Department of Electronics and Communication Engineering, National Institute of Technology (NIT), Tiruchirappalli, India,
Int J Comput Assist Radiol Surg. 2014 May;9(3):459-72. doi: 10.1007/s11548-013-0938-z. Epub 2013 Sep 8.
An efficient algorithm for magnetic resonance (MR) image reconstruction is needed, especially when sparse sampling is employed to accelerate data acquisition. The aim of this paper is to solve the sparse MRI problem based on nonlocal total variation (NLTV) and framelet sparsity using the split Bregman algorithm. A new method was developed and tested in a variety of MR image acquisitions.
The proposed method minimizes a linear combination of NLTV, least square data fitting and framelet terms to reconstruct the MR images from undersampled k-space data. The NLTV and framelet sparsity are taken as the L₁-regularization functional and solved by using the split Bregman method. Experiments were conducted to compare the proposed algorithm with several different reconstruction methods, including the operator splitting algorithm, variable splitting method, composite splitting algorithm and its accelerated version called the fast composite splitting algorithm. A detailed evaluation study was done on the reconstruction of MR images which represent varying degrees of object structural complexity. Both qualitative visualization-based and quantitative metric-based evaluations were done.
Numerical results on various data corresponding to different sampling rates showed the advantages of the new method in preserving geometrical features, textures and fine structures. The proposed algorithm was compared with previous methods in terms of the reconstruction accuracy and computational complexity with favorable results.
An efficient new algorithm was developed for compressed MR image reconstruction based on NLTV and framelet sparsity. The algorithm effectively solves a hybrid regularizer based on framelet sparsity and NLTV using the split Bregman method. NLTV makes the recovered image quality sharper by preserving the edges or boundaries more accurately, and framelets often improve image quality. The comparison with alternative method yielded results that demonstrate the superiority of the proposed algorithm for compressed MR image reconstruction.
需要一种高效的磁共振（MR）图像重建算法，特别是在采用稀疏采样加速数据采集时。本文旨在基于非局部全变分（NLTV）和框架稀疏性，利用分裂布格曼算法解决稀疏 MRI 问题。开发了一种新方法，并在多种 MR 图像采集实验中进行了测试。
该方法通过最小化 NLTV、最小二乘数据拟合和框架项的线性组合，从欠采样 k 空间数据重建 MR 图像。将 NLTV 和框架稀疏性作为 L₁正则化函数，利用分裂布格曼法求解。实验比较了该算法与几种不同的重建方法，包括算子分裂算法、变量分裂方法、复合分裂算法及其加速版本快速复合分裂算法。对代表不同物体结构复杂度的 MR 图像进行了详细的重建评估研究。进行了定性可视化和定量度量评估。
针对不同采样率的各种数据的数值结果表明，该方法在保持几何特征、纹理和精细结构方面具有优势。在重建精度和计算复杂度方面，该算法与以前的方法进行了比较，结果是有利的。
提出了一种基于 NLTV 和框架稀疏性的高效压缩 MR 图像重建新算法。该算法利用分裂布格曼方法有效地解决了基于框架稀疏性和 NLTV 的混合正则化问题。NLTV 通过更准确地保留边缘或边界，使恢复的图像质量更加清晰，而框架通常可以提高图像质量。与替代方法的比较结果表明，该算法在压缩 MR 图像重建方面具有优越性。
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