基于快速傅里叶变换的快速迭代收缩阈值算法(fast iterative shrinkage threshold algorithm based on fast Fourier transform, FFT-FISTA)具有较高的计算效率,但其忽略点扩散函数的空间变化及卷绕误差,造成声源识别性能的损失,为此提...基于快速傅里叶变换的快速迭代收缩阈值算法(fast iterative shrinkage threshold algorithm based on fast Fourier transform, FFT-FISTA)具有较高的计算效率,但其忽略点扩散函数的空间变化及卷绕误差,造成声源识别性能的损失,为此提出基于函数波束形成的改进FFT-FISTA算法。改进算法以函数波束形成输出作为FFT-FISTA算法的迭代输入,建立函数波束形成、声源分布及升幂空间转移不变点扩散函数的线性方程组,基于周期边界条件下的快速傅里叶变换进行迭代求解,使被运算的非周期函数变为一个周期函数,解决补零边界带来的波数泄漏问题,可提高运算准确性,进一步提升成像性能;通过指数运算锐化点扩散函数主瓣,拓展点扩散函数空间转移不变性假设的适用性。仿真和试验结果表明,相较于常规FFT-FISTA算法,改进算法能提升成像空间分辨率及动态范围,扩大FFT-FISTA算法的有效成像区域,压缩气体泄漏试验结果验证了改进算法的有效性。展开更多
Most existing parametric approaches for detecting linear or nonlinear Granger causality(GC)face challenges in estimating appropriate time delays,a critical factor for accurate GC detection.This issue becomes particula...Most existing parametric approaches for detecting linear or nonlinear Granger causality(GC)face challenges in estimating appropriate time delays,a critical factor for accurate GC detection.This issue becomes particularly pronounced in nonlinear complex systems,which are often opaque and consist of numerous components or variables.In this paper,we propose a novel temporal convolutional network(TCN)-based end-to-end GC detection approach called the interpretable temporal convolutional framework(ITCF).Unlike conventional deep learning models,which act like a“black box”and are difficult to analyse the interactions between variables,the proposed ITCF is able to detect both linear and nonlinear GC and automatically estimate time delay during the multivariant time series prediction.Specifically,GC is obtained by employing the least absolute shrinkage and selection operator(Lasso)regression during the prediction of multivariate time series using TCN.Then,time delays can be estimated by interpreting the TCN kernels.We propose a convolutional hierarchical group Lasso(cHGL),a hierarchical regularisation approach to effectively utilise temporal information within each TCN channel for enhanced GC detection.Additionally,as far as we are concerned,this paper is the first to integrate the Iterative Soft-Thresholding Algorithm into the backpropagation of TCN to optimise the proposed cHGL,which enables causal channel selection and induces sparsity within each TCN channel to remove redundant temporal information,ultimately creating an end-to-end GC detection framework.The testing results of four experiments,involving two simulations and two real data,demonstrate that the proposed ITCF,in comparison with state-ofthe-art,offers a more reliable estimation of GC relationships in complex systems featuring intricate dynamics,limited data lengths,or numerous variables.展开更多
为提高快速迭代收缩阈值算法(Fast Iterative Shrinkage-Thresholding Algorithm,FISTA)在反卷积波束形成中的空间分辨率以及计算速度,采用基于快速傅里叶变换的声学模型,引入过松弛方法和“贪婪”重启策略,提出两种改进的快速迭代收缩...为提高快速迭代收缩阈值算法(Fast Iterative Shrinkage-Thresholding Algorithm,FISTA)在反卷积波束形成中的空间分辨率以及计算速度,采用基于快速傅里叶变换的声学模型,引入过松弛方法和“贪婪”重启策略,提出两种改进的快速迭代收缩阈值算法,即基于快速傅里叶变换的过松弛单调快速迭代收缩阈值算法(Over-relaxed Monotone Fast Iterative Shrinkage-Thresholding Algorithm based on Fast Fourier Transform,FFT-OMFISTA)和基于快速傅里叶变换的“贪婪”快速迭代收缩阈值算法("Greedy"Fast Iterative Shrinkage-Thresholding Algorithm based on Fast Fourier Transform,FFT-GFISTA),并应用于反卷积波束形成的求解过程中。设计了单声源和双声源的仿真与实验,验证了所提算法的有效性与优越性。结果表明,两种所提算法都具有良好的性能,都能在声源定位中实现更高的空间分辨率以及更快的计算速度。展开更多
