scholarly journals A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

2014 ◽  
Vol 7 (4) ◽  
pp. 5623-5659 ◽  
Author(s):  
J. Ray ◽  
J. Lee ◽  
V. Yadav