scholarly journals Atmospheric Inverse Modeling via Sparse Reconstruction

2016 ◽  
Author(s):  
Nils Hase ◽  
Scot M. Miller ◽  
Peter Maaß ◽  
Justus Notholt ◽  
Mathias Palm ◽  
...  
Keyword(s):  
Inverse Problems ◽  
Inverse Modeling ◽  
Hot Spots ◽  
Atmospheric Science ◽  
Methane Emissions ◽  
Point Sources ◽  
Sparse Reconstruction ◽  
Atmospheric Measurements ◽  
Localized Structures ◽  
Ill Posed

Abstract. Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill-equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied math and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well, but adds details on the grid scale. This can be of great value in many research projects. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

scholarly journals Atmospheric inverse modeling via sparse reconstruction

2017 ◽  
Vol 10 (10) ◽  
pp. 3695-3713 ◽  
Author(s):  
Nils Hase ◽  
Scot M. Miller ◽  
Peter Maaß ◽  
Justus Notholt ◽  
Mathias Palm ◽  
...  
Keyword(s):  
Inverse Problems ◽  
Inverse Modeling ◽  
Hot Spots ◽  
Applied Mathematics ◽  
Atmospheric Science ◽  
Point Sources ◽  
Sparse Reconstruction ◽  
Atmospheric Measurements ◽  
Localized Structures ◽  
Ill Posed

Abstract. Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Methods of solving ill-posed inverse problems

1983 ◽  
Vol 45 (5) ◽  
pp. 1237-1245 ◽  
Author(s):  
O. M. Alifanov
Keyword(s):  
Inverse Problems ◽  
Ill Posed

Rewetting of Cutaway Peatlands: Are We Re-Creating Hot Spots of Methane Emissions?

2009 ◽  
Vol 17 (6) ◽  
pp. 796-806 ◽  
Author(s):  
David Wilson ◽  
Jukka Alm ◽  
Jukka Laine ◽  
Kenneth A. Byrne ◽  
Edward P. Farrell ◽  
...  
Keyword(s):  
Hot Spots ◽  
Methane Emissions

Regularization of Some One-Dimensional Inverse Problems for Identification of Nonlinear Surface Phenomena

1995 ◽  
Author(s):  
C. W. Groetsch ◽  
Martin Hanke
Keyword(s):  
Inverse Problems ◽  
Model Identification ◽  
Surface Phenomena ◽  
Unbounded Operators ◽  
General Technique ◽  
Regularization Technique ◽  
One Dimensional ◽  
Data Errors ◽  
Ill Posed ◽  
Nonlinear Surface

Abstract A simple numerical method for some one-dimensional inverse problems of model identification type arising in nonlinear heat transfer is discussed. The essence of the method is to express the nonlinearity in terms of an integro-differential operator, the values of which are approximated by a linear spline technique. The inverse problems are mildly ill-posed and therefore call for regularization when data errors are present. A general technique for stabilization of unbounded operators may be applied to regularize the process and a specific regularization technique is illustrated on a model problem.

Hierarchical and Multi-resolution Neuron Network Computing for Complex Inverse Problems-An Approach Based on Brain-inspired Computing and Learning Method

2021 ◽  
Vol 01 ◽  
Author(s):  
Mingyong Zhou
Keyword(s):  
Deep Learning ◽  
Inverse Problems ◽  
Radar Imaging ◽  
Network Computing ◽  
Neuron Network ◽  
Impedance Tomography ◽  
General Complex ◽  
Mathematical Algorithms ◽  
Ill Posed ◽  
Regular Operators

Background: Complex inverse problems such as Radar Imaging and CT/EIT imaging are well investigated in mathematical algorithms with various regularization methods. However it is difficult to obtain stable inverse solutions with fast convergence and high accuracy at the same time due to the ill-posed property and non-linear property. Objective: In this paper, we propose a hierarchical and multi-resolution scalable method from both algorithm perspective and hardware perspective to achieve fast and accurate solu-tions for inverse problems by taking radar and EIT imaging as examples. Method: We present an extension of discussion on neuromorphic computing as brain-inspired computing method and the learning/training algorithm to design a series of problem specific AI “brains” (with different memristive values) to solve a general complex ill-posed inverse problems that are traditionally solved by mathematical regular operators. We design a hierarchical and multi-resolution scalable method and an algorithm framework to train AI deep learning neuron network and map into the memristive circuit so that the memristive val-ues are optimally obtained. We propose FPGA as an emulation implementation for neuro-morphic circuit as well. Result: We compared the methodology between our approach and traditional regulariza-tion method. In particular we use Electrical Impedance Tomography (EIT) and Radar imaging as typical examples to compare how to design an AI deep learning neuron network architec-tures to solve inverse problems. Conclusion: With EIT imaging as a typical example, we show that any moderate complex inverse problem, as long as it can be described as combinational problem, AI deep learning neuron network is a practical alternative approach to try to solve the inverse problems with any given expected resolution accuracy, as long as the neuron network width is large enough and computational power is strong enough for all combination samples training purpose.

