灵活性;最后,通过仿真对范数优化后的重建图像质量进行分析,说明不同范数优化对重建图像的影响,并探讨了范数优化中相关参数及优化目标函数的选择问题.

The image reconstruction of parallel magnetic resonance image(PMRI) by norm optimization is studied.First,based on the analysis of two most widely used algorithms,sensitivity encoding(SENSE) and generalized autocalibrating partially parallel acquisitions(GRAPPA),the image reconstruction processes are described in the form of matrix equation Ax=b.Then,the norm optimization technique is introduced to construct the models and estimate the parameters.Through the optimization object functions under different matrix models,the freedom of optimization and the flexibility of the algorithm are advanced.Finally,the advantages of the proposed norm optimization are shown by in vivo data image reconstruction examples.The effect of different norm optimization on the reconstructed image and the application of norm optimization on noise suppression are demonstrated.Furthermore,the choose of suitable norm optimization parameters and objective functions in different situations is discussed.