摘要基于快速傅里叶变换的快速迭代收缩阈值算法(fast iterative shrinkage threshold algorithm based on fast Fourier transform, FFT-FISTA)具有较高的计算效率,但其忽略点扩散函数的空间变化及卷绕误差,造成声源识别性能的损失,为此提出基于函数波束形成的改进FFT-FISTA算法。改进算法以函数波束形成输出作为FFT-FISTA算法的迭代输入,建立函数波束形成、声源分布及升幂空间转移不变点扩散函数的线性方程组,基于周期边界条件下的快速傅里叶变换进行迭代求解,使被运算的非周期函数变为一个周期函数,解决补零边界带来的波数泄漏问题,可提高运算准确性,进一步提升成像性能;通过指数运算锐化点扩散函数主瓣,拓展点扩散函数空间转移不变性假设的适用性。仿真和试验结果表明,相较于常规FFT-FISTA算法,改进算法能提升成像空间分辨率及动态范围,扩大FFT-FISTA算法的有效成像区域,压缩气体泄漏试验结果验证了改进算法的有效性。
摘要Most existing parametric approaches for detecting linear or nonlinear Granger causality(GC)face challenges in estimating appropriate time delays,a critical factor for accurate GC detection.This issue becomes particularly pronounced in nonlinear complex systems,which are often opaque and consist of numerous components or variables.In this paper,we propose a novel temporal convolutional network(TCN)-based end-to-end GC detection approach called the interpretable temporal convolutional framework(ITCF).Unlike conventional deep learning models,which act like a“black box”and are difficult to analyse the interactions between variables,the proposed ITCF is able to detect both linear and nonlinear GC and automatically estimate time delay during the multivariant time series prediction.Specifically,GC is obtained by employing the least absolute shrinkage and selection operator(Lasso)regression during the prediction of multivariate time series using TCN.Then,time delays can be estimated by interpreting the TCN kernels.We propose a convolutional hierarchical group Lasso(cHGL),a hierarchical regularisation approach to effectively utilise temporal information within each TCN channel for enhanced GC detection.Additionally,as far as we are concerned,this paper is the first to integrate the Iterative Soft-Thresholding Algorithm into the backpropagation of TCN to optimise the proposed cHGL,which enables causal channel selection and induces sparsity within each TCN channel to remove redundant temporal information,ultimately creating an end-to-end GC detection framework.The testing results of four experiments,involving two simulations and two real data,demonstrate that the proposed ITCF,in comparison with state-ofthe-art,offers a more reliable estimation of GC relationships in complex systems featuring intricate dynamics,limited data lengths,or numerous variables.
摘要为提高快速迭代收缩阈值算法(Fast Iterative Shrinkage-Thresholding Algorithm,FISTA)在反卷积波束形成中的空间分辨率以及计算速度,采用基于快速傅里叶变换的声学模型,引入过松弛方法和“贪婪”重启策略,提出两种改进的快速迭代收缩阈值算法,即基于快速傅里叶变换的过松弛单调快速迭代收缩阈值算法(Over-relaxed Monotone Fast Iterative Shrinkage-Thresholding Algorithm based on Fast Fourier Transform,FFT-OMFISTA)和基于快速傅里叶变换的“贪婪”快速迭代收缩阈值算法("Greedy"Fast Iterative Shrinkage-Thresholding Algorithm based on Fast Fourier Transform,FFT-GFISTA),并应用于反卷积波束形成的求解过程中。设计了单声源和双声源的仿真与实验,验证了所提算法的有效性与优越性。结果表明,两种所提算法都具有良好的性能,都能在声源定位中实现更高的空间分辨率以及更快的计算速度。