scholarly journals A novel Fourier-based deconvolution algorithm with improved efficiency and convergence

2019 ◽  
Vol 39 (4) ◽  
pp. 866-878
Author(s):  
Linbang Shen ◽  
Zhigang Chu ◽  
Yongxiang Zhang ◽  
Yang Yang
Keyword(s):  
Computational Efficiency ◽  
Weight Coefficient ◽  
Identification Performance ◽  
Acoustic Source ◽  
Good Convergence ◽  
Solution Convergence ◽  
Iterative Shrinkage ◽  
Acoustic Identification ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

Various deconvolution algorithms for acoustic source are developed to improve spatial resolution and suppress sidelobe of the conventional beamforming. To improve the computational efficiency and solution convergence of deconvolution, this paper proposes a Fourier-based improved fast iterative shrinkage thresholding algorithm. Simulations and experiments show that Fourier-based improved fast iterative shrinkage thresholding algorithm can achieve excellent acoustic identification performance, with high computational efficiency and good convergence. For Fourier-based improved fast iterative shrinkage thresholding algorithm, the larger the weight coefficient, the narrower the mainlobe width, and the better the convergence, but the spurious source also increases. The recommended weight coefficient for the array described herein is 3. In addition, like other Fourier-based deconvolution algorithms, Fourier-based improved fast iterative shrinkage thresholding algorithm using irregular focus grid can obtain better acoustic source identification performance than using the conventional regular focus grid.

scholarly journals Improving the Sound Source Identification Performance of Sparsity Constrained Deconvolution Beamforming Utilizing SFISTA

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Linbang Shen ◽  
Zhigang Chu ◽  
Long Tan ◽  
Debing Chen ◽  
Fangbiao Ye
Keyword(s):  
Sound Source ◽  
Source Identification ◽  
Theoretical Background ◽  
Identification Performance ◽  
Sound Source Identification ◽  
Iterative Shrinkage ◽  
Quantification Accuracy ◽  
Smoothing Parameters ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

In this paper, an alternative sparsity constrained deconvolution beamforming utilizing the smoothing fast iterative shrinkage-thresholding algorithm (SFISTA) is proposed for sound source identification. Theoretical background and solving procedures are introduced. The influence of SFISTA regularization and smoothing parameters on the sound source identification performance is analyzed, and the recommended values of the parameters are obtained for the presented cases. Compared with the sparsity constrained deconvolution approach for the mapping of acoustic sources (SC-DAMAS) and the fast iterative shrinkage-thresholding algorithm (FISTA), the proposed SFISTA with appropriate regularization and smoothing parameters has faster convergence speed, higher quantification accuracy and computational efficiency, and more insensitivity to measurement noise.

Accelerated 3D blind separation of convolved mixtures based on the fast iterative shrinkage thresholding algorithm for adaptive multiple subtraction

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. V99-V113 ◽  
Author(s):  
Zhong-Xiao Li ◽  
Zhen-Chun Li
Keyword(s):  
Field Data ◽  
Optimization Problem ◽  
Computational Cost ◽  
Computation Time ◽  
Blind Separation ◽  
L1 Norm ◽  
Norm Minimization ◽  
Iterative Shrinkage ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

After multiple prediction, adaptive multiple subtraction is essential for the success of multiple removal. The 3D blind separation of convolved mixtures (3D BSCM) method, which is effective in conducting adaptive multiple subtraction, needs to solve an optimization problem containing L1-norm minimization constraints on primaries by the iterative reweighted least-squares (IRLS) algorithm. The 3D BSCM method can better separate primaries and multiples than the 1D/2D BSCM method and the method with energy minimization constraints on primaries. However, the 3D BSCM method has high computational cost because the IRLS algorithm achieves nonquadratic optimization with an LS optimization problem solved in each iteration. In general, it is good to have a faster 3D BSCM method. To improve the adaptability of field data processing, the fast iterative shrinkage thresholding algorithm (FISTA) is introduced into the 3D BSCM method. The proximity operator of FISTA can solve the L1-norm minimization problem efficiently. We demonstrate that our FISTA-based 3D BSCM method achieves similar accuracy of estimating primaries as that of the reference IRLS-based 3D BSCM method. Furthermore, our FISTA-based 3D BSCM method reduces computation time by approximately 60% compared with the reference IRLS-based 3D BSCM method in the synthetic and field data examples.

scholarly journals Fast Algorithms for the Anisotropic LLT Model in Image Denoising

2011 ◽  
Vol 1 (3) ◽  
pp. 264-283 ◽  
Author(s):  
Zhi-Feng Pang ◽  
Li-Lian Wang ◽  
Yu-Fei Yang
Keyword(s):  
Convergence Rate ◽  
Image Denoising ◽  
Projection Method ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Minimization Problems ◽  
Iterative Shrinkage ◽  
Speed Up ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

AbstractIn this paper, we propose a new projection method for solving a general minimization problems with twoL1-regularization terms for image denoising. It is related to the split Bregman method, but it avoids solving PDEs in the iteration. We employ the fast iterative shrinkage-thresholding algorithm (FISTA) to speed up the proposed method to a convergence rateO(k−2). We also show the convergence of the algorithms. Finally, we apply the methods to the anisotropic Lysaker, Lundervold and Tai (LLT) model and demonstrate their efficiency.

scholarly journals A Sparse Spike Deconvolution Algorithm Based on a Recurrent Neural Network and the Iterative Shrinkage-Thresholding Algorithm

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3074 ◽  
Author(s):  
Shulin Pan ◽  
Ke Yan ◽  
Haiqiang Lan ◽  
José Badal ◽  
Ziyu Qin
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Seismic Data ◽  
Real Data ◽  
Training Dataset ◽  
Reflection Coefficients ◽  
Deconvolution Algorithm ◽  
Iterative Shrinkage ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

Conventional sparse spike deconvolution algorithms that are based on the iterative shrinkage-thresholding algorithm (ISTA) are widely used. The aim of this type of algorithm is to obtain accurate seismic wavelets. When this is not fulfilled, the processing stops being optimum. Using a recurrent neural network (RNN) as deep learning method and applying backpropagation to ISTA, we have developed an RNN-like ISTA as an alternative sparse spike deconvolution algorithm. The algorithm is tested with both synthetic and real seismic data. The algorithm first builds a training dataset from existing well-logs seismic data and then extracts wavelets from those seismic data for further processing. Based on the extracted wavelets, the new method uses ISTA to calculate the reflection coefficients. Next, inspired by the backpropagation through time (BPTT) algorithm, backward error correction is performed on the wavelets while using the errors between the calculated reflection coefficients and the reflection coefficients corresponding to the training dataset. Finally, after performing backward correction over multiple iterations, a set of acceptable seismic wavelets is obtained, which is then used to deduce the sequence of reflection coefficients of the real data. The new algorithm improves the accuracy of the deconvolution results by reducing the effect of wrong seismic wavelets that are given by conventional ISTA. In this study, we account for the mechanism and the derivation of the proposed algorithm, and verify its effectiveness through experimentation using theoretical and real data.

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