Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM 87131, USA.
Biomed Eng Online. 2012 May 20;11:25. doi: 10.1186/1475-925X-11-25.
Compressive sensing can provide a promising framework for accelerating fMRI image acquisition by allowing reconstructions from a limited number of frequency-domain samples. Unfortunately, the majority of compressive sensing studies are based on stochastic sampling geometries that cannot guarantee fast acquisitions that are needed for fMRI. The purpose of this study is to provide a comprehensive optimization framework that can be used to determine the optimal 2D stochastic or deterministic sampling geometry, as well as to provide optimal reconstruction parameter values for guaranteeing image quality in the reconstructed images.
We investigate the use of frequency-space (k-space) sampling based on: (i) 2D deterministic geometries of dyadic phase encoding (DPE) and spiral low pass (SLP) geometries, and (ii) 2D stochastic geometries based on random phase encoding (RPE) and random samples on a PDF (RSP). Overall, we consider over 36 frequency-sampling geometries at different sampling rates. For each geometry, we compute optimal reconstructions of single BOLD fMRI ON & OFF images, as well as BOLD fMRI activity maps based on the difference between the ON and OFF images. We also provide an optimization framework for determining the optimal parameters and sampling geometry prior to scanning.
For each geometry, we show that reconstruction parameter optimization converged after just a few iterations. Parameter optimization led to significant image quality improvements. For activity detection, retaining only 20.3% of the samples using SLP gave a mean PSNR value of 57.58 dB. We also validated this result with the use of the Structural Similarity Index Matrix (SSIM) image quality metric. SSIM gave an excellent mean value of 0.9747 (max = 1). This indicates that excellent reconstruction results can be achieved. Median parameter values also gave excellent reconstruction results for the ON/OFF images using the SLP sampling geometry (mean SSIM > =0.93). Here, median parameter values were obtained using mean-SSIM optimization. This approach was also validated using leave-one-out.
We have found that compressive sensing parameter optimization can dramatically improve fMRI image reconstruction quality. Furthermore, 2D MRI scanning based on the SLP geometries consistently gave the best image reconstruction results. The implication of this result is that less complex sampling geometries will suffice over random sampling. We have also found that we can obtain stable parameter regions that can be used to achieve specific levels of image reconstruction quality when combined with specific k-space sampling geometries. Furthermore, median parameter values can be used to obtain excellent reconstruction results.
压缩感知可以通过从有限数量的频域样本中进行重建，为 fMRI 图像采集提供有前途的框架。不幸的是，大多数压缩感知研究都是基于随机采样几何形状，无法保证 fMRI 所需的快速采集。本研究的目的是提供一个全面的优化框架，可用于确定最佳的 2D 随机或确定性采样几何形状，并为保证重建图像中的图像质量提供最佳的重建参数值。
我们研究了基于以下两种方法的频域（k 空间）采样：（i）基于二进相位编码（DPE）和螺旋低通（SLP）几何形状的 2D 确定性几何形状，以及（ii）基于随机相位编码（RPE）和 PDF 上的随机采样（RSP）的 2D 随机几何形状。总体而言，我们考虑了不同采样率下的 36 种不同的频率采样几何形状。对于每种几何形状，我们都计算了单 BOLD fMRI ON 和 OFF 图像以及基于 ON 和 OFF 图像之间差异的 BOLD fMRI 活动图的最佳重建。我们还提供了一个优化框架，用于在扫描之前确定最佳参数和采样几何形状。
对于每种几何形状，我们都表明，在仅仅几次迭代后，重建参数优化就会收敛。参数优化导致图像质量显著提高。对于活动检测，仅使用 SLP 保留 20.3％的样本即可获得 57.58 dB 的平均 PSNR 值。我们还使用结构相似性指数矩阵（SSIM）图像质量度量验证了这一结果。SSIM 给出了极好的平均值 0.9747（最大值为 1）。这表明可以实现极好的重建结果。使用 SLP 采样几何形状时，中值参数值也为 ON/OFF 图像提供了极好的重建结果（平均 SSIM≥0.93）。这里，中值参数值是使用平均 SSIM 优化获得的。此方法还使用留一法进行了验证。
我们发现，压缩感知参数优化可以极大地提高 fMRI 图像重建质量。此外，基于 SLP 几何形状的 2D MRI 扫描始终可以获得最佳的图像重建结果。这一结果的含义是，在随机采样中，更简单的采样几何形状就足够了。我们还发现，当与特定的 k 空间采样几何形状结合使用时，我们可以获得稳定的参数区域，这些区域可以用于达到特定的图像重建质量水平。此外，可以使用中值参数值获得极好的重建结果。
