Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Magn Reson Med. 2011 Dec;66(6):1601-15. doi: 10.1002/mrm.22956. Epub 2011 Jun 10.
Clinical imaging with structural MRI routinely relies on multiple acquisitions of the same region of interest under several different contrast preparations. This work presents a reconstruction algorithm based on Bayesian compressed sensing to jointly reconstruct a set of images from undersampled k-space data with higher fidelity than when the images are reconstructed either individually or jointly by a previously proposed algorithm, M-FOCUSS. The joint inference problem is formulated in a hierarchical Bayesian setting, wherein solving each of the inverse problems corresponds to finding the parameters (here, image gradient coefficients) associated with each of the images. The variance of image gradients across contrasts for a single volumetric spatial position is a single hyperparameter. All of the images from the same anatomical region, but with different contrast properties, contribute to the estimation of the hyperparameters, and once they are found, the k-space data belonging to each image are used independently to infer the image gradients. Thus, commonality of image spatial structure across contrasts is exploited without the problematic assumption of correlation across contrasts. Examples demonstrate improved reconstruction quality (up to a factor of 4 in root-mean-square error) compared with previous compressed sensing algorithms and show the benefit of joint inversion under a hierarchical Bayesian model.
临床影像学中的结构磁共振成像通常依赖于对同一感兴趣区域在几种不同对比准备下进行多次采集。本工作提出了一种基于贝叶斯压缩感知的重建算法，可从欠采样的 k 空间数据中以比单独或通过先前提出的算法（M-FOCUSS）联合重建图像更高的保真度来重建一组图像。联合推理问题在分层贝叶斯设置中进行了公式化，其中解决每个逆问题对应于找到与每个图像相关联的参数（这里，图像梯度系数）。对于单个体积空间位置，对比度之间的图像梯度方差是单个超参数。同一解剖区域的所有图像，但具有不同的对比特性，有助于超参数的估计，一旦找到超参数，就可以独立使用属于每个图像的 k 空间数据来推断图像梯度。因此，利用了对比度之间的图像空间结构的共性，而没有跨对比度相关性的问题假设。示例表明与以前的压缩感知算法相比，重建质量得到了提高（均方根误差提高了 4 倍），并且在分层贝叶斯模型下显示了联合反演的优势。
