scholarly journals Performance Evaluation of Group Sparse Reconstruction and Total Variation Minimization for Target Imaging in Stratified Subsurface Media

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1245 ◽  
Author(s):  
Fauzia Ahmad ◽  
Ahmad Hoorfar ◽  
Wenji Zhang
Keyword(s):  
Total Variation ◽  
Sparse Reconstruction ◽  
L1 Norm ◽  
Total Variation Minimization ◽  
Electromagnetic Data ◽  
Norm Minimization ◽  
Reconstruction Methods ◽  
Reconstruction Performance ◽  
Target Imaging ◽  
Quantitative Performance

Sparse reconstruction methods have been successfully applied for efficient radar imaging of targets embedded in stratified dielectric subsurface media. Recently, a total variation minimization (TVM) based approach was shown to provide superior image reconstruction performance over standard L1-norm minimization-based method, especially in case of non-point-like targets. Alternatively, group sparse reconstruction (GSR) schemes can also be employed to account for embedded target extent. In this paper, we provide qualitative and quantitative performance evaluations of TVM and GSR schemes for efficient and reliable target imaging in stratified subsurface media. Using numerical electromagnetic data of targets buried in the ground, we demonstrate that GSR and TVM provide comparable reconstruction performance qualitatively, with GSR exhibiting a slight superiority over TVM quantitatively, albeit at the expense of less flexibility in regularization parameters.

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.

Magnetic inversion to recover the subsurface block structures based on L1 norm and total variation regularization

2021 ◽  
Author(s):  
Mitsuru Utsugi
Keyword(s):  
Total Variation ◽  
Magnetic Data ◽  
Preconditioned Conjugate Gradient ◽  
Inversion Method ◽  
Total Variation Regularization ◽  
Subsurface Structure ◽  
L1 Norm ◽  
Magnetic Inversion ◽  
Original Definition ◽  
Primal Dual

Summary This paper presents a new sparse inversion method based on L1 norm regularization for 3D magnetic data. In isolation, L1 norm regularization yields model elements which are unconstrained by the input data to be exactly zero, leading to a sparse model with compact and focused structure. Here, we complement the L1 norm with a penalty minimizing total variation, the L1 norm of the model gradients; it is expected that the sharp boundaries of the subsurface structure are not compromised by incorporating this penalty. Although this penalty is widely used in the geophysical inversion studies, it is often replaced by an alternative quadratic penalty to ease solution of the penalized inversion problem; in this study, the original definition of the total variation, i.e., form of the L1 norm of the model gradients, is used. To solve the problem with this combined penalty of L1 norm and total variation, this study introduces alternative direction method of multipliers (ADMM), which is a primal-dual optimization algorithm that solves convex penalized problems based on the optimization of an augmented Lagrange function. To improve the computational efficiency of the algorithm to make this method applicable to large-scale magnetic inverse problems, this study applies matrix compression using the wavelet transform and the preconditioned conjugate gradient method. The inversion method is applied to both synthetic tests and real data, the synthetic tests demonstrate that, when subsurface structure is blocky, it can be reproduced almost perfectly.

Group Sparsity Regularization Based Compressed Sensing MR Image Reconstruction

2014 ◽  
Vol 989-994 ◽  
pp. 3946-3951
Author(s):  
Xin Jin ◽  
Ming Feng Jiang ◽  
Jie Feng
Keyword(s):  
Compressed Sensing ◽  
Group Structure ◽  
Direct Method ◽  
Group Sparsity ◽  
Mr Image ◽  
Assignment Method ◽  
Group Assignment ◽  
Reconstruction Methods ◽  
Reconstruction Performance ◽  
Space Data

Exploiting the sparsity of MR signals, Compressed Sensing MR imaging (CS-MRI) is one of the most promising approaches to reconstruct a MR image with good quality from highly under-sampled k-space data. The group sparse method, which exploits additional sparse representation of the spatial group structure, can promote the overall sparsity degree, thereby leading to better reconstruction performance. In this work, an efficient superpixel/group assignment method, simple linear iterative clustering (SLIC), is incorporated to CS-MRI studies. A variable splitting strategy and classic alternating direct method is employed to solve the group sparse problem. The results indicate that the proposed method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction methods.

scholarly journals MPTV: Matching Pursuit-Based Total Variation Minimization for Image Deconvolution

2019 ◽  
Vol 28 (4) ◽  
pp. 1851-1865 ◽  
Author(s):  
Dong Gong ◽  
Mingkui Tan ◽  
Qinfeng Shi ◽  
Anton van den Hengel ◽  
Yanning Zhang
Keyword(s):  
Total Variation ◽  
Matching Pursuit ◽  
Image Deconvolution ◽  
Total Variation Minimization
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