scholarly journals The Regularized Weak Functional Matching Pursuit for linear inverse problems

2019 ◽  
Vol 27 (3) ◽  
pp. 317-340 ◽  
Author(s):  
Max Kontak ◽  
Volker Michel
Keyword(s):  
Inverse Problems ◽  
Matching Pursuit ◽  
A Priori ◽  
Computation Time ◽  
Point Of View ◽  
Computational Point ◽  
Linear Inverse Problems ◽  
Infinite Dimensional ◽  
Frame Condition ◽  
Ill Posed

Abstract In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90  of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

scholarly journals Optimization Learning: Perspective, Method, and Applications

2020 ◽  
Author(s):  
Risheng Liu
Keyword(s):  
Inverse Problems ◽  
Theoretical Analysis ◽  
Iterative Methods ◽  
State Of The Art ◽  
Learning Paradigm ◽  
Rigorous Analysis ◽  
The Core ◽  
Globally Convergent ◽  
Ill Posed ◽  
Art Performance

Numerous tasks at the core of statistics, learning, and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is still a laborious process, which can only be guided by intuitions or empirical insights. Moreover, there is a lack of rigorous analysis of the convergence behaviors of these reimplemented iterations, and thus the significance of such methods is a little bit vague. We move beyond these limits and propose a theoretically guaranteed optimization learning paradigm, a generic and provable paradigm for nonconvex inverse problems, and develop a series of convergent deep models. Our theoretical analysis reveals that the proposed optimization learning paradigm allows us to generate globally convergent trajectories for learning-based iterative methods. Thanks to the superiority of our framework, we achieve state-of-the-art performance on different real applications.

scholarly journals Quantifying methane point sources from fine-scale (GHGSat) satellite observations of atmospheric methane plumes

2018 ◽  
Author(s):  
Daniel J. Varon ◽  
Daniel J. Jacob ◽  
Jason McKeever ◽  
Dylan Jervis ◽  
Berke O. A. Durak ◽  
...  
Keyword(s):  
Wind Speed ◽  
Methane Emissions ◽  
Point Sources ◽  
Small Scale ◽  
Atmospheric Methane ◽  
Flux Method ◽  
Pixel Resolution ◽  
Cross Sectional ◽  
Source Rate ◽  
The Cross

Abstract. Anthropogenic methane emissions originate from a large number of relatively small point sources. The planned GHGSat satellite fleet aims to quantify emissions from individual point sources by measuring methane column plumes over selected ~ 10 × 10 km2 domains with ≤ 50 × 50 m2 pixel resolution and 1–5 % measurement precision. Here we develop algorithms for retrieving point source rates from such measurements. We simulate a large ensemble of instantaneous methane column plumes at 50 × 50 m2 pixel resolution for a range of atmospheric conditions using the Weather Research and Forecasting model (WRF) in large eddy simulation (LES) mode and adding instrument noise. We show that standard methods to infer source rates by Gaussian plume inversion or source pixel mass balance are prone to large errors because the turbulence cannot be properly parameterized on the small scale of instantaneous methane plumes. The integrated mass enhancement (IME) method, which relates total plume mass to source rate, and the cross-sectional flux method, which infers source rate from fluxes across plume transects, are better adapted to the problem. We show that the IME method with local measurements of the 10-m wind speed can infer source rates with error of 0.07–0.17 t h−1 + 5–12 % depending on instrument precision (1–5 %). The cross-sectional flux method has slightly larger errors (0.07–0.26 t h−1 + 8–12 %) but a simpler physical basis. For comparison, point sources larger than 0.5 t h−1 contribute more than 75 % of methane emissions reported to the U.S. Greenhouse Gas Reporting Program. Additional error applies if local wind speed measurements are not available, and may dominate the overall error at low wind speeds. Low winds are beneficial for source detection but not for source quantification.

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