Department of Medical Physics, Cross Cancer Institute 11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada.
Med Phys. 2013 May;40(5):052302. doi: 10.1118/1.4800642.
To investigate the modulation transfer function (MTF) behavior of compressed sensing (CS) MR spectroscopic imaging (MRSI) with regard to CS reconstruction weights and the acquired peak signal-to-noise ratio (SNR); which may have an effect on MTF due to the nonlinear nature of the CS reconstruction process.
A specially designed phantom consisting of wedges arranged in a fan pattern was used to calculate the MTF of the MRSI scans. Arc profiles of the phantom yield a square wave with a spatial frequency inversely proportional to the radius of the profile. The MTF was derived by considering the amplitude ratio of the fundamental frequency between the ideal square wave and the reconstructed output. As compressed sensing relies on nonlinear reconstruction and a minimization algorithm that requires the definition of reconstruction weights, the behavior of the MTF with respect to the choice of reconstruction weights and peak SNR is not intuitive. As such, simulations were used to investigate the response of the MTF to CS reconstruction weights at varying peak SNRs. The resulting optimized reconstruction weight was used to reconstruct an experimental CS-MRSI scan of the phantom and compare the corresponding MTF to those of a fully sampled dataset, and a time-equivalent Nyquist-sampled low-resolution dataset.
Simulations showed that MTFs of CS-MRSI datasets varied widely with different reconstruction weights. Moreover, the response of the MTF to peak SNR was not consistent across the range of reconstruction weights. An optimized reconstruction weight was derived from the simulations and used in reconstructing the experimental dataset. The MTF of the experimental CS-MRSI dataset showed improvement over the equivalent Nyquist sampled dataset at the resolution limit of 0.1 MTF, while it suffered from reduced response at low resolutions between 0.4 and 0.8 lp/cm.
The authors have shown that in certain cases small variations in the reconstruction weights yield a measureable effect on the CS reconstructed images, particularly with regard to MTF. Furthermore, it was found that peak SNR affects CS-MRSI MTF especially at higher wavelet reconstruction weights. Accordingly, prior knowledge of the expected peak SNR is essential to optimize the CS reconstruction process. Their phantom-MTF technique provides a quantitative performance measure of MRSI sequences, through which they were able to quantify a loss of 32.4% in spatial resolution for CS-MRSI at 0.1 MTF compared to a loss of 48.6% for the time-equivalent Nyquist-sampled low-resolution scans. They also showed that CS-MRSI suffered decreased low-resolution response as opposed to the equivalent low-resolution datasets.
研究压缩感知（CS）磁共振波谱成像（MRSI）的调制传递函数（MTF）行为与 CS 重建权重和采集的峰值信噪比（SNR）之间的关系；由于 CS 重建过程的非线性性质，这可能会对 MTF 产生影响。
使用专门设计的楔形扇形图案的体模来计算 MRSI 扫描的 MTF。体模的弧形轮廓产生与轮廓半径成反比的空间频率的方波。通过考虑理想方波和重建输出之间的基频幅度比来得出 MTF。由于压缩感知依赖于非线性重建和需要定义重建权重的最小化算法，因此 MTF 随重建权重和峰值 SNR 的选择而变化的行为并非直观。因此，使用模拟来研究 MTF 对不同峰值 SNR 下 CS 重建权重的响应。使用优化后的重建权重来重建体模的实验性 CS-MRSI 扫描，并将相应的 MTF 与完全采样数据集和等效奈奎斯特采样的低分辨率数据集的 MTF 进行比较。
模拟表明，CS-MRSI 数据集的 MTF 随不同的重建权重而变化很大。此外，MTF 对峰值 SNR 的响应在整个重建权重范围内并不一致。从模拟中得出一个优化的重建权重，并将其用于重建实验数据集。与等效奈奎斯特采样数据集相比，实验性 CS-MRSI 数据集的 MTF 在 0.1 MTF 的分辨率极限处有所提高，而在 0.4 到 0.8 lp/cm 的低分辨率处响应降低。
作者表明，在某些情况下，重建权重的微小变化会对 CS 重建图像产生可测量的影响，尤其是在 MTF 方面。此外，发现峰值 SNR 尤其在较高的小波重建权重下会影响 CS-MRSI 的 MTF。因此，预先了解预期的峰值 SNR 对于优化 CS 重建过程至关重要。他们的体模-MTF 技术为 MRSI 序列提供了一种定量性能衡量标准，通过该技术，他们能够量化 CS-MRSI 在 0.1 MTF 处的空间分辨率损失为 32.4%，而等效的时间等效奈奎斯特采样的低分辨率扫描的损失为 48.6%。他们还表明，CS-MRSI 的低分辨率响应降低，而不是等效的低分辨率数据集。
