School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Iran.
Comput Biol Med. 2021 Sep;136:104653. doi: 10.1016/j.compbiomed.2021.104653. Epub 2021 Jul 17.
Modern medicine cannot ignore the significance of elastography in diagnosis and treatment plans. Despite improvements in accuracy and spatial resolution of elastograms, robustness against noise remains a neglected attribute. A method that can perform in a satisfactory manner under noisy conditions may prove useful for various elastography methods. Here, we propose a method based on eigenvalue decomposition (EVD). In this method, the estimated time delay is defined as the index of the maximum element in the eigenvector that corresponds to the minimum eigenvalue in the covariance matrix of the received signal. Moreover, the implementation of the least-squares (LS) solution and the lower-upper (LU) decomposition contributes to improving the speed of computation and the accuracy of the estimation under low signal-to-noise ratio (SNR) conditions. To assess the performance of the proposed algorithm, it is evaluated along with generalized cross-correlation (GCC) and EVD. The simulation results clearly confirm that the jitter variance achieved in the proposed algorithm outperforms GCC and EVD in the proximity of the Cramer-Rau lower band. Moreover, our algorithm provides satisfactory performance in terms of variance and bias against sub-sample delay at low SNRS. According to the experimental results, the calculated values of the elastographic signal-to-noise ratio (SNRe) and the elastographic contrast-to-noise ratio (CNRe) of the proposed algorithm were 16.7 and 20.09, respectively, clearly better than the values of the other two methods. Furthermore, the proposed algorithm offers less execution time (about 30% of GCC), with a computational complexity equal to GCC and better than EVD.
现代医学不能忽视弹性成像在诊断和治疗计划中的意义。尽管弹性图的准确性和空间分辨率有所提高，但抗噪稳健性仍然是一个被忽视的属性。一种能够在噪声条件下表现良好的方法可能对各种弹性成像方法都很有用。在这里，我们提出了一种基于特征值分解（EVD）的方法。在该方法中，估计的时间延迟被定义为对应于接收信号协方差矩阵中最小特征值的特征向量中最大元素的索引。此外，最小二乘（LS）解和上下（LU）分解的实现有助于提高计算速度和在低信噪比（SNR）条件下的估计精度。为了评估所提出算法的性能，将其与广义互相关（GCC）和 EVD 进行了评估。仿真结果清楚地证实，在所提出的算法中实现的抖动方差在接近克拉默-劳下限带的情况下优于 GCC 和 EVD。此外，我们的算法在低 SNR 下的亚采样延迟的方差和偏差方面具有令人满意的性能。根据实验结果，所提出算法的弹性信噪比（SNRe）和弹性对比噪声比（CNRe）的计算值分别为 16.7 和 20.09，明显优于其他两种方法的值。此外，所提出的算法的执行时间（约为 GCC 的 30%）更短，计算复杂度与 GCC 相同，优于 EVD。
