scholarly journals Construction model for total variation regularization parameter

2014 ◽  
Vol 22 (9) ◽  
pp. 10500 ◽  
Author(s):  
Guanghua Gong ◽  
Hongming Zhang ◽  
Minyu Yao
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Total Variation Regularization ◽  
Construction Model

Total variation regularization for depth-to-basement estimate: Part 2 — Physicogeologic meaning and comparisons with previous inversion methods

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. I13-I20 ◽  
Author(s):  
Williams A. Lima ◽  
Cristiano M. Martins ◽  
João B. Silva ◽  
Valeria C. Barbosa
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Total Variation Regularization ◽  
Discontinuous Solutions ◽  
Mathematical Basis ◽  
Inversion Methods ◽  
Tv Regularization ◽  
Entropic Regularization

We applied the mathematical basis of the total variation (TV) regularization to analyze the physicogeologic meaning of the TV method and compared it with previous gravity inversion methods (weighted smoothness and entropic Regularization) to estimate discontinuous basements. In the second part, we analyze the physicogeologic meaning of the TV method and compare it with previous gravity inversion methods (weighted smoothness and entropic regularization) to estimate discontinuous basements. Presenting a mathematical review of these methods, we show that minimizing the TV stabilizing function favors discontinuous solutions because a smooth solution, to honor the data, must oscillate, and the presence of these oscillations increases the value of the TV stabilizing function. These three methods are applied to synthetic data produced by a simulated 2D graben bordered by step faults. TV regularization and weighted smoothness are also applied to the real anomaly of Steptoe Valley, Nevada, U.S.A. In all applications, the three methods perform similarly. TV regularization, however, has the advantage, compared with weighted smoothness, of requiring no a priori information about the maximum depth of the basin. As compared with entropic regularization, TV regularization is much simpler to use because it requires, in general, the tuning of just one regularization parameter.

scholarly journals Sub-Pixel Mapping Model Based on Total Variation Regularization and Learned Spatial Dictionary

2021 ◽  
Vol 13 (2) ◽  
pp. 190
Author(s):  
Bouthayna Msellmi ◽  
Daniele Picone ◽  
Zouhaier Ben Rabah ◽  
Mauro Dalla Mura ◽  
Imed Riadh Farah
Keyword(s):  
Total Variation ◽  
Dictionary Learning ◽  
Regularization Parameter ◽  
Spatial Localization ◽  
Hyperspectral Data ◽  
Total Variation Regularization ◽  
Data Set ◽  
Mixed Pixel ◽  
Pixel Mapping ◽  
Spatial Regularization

In this research study, we deal with remote sensing data analysis over high dimensional space formed by hyperspectral images. This task is generally complex due to the large spectral, spatial richness, and mixed pixels. Thus, several spectral un-mixing methods have been proposed to discriminate mixing spectra by estimating the classes and their presence rates. However, information related to mixed pixel composition is very interesting for some applications, but it is insufficient for many others. Thus, it is necessary to have much more data about the spatial localization of the classes detected during the spectral un-mixing process. To solve the above-mentioned problem and specify the spatial location of the different land cover classes in the mixed pixel, sub-pixel mapping techniques were introduced. This manuscript presents a novel sub-pixel mapping process relying on K-SVD (K-singular value decomposition) learning and total variation as a spatial regularization parameter (SMKSVD-TV: Sub-pixel Mapping based on K-SVD dictionary learning and Total Variation). The proposed approach adopts total variation as a spatial regularization parameter, to make edges smooth, and a pre-constructed spatial dictionary with the K-SVD dictionary training algorithm to have more spatial configurations at the sub-pixel level. It was tested and validated with three real hyperspectral data. The experimental results reveal that the attributes obtained by utilizing a learned spatial dictionary with isotropic total variation allowed improving the classes sub-pixel spatial localization, while taking into account pre-learned spatial patterns. It is also clear that the K-SVD dictionary learning algorithm can be applied to construct a spatial dictionary, particularly for each data set.

scholarly journals Multichannel Parallel Deblurring and Collaborative Registration Using Gaussian Total Variation Regularization for Image Fusion

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Shiping Guo ◽  
Hongqiang Lv ◽  
Yongyi Liu ◽  
Rongzhi Zhang ◽  
Jisheng Li
Keyword(s):  
Image Fusion ◽  
Total Variation ◽  
Regularization Parameter ◽  
Total Variation Regularization ◽  
Total Variation Norm ◽  
Hybrid Strategy ◽  
Gaussian Derivative ◽  
Mathematical Formalization ◽  
Degraded Images ◽  
Gaussian Operator

We focus on the multichannel image fusion problem for the purpose of reaching the diffraction-limited resolution of turbulence-degraded images observed by multiple acquisition channels. A hybrid strategy consisting of multichannel parallel deblurring followed by collaborative registration is developed for the final fusion. In particular, a Gaussian total variation regularization scheme taking advantage of low-order Gaussian derivative operators is proposed, which integrates the deblurring and registration problems into a unified mathematical formalization. Specifically, the gradient magnitude of Gaussian operator is proposed to define the total variation norm, and the Laplacian of Gaussian operator is used to adjust the regularization parameter when searching the extremum in each iterative step. In addition, the coordination technique involving the regularization parameter among different channels is also considered.

scholarly journals A Novel Image-Restoration Method Based on High-Order Total Variation Regularization Term

Electronics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 867 ◽  
Author(s):  
Jianhong Xiang ◽  
Pengfei Ye ◽  
Linyu Wang ◽  
Mingqi He
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Regularization Parameter ◽  
Signal To Noise Ratio ◽  
High Order ◽  
Computational Time ◽  
Total Variation Regularization ◽  
Selection Scheme ◽  
Staircase Effect ◽  
Restoration Method

This paper presents two new models for solving image the deblurring problem in the presence of impulse noise. One involves a high-order total variation (TV) regularizer term in the corrected total variation L1 (CTVL1) model and is named high-order corrected TVL1 (HOCTVL1). This new model can not only suppress the defects of the staircase effect, but also improve the quality of image restoration. In most cases, the regularization parameter in the model is a fixed value, which may influence processing results. Aiming at this problem, the spatially adapted regularization parameter selection scheme is involved in HOCTVL1 model, and spatially adapted HOCTVL1 (SAHOCTVL1) model is proposed. When dealing with corrupted images, the regularization parameter in SAHOCTVL1 model can be updated automatically. Many numerical experiments are conducted in this paper and the results show that the two models can significantly improve the effects both in visual quality and signal-to-noise ratio (SNR) at the expense of a small increase in computational time. Compared to HOCTVL1 model, SAHOCTVL1 model can restore more texture details, though it may take more time.

scholarly journals An Improved Particle Swarm Optimization Based on Total Variation Regularization and Projection Constraint with Applications in Ground-Penetrating Radar Inversion: A Model Simulation Study

2021 ◽  
Vol 13 (13) ◽  
pp. 2514
Author(s):  
Qianwei Dai ◽  
Hao Zhang ◽  
Bin Zhang
Keyword(s):  
Particle Swarm Optimization ◽  
Total Variation ◽  
Ground Penetrating Radar ◽  
Particle Swarm ◽  
Premature Convergence ◽  
Total Variation Regularization ◽  
Interface Model ◽  
Swarm Optimization ◽  
Tv Regularization ◽  
Ground Penetrating

The chaos oscillation particle swarm optimization (COPSO) algorithm is prone to binge trapped in the local optima when dealing with certain complex models in ground-penetrating radar (GPR) data inversion, because it inherently suffers from premature convergence, high computational costs, and extremely slow convergence times, especially in the middle and later periods of iterative inversion. Considering that the bilateral connections between different particle positions can improve both the algorithmic searching efficiency and the convergence performance, we first develop a fast single-trace-based approach to construct an initial model for 2-D PSO inversion and then propose a TV-regularization-based improved PSO (TVIPSO) algorithm that employs total variation (TV) regularization as a constraint technique to adaptively update the positions of particles. B by adding the new velocity variations and optimal step size matrices, the search range of the random particles in the solution space can be significantly reduced, meaning blindness in the search process can be avoided. By introducing constraint-oriented regularization to allow the optimization search to move out of the inaccurate region, the premature convergence and blurring problems can be mitigated to further guarantee the inversion accuracy and efficiency. We report on three inversion experiments involving multilayered, fluctuated terrain models and a typical complicated inner-interface model to demonstrate the performance of the proposed algorithm. The results of the fluctuated terrain model show that compared with the COPSO algorithm, the fitness error (MAE) of the TVIPSO algorithm is reduced from 2.3715 to 1.0921, while for the complicated inner-interface model the fitness error (MARE) of the TVIPSO algorithm is reduced from 1.9539 to 1.5674.

A new nonlinear reconstruction method based on total variation regularization of neutron penumbral imaging

2011 ◽  
Vol 82 (9) ◽  
pp. 093504 ◽  
Author(s):  
Weixin Qian ◽  
Shuangxi Qi ◽  
Wanli Wang ◽  
Jinming Cheng ◽  
Dongbing Liu
Keyword(s):  
Total Variation ◽  
Total Variation Regularization ◽  
Reconstruction Method ◽  
Penumbral Imaging
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