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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Optimization of the autocorrelation weighting function for the time-domain calculation of spectral centroids
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Optimization of the autocorrelation weighting function for the time-domain calculation of spectral centroids

机译：频谱质心时域计算的自相关加权函数的优化

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摘要

Spectral centroid from the backscattered ultrasound provides important information about the attenuation properties of soft tissues and Doppler effects of blood flows. Because the spectral centroid is originally determined from the power spectrum of backscattered ultrasound signals in the frequency domain, it is natural to calculate it after converting time-domain signals into spectral domain signals, using the fast Fourier transform (FFT). Recent research, however, derived the time-domain equations for calculating the spectral centroid using a Parseval's theorem, to avoid the calculation of the Fourier transform. The work only presented the final result, which showed that the computational time of the proposed time-domain method was 4.4 times faster than that of the original FFT-based method, whereas the average estimation error was negligible. In this paper, we present the optimal design of the autocorrelation weighting function, which is used for the timedomain spectral centroid estimation process, to reduce the computational time significantly. We also carry out a comprehensive analysis of the computational complexities of the FFTbased and time-domain methods with respect to the length of ultrasound signal segments. The simulation results using numerical phantoms show that, with the optimized autocorrelation weighting function, we only need approximately 3% of the full set of data points. In addition to that, because the proposed optimization technique requires a fixed number of data points to calculate the spectral centroid, the execution time is constant as the length of the data segment increases, whereas the execution time of the conventional FFT-based method is increased. Analysis of the computational complexities between the proposed method and the conventional FFT-based method presents O(N) and O(NlogN), respectively.
机译：来自反向散射超声的光谱质心提供了有关软组织的衰减特性和血流的多普勒效应的重要信息。由于频谱质心最初是由频域中的反向散射超声信号的功率谱确定的，因此在使用快速傅立叶变换（FFT）将时域信号转换为频谱域信号之后，自然会对其进行计算。但是，最近的研究推导了使用Parseval定理来计算频谱质心的时域方程，从而避免了傅立叶变换的计算。这项工作仅给出了最终结果，表明所提出的时域方法的计算时间比原始的基于FFT的方法快4.4倍，而平均估计误差却可以忽略不计。在本文中，我们提出了用于时域频谱质心估计过程的自相关加权函数的优化设计，以显着减少计算时间。我们还针对超声波信号段的长度对基于FFT的方法和时域方法的计算复杂性进行了全面分析。使用数字体模的仿真结果表明，利用优化的自相关加权函数，我们只需要约3％的数据集。除此之外，由于建议的优化技术需要固定数量的数据点来计算频谱质心，因此执行时间随着数据段长度的增加而恒定，而传统基于FFT的方法的执行时间却增加了。分析所提出的方法与传统的基于FFT的方法之间的计算复杂性，分别给出O（N）和O（NlogN）。

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