Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
IEEE Trans Med Imaging. 2011 Sep;30(9):1649-60. doi: 10.1109/TMI.2011.2140121. Epub 2011 Apr 7.
In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.
在这项工作中，我们利用小波可以用相对较少的系数很好地表示磁共振图像这一特性，从具有任意 k 空间轨迹的欠采样数据中改进磁共振成像 (MRI) 重建。重建被表述为一个优化问题，可以使用迭代收缩/阈值算法 (ISTA) 来解决，不幸的是，该算法收敛速度较慢。为了使该方法更实用，我们提出了一种变体，它结合了凸优化的最新进展，并可以针对给定的特定 k 空间轨迹进行调整。我们提出了一种数学分析，解释了算法的性能。使用模拟和体内数据，我们表明我们的非线性方法速度很快，因为它将 ISTA 加速了近两个数量级。我们还表明，它在图像质量方面仍然与 TV 正则化具有竞争力。
