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.

Feature Extraction Techniques for Airborne Hyperspectral Images – Implication for Mineral Exploration

2021 ◽  
Author(s):  
Rupsa Chakraborty ◽  
Gabor Kereszturi ◽  
Reddy Pullanagari ◽  
Patricia Durance ◽  
Salman Ashraf ◽  
...  
Keyword(s):  
Feature Extraction ◽  
Total Variation ◽  
Spatial Resolution ◽  
Hyperspectral Data ◽  
Hyperspectral Images ◽  
Total Variation Regularization ◽  
Elemental Distribution ◽  
Ground Truth Data ◽  
Resolution Data ◽  
Mineral Prospecting

<p>Geochemical mineral prospecting approaches are mostly point-based surveys which then rely on statistical spatial extrapolation methods to cover larger areas of interest. This leads to a trade-off between increasing sampling density and associated attributes (e.g., elemental distribution). Airborne hyperspectral data is typically high-resolution data, whilst being spatially continuous, and spectrally contiguous, providing a versatile baseline to complement ground-based prospecting approaches and monitoring. In this study, we benchmark various shallow and deep feature extraction algorithms, on airborne hyperspectral data at three different spatial resolutions, 0.8 m, 2 m and 3 m. Spatial resolution is a key factor to detailed scale-dependent mineral prospecting and geological mapping. Airborne hyperspectral data has potential to advance our understanding for delineating new mineral deposits. This approach can be further extended to large areas using forthcoming spaceborne hyperspectral platforms, where procuring finer spatial resolution data is highly challenging. The study area is located along the Rise and Shine Shear Zone (RSSZ) within the Otago schist, in the South Island (New Zealand). The RSSZ contains gold and associated hydrothermal sulphides and carbonate minerals that are disseminated through sheared upper green schist facies rocks on the 10-metre scale, as well as localized (metre-scale) quartz-rich zones. Soil and rock samples from 63 locations were collected, scattered around known mineralised and unmineralized zones, providing ground truth data for benchmarking. The separability between the mineralized and the non-mineralised samples through laboratory based spectral datasets was analysed by applying Partial least squares discriminant analysis (PLS-DA) on the XRF spectra and laboratory based hyperspectral data separately. The preliminary results indicate that even in partially vegetated zones mineralised regions can be mapped out relatively accurately from airborne hyperspectral images using orthogonal total variation component analysis (OTVCA). This focuses on feature extraction by optimising a cost function that best fits the hyperspectral data in a lower dimensional feature space while monitoring the spatial smoothness of the features by applying total variation regularization.</p>

Iterative image reconstruction for sparse-view CT via total variation regularization and dictionary learning

2019 ◽  
Vol 27 (3) ◽  
pp. 573-590
Author(s):  
Xianyu Zhao ◽  
Changhui Jiang ◽  
Qiyang Zhang ◽  
Yongshuai Ge ◽  
Dong Liang ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Total Variation ◽  
Dictionary Learning ◽  
Total Variation Regularization ◽  
Iterative Image Reconstruction

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

scholarly journals Unsupervised deep learning with higher-order total-variation regularization for multidimensional seismic data reconstruction

Geophysics ◽  
2021 ◽  
pp. 1-62
Author(s):  
Thomas André Larsen Greiner ◽  
Jan Erik Lie ◽  
Odd Kolbjørnsen ◽  
Andreas Kjelsrud Evensen ◽  
Espen Harris Nilsen ◽  
...  
Keyword(s):  
Deep Learning ◽  
Total Variation ◽  
Field Data ◽  
Barents Sea ◽  
Broad Band ◽  
Total Variation Regularization ◽  
Data Set ◽  
L2 Norm ◽  
Unsupervised Deep Learning ◽  
Seismic Wavefield

In 3D marine seismic acquisition, the seismic wavefield is not sampled uniformly in the spatial directions. This leads to a seismic wavefield consisting of irregularly and sparsely populated traces with large gaps between consecutive sail-lines especially in the near-offsets. The problem of reconstructing the complete seismic wavefield from a subsampled and incomplete wavefield, is formulated as an underdetermined inverse problem. We investigate unsupervised deep learning based on a convolutional neural network (CNN) for multidimensional wavefield reconstruction of irregularly populated traces defined on a regular grid. The proposed network is based on an encoder-decoder architecture with an overcomplete latent representation, including appropriate regularization penalties to stabilize the solution. We proposed a combination of penalties, which consists of the L2-norm penalty on the network parameters, and a first- and second-order total-variation (TV) penalty on the model. We demonstrate the performance of the proposed method on broad-band synthetic data, and field data represented by constant-offset gathers from a source-over-cable data set from the Barents Sea. In the field data example we compare the results to a full production flow from a contractor company, which is based on a 5D Fourier interpolation approach. In this example, our approach displays improved reconstruction of the wavefield with less noise in the sparse near-offsets compared to the industry approach, which leads to improved structural definition of the near offsets in the migrated sections.

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 A Multiscale Hierarchical Model for Sparse Hyperspectral Unmixing

2019 ◽  
Vol 11 (5) ◽  
pp. 500 ◽  
Author(s):  
Jinlin Zou ◽  
Jinhui Lan
Keyword(s):  
Hierarchical Model ◽  
Computational Cost ◽  
Optimal Solution ◽  
Hyperspectral Data ◽  
Computational Time ◽  
Total Variation Regularization ◽  
Endmember Extraction ◽  
Mixed Pixel ◽  
Hyperspectral Unmixing ◽  
Original Domain

Due to the complex background and low spatial resolution of the hyperspectral sensor, observed ground reflectance is often mixed at the pixel level. Hyperspectral unmixing (HU) is a hot-issue in the remote sensing area because it can decompose the observed mixed pixel reflectance. Traditional sparse hyperspectral unmixing often leads to an ill-posed inverse problem, which can be circumvented by spatial regularization approaches. However, their adoption has come at the expense of a massive increase in computational cost. In this paper, a novel multiscale hierarchical model for a method of sparse hyperspectral unmixing is proposed. The paper decomposes HU into two domain problems, one is in an approximation scale representation based on resampling the method’s domain, and the other is in the original domain. The use of multiscale spatial resampling methods for HU leads to an effective strategy that deals with spectral variability and computational cost. Furthermore, the hierarchical strategy with abundant sparsity representation in each layer aims to obtain the global optimal solution. Both simulations and real hyperspectral data experiments show that the proposed method outperforms previous methods in endmember extraction and abundance fraction estimation, and promotes piecewise homogeneity in the estimated abundance without compromising sharp discontinuities among neighboring pixels. Additionally, compared with total variation regularization, the proposed method reduces the computational time effectively.

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