Narayanan M V, King M A, Wernick M N, Byrne C L, Soares E J, Pretorius P H
University of Massachusetts Medical School, Worcester 01655, USA.
IEEE Trans Med Imaging. 2000 May;19(5):423-33. doi: 10.1109/42.870253.
Spatiotemporal reconstruction of cardiac-gated SPECT images permits us to obtain valuable information related to cardiac function. However, the task of reconstructing this four-dimensional (4-D) data set is computation intensive. Typically, these studies are reconstructed frame-by-frame: a nonoptimal approach because temporal correlations in the signal are not accounted for. In this work, we show that the compression and signal decorrelation properties of the Karhunen-Loève (KL) transform may be used to greatly simplify the spatiotemporal reconstruction problem. The gated projections are first KL transformed in the temporal direction. This results in a sequence of KL-transformed projection images for which the signal components are uncorrelated along the time axis. As a result, the 4-D reconstruction task is simplified to a series of three-dimensional (3-D) reconstructions in the KL domain. The reconstructed KL components are subsequently inverse KL transformed to obtain the entire spatiotemporal reconstruction set. Our simulation and clinical results indicate that KL processing provides image sequences that are less noisy than are conventional frame-by-frame reconstructions. Additionally, by discarding high-order KL components that are dominated by noise, we can achieve savings in computation time because fewer reconstructions are needed in comparison to conventional frame-by-frame reconstructions.
心脏门控单光子发射计算机断层扫描（SPECT）图像的时空重建使我们能够获取与心脏功能相关的有价值信息。然而，重建这个四维（4-D）数据集的任务计算量很大。通常，这些研究是逐帧重建的：这是一种非最优方法，因为没有考虑信号中的时间相关性。在这项工作中，我们表明，卡尔胡宁 - 勒夫（KL）变换的压缩和信号去相关特性可用于大大简化时空重建问题。首先在时间方向上对门控投影进行KL变换。这会产生一系列KL变换后的投影图像，其信号分量沿时间轴不相关。结果，4-D重建任务简化为在KL域中的一系列三维（3-D）重建。随后对重建的KL分量进行KL逆变换以获得整个时空重建集。我们的模拟和临床结果表明，KL处理提供的图像序列比传统的逐帧重建噪声更少。此外，通过丢弃由噪声主导的高阶KL分量，与传统的逐帧重建相比，由于需要的重建次数更少，我们可以节省计算时间。
