论文标题
通过分析延续多型线圈MRI
Multi-coil MRI by analytic continuation
论文作者
论文摘要
我们根据分析延续思想提出了新的重建和稳定分析方法，用于二维，多型线圈MRI。我们表明，2-D，有限的数据MRI逆问题，$ \ textbf {k} $ - space（傅立叶空间）的丢失部分与$ k_1 $或$ k_2 $平行（即$ \ textbf {k} $ - 太空轴）平行于1-D型Fredholm typerverse iNFERVERSERVERSE。然后求解弗雷德霍尔姆方程以恢复1-D线概况上的2-D图像（````s s lice by-slice''成像）。该技术在体内图像的一系列医疗图像（例如，大脑，脊柱，心脏，心脏，心脏，心脏）和幻影数据上进行测试。在结构相似的情况下，在结构相似的方法中，在结构相似的方法中，在结构相似的方法上进行了测试。 $ \ textbf {k} $ - 空间数据是随机的子采样，以模拟运动损坏。
We present novel reconstruction and stability analysis methodologies for two-dimensional, multi-coil MRI, based on analytic continuation ideas. We show that the 2-D, limited-data MRI inverse problem, whereby the missing parts of $\textbf{k}$-space (Fourier space) are lines parallel to either $k_1$ or $k_2$ (i.e., the $\textbf{k}$-space axis), can be reduced to a set of 1-D Fredholm type inverse problems. The Fredholm equations are then solved to recover the 2-D image on 1-D line profiles (``slice-by-slice" imaging). The technique is tested on a range of medical in vivo images (e.g., brain, spine, cardiac), and phantom data. Our method is shown to offer optimal performance, in terms of structural similarity, when compared against similar methods from the literature, and when the $\textbf{k}$-space data is sub-sampled at random so as to simulate motion corruption. In addition, we present a Singular Value Decomposition (SVD) and stability analysis of the Fredholm operators, and compare the stability properties of different $\textbf{k}$-space sub-sampling schemes (e.g., random vs uniform accelerated sampling).
