基于同伦l0范数最小化重建的三维动态磁共振成像

doi:10.11938/cjmr20212912

摘要/Abstract

摘要：

高欠采倍数的动态磁共振图像重建具有重要意义，是同时实现高时间分辨率和高空间分辨率动态对比度增强成像的重要环节.本研究提出一种结合黄金角变密度螺旋采样、并行成像和基于同伦l₀范数最小化的压缩感知的图像重建的三维动态磁共振成像方法.黄金角变密度螺旋采样轨迹被用来连续获取k空间数据，具有数据采集效率高、对运动不敏感等优点.在重建算法中，将多线圈稀疏约束应用于时间总变分域，使用基于l₀范数最小化的非线性重建算法代替传统的l₁范数最小化算法，进一步提高了欠采样率.仿真实验和在体实验表明本文所提的方法在保持图像质量的同时，也可以实现较高的空间分辨率和时间分辨率，初步验证了基于同伦l₀范数最小化重建在三维动态磁共振成像上的优势和临床价值.

关键词: 三维动态磁共振成像, 黄金角螺旋, l₀范数最小化, 高时空分辨率, 运动不敏感

Abstract:

Recovering dynamic magnetic resonance imaging (MRI) from highly undersampled raw data is of great significance, and is an important approach for achieving both high temporal and spatial resolution in dynamic contrast enhanced imaging. In this study, a method for 3D dynamic MRI with high spatiotemporal resolution and motion insensitivity was developed, which combines golden angle variable density spiral trajectory, parallel imaging and homotopic l₀ minimization-based compressed sensing. Golden angle variable density spiral trajectory, which has the advantages of high data acquisition efficiency and motion insensitivity, was used to acquire k-space data. In the reconstruction algorithm, multicoil sparsity constrain was applied in the temporal total variation domain and l₀ minimization, instead of traditional l₁ minimization, was adopted, which could further increase the undersampling rate. Simulations and in vivo experiments demonstrated that high spatial resolution and temporal resolution can be achieved by the proposed method while maintaining the image quality. This study also suggested the advantages of homotopic l₀ norm-based 3D dynamic MRI reconstruction and its clinical potential.

Key words: 3D dynamic magnetic resonance imaging, golden angle spiral, l₀ minimization, high spatiotemporal resolution, motion-insensitive

中图分类号:

O482.53

李嫣嫣,李律,李雪松,郭华. 基于同伦l₀范数最小化重建的三维动态磁共振成像[J]. 波谱学杂志, 2022, 39(1): 20-32.

Yan-yan LI,Lv LI,Xue-song LI,Hua GUO. 3D Dynamic MRI with Homotopic l₀ Minimization Reconstruction[J]. Chinese Journal of Magnetic Resonance, 2022, 39(1): 20-32.

图/表 8

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基于同伦l₀范数最小化重建的三维动态磁共振成像

3D Dynamic MRI with Homotopic l₀ Minimization Reconstruction

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目标函数：$ \min \left\{ {\left\\| {F \cdot S \cdot d - m} \right\\|_2^2 + \lambda {{\left\\| {T \cdot d} \right\\|}_0}} \right\} $
输入：F –非均匀快速傅里叶变换算子 S –线圈敏感度图 m – k空间测量数据
$ T $ –时间域上的TV算子
输出：d –目标函数的数值近似解
初始化：$ d = {(FS)^{\text{T}}}m, {\text{ }}\sigma \gg 0, {\text{ }}\beta \in (0, 1), {\text{ }}to{l_{outer}}, {\text{ }}to{l_{inner}} $
迭代：while $ ((\|\|d - {d_{outer}}\|{\|_2}/\|\|{d_{outer}}\|{\|_2})) \geqslant to{l_{outer}} $
$ {d_{outer}} = d, {\text{ }}\sigma = \sigma \times \beta $
while $ ((\|\|d - {d_{inner}}\|{\|_2}/\|\|{d_{inner}}\|{\|_2})) \geqslant to{l_{inner}} $
$ {d_{inner}} = d $ 使用共轭梯度法求解$ B(d)\Delta = - L(d, \sigma , \lambda ) $中的$ \Delta $ $ d = d + \Delta $ end
end