scholarly journals Using generalized cross validation to select regularization parameter for total variation regularization problems

2018 ◽  
Vol 12 (5) ◽  
pp. 1103-1120 ◽  
Author(s):  
You-Wei Wen ◽  
◽  
Raymond Honfu Chan ◽  
Keyword(s):  
Total Variation ◽  
Cross Validation ◽  
Regularization Parameter ◽  
Total Variation Regularization ◽  
Generalized Cross Validation

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.

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