To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achiev...To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achieves high-quality AFM imaging via line-by-line corrections for each distorted profile along the fast axis.The key to this line-by-line correction is to accurately simulate the profile distortion of each scanning row.Therefore,a data preprocessing approach is first developed to roughly filter out most of the height data that impairs the accuracy of distortion modeling.This process is implemented through an internal double-screening mechanism.A line-fitting method is adopted to preliminarily screen out the obvious specimens.Lifting wavelet analysis is then carried out to identify the base parts that are mistakenly filtered out as specimens so as to preserve most of the base profiles and provide a good basis for further distortion modeling.Next,an iterative thresholding algorithm is developed to precisely simulate the profile distortion.By utilizing the roughly screened base profile,the optimal threshold,which is used to screen out the pure bases suitable for distortion modeling,is determined through iteration with a specified error rule.On this basis,the profile distortion is accurately modeled through line fitting on the finely screened base data,and the correction is implemented by subtracting the modeling result from the distorted profile.Finally,the effectiveness of the proposed method is verified through experiments and applications.展开更多
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
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
Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermin...Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.21933006.
文摘To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achieves high-quality AFM imaging via line-by-line corrections for each distorted profile along the fast axis.The key to this line-by-line correction is to accurately simulate the profile distortion of each scanning row.Therefore,a data preprocessing approach is first developed to roughly filter out most of the height data that impairs the accuracy of distortion modeling.This process is implemented through an internal double-screening mechanism.A line-fitting method is adopted to preliminarily screen out the obvious specimens.Lifting wavelet analysis is then carried out to identify the base parts that are mistakenly filtered out as specimens so as to preserve most of the base profiles and provide a good basis for further distortion modeling.Next,an iterative thresholding algorithm is developed to precisely simulate the profile distortion.By utilizing the roughly screened base profile,the optimal threshold,which is used to screen out the pure bases suitable for distortion modeling,is determined through iteration with a specified error rule.On this basis,the profile distortion is accurately modeled through line fitting on the finely screened base data,and the correction is implemented by subtracting the modeling result from the distorted profile.Finally,the effectiveness of the proposed method is verified through experiments and applications.
文摘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。
文摘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。
基金Supported by the National Natural Science Foundation ofChina(No.61271240)Jiangsu Province Natural Science Fund Project(No.BK2010077)Subject of Twelfth Five Years Plans in Jiangsu Second Normal University(No.417103)
文摘Matrix completion is the extension of compressed sensing.In compressed sensing,we solve the underdetermined equations using sparsity prior of the unknown signals.However,in matrix completion,we solve the underdetermined equations based on sparsity prior in singular values set of the unknown matrix,which also calls low-rank prior of the unknown matrix.This paper firstly introduces basic concept of matrix completion,analyses the matrix suitably used in matrix completion,and shows that such matrix should satisfy two conditions:low rank and incoherence property.Then the paper provides three reconstruction algorithms commonly used in matrix completion:singular value thresholding algorithm,singular value projection,and atomic decomposition for minimum rank approximation,puts forward their shortcoming to know the rank of original matrix.The Projected Gradient Descent based on Soft Thresholding(STPGD),proposed in this paper predicts the rank of unknown matrix using soft thresholding,and iteratives based on projected gradient descent,thus it could estimate the rank of unknown matrix exactly with low computational complexity,this is verified by numerical experiments.We also analyze the convergence and computational complexity of the STPGD algorithm,point out this algorithm is guaranteed to converge,and analyse the number of iterations needed to reach reconstruction error.Compared the computational complexity of the STPGD algorithm to other algorithms,we draw the conclusion that the STPGD algorithm not only reduces the computational complexity,but also improves the precision of the reconstruction solution.
