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
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
Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-f...Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-forms,which leverage sparse coding(SC),have gained significant attention in the geosciences due to their ability to achieve high TF resolution.However,the iterative approaches typically employed in sparse TF transforms are computationally intensive,making them impractical for real seismic data analysis.To address this issue,we propose an interpretable convolutional sparse coding(CSC)network to achieve high TF resolution.The proposed model is generated based on the traditional short-time Fourier transform(STFT)transform and a modified UNet,named ULISTANet.In this design,we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm(LISTA)blocks,a specialized form of CSC.The LISTA block,which evolves from the traditional iterative shrinkage thresholding algorithm(ISTA),is optimized for extracting sparse features more effectively.Furthermore,we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet.Finally,the proposed method’s performance is subsequently validated using both synthetic and field data,demonstrating its potential for enhanced seismic data analysis.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.
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.
基金supported by the National Natural Science Foundation of China under Grant 42474139the Key Research and Development Program of Shaanxi under Grant 2024GX-YBXM-067.
文摘Seismic time-frequency(TF)transforms are essential tools in reservoir interpretation and signal processing,particularly for characterizing frequency variations in non-stationary seismic data.Recently,sparse TF trans-forms,which leverage sparse coding(SC),have gained significant attention in the geosciences due to their ability to achieve high TF resolution.However,the iterative approaches typically employed in sparse TF transforms are computationally intensive,making them impractical for real seismic data analysis.To address this issue,we propose an interpretable convolutional sparse coding(CSC)network to achieve high TF resolution.The proposed model is generated based on the traditional short-time Fourier transform(STFT)transform and a modified UNet,named ULISTANet.In this design,we replace the conventional convolutional layers of the UNet with learnable iterative shrinkage thresholding algorithm(LISTA)blocks,a specialized form of CSC.The LISTA block,which evolves from the traditional iterative shrinkage thresholding algorithm(ISTA),is optimized for extracting sparse features more effectively.Furthermore,we create a synthetic dataset featuring complex frequency-modulated signals to train ULISTANet.Finally,the proposed method’s performance is subsequently validated using both synthetic and field data,demonstrating its potential for enhanced seismic data analysis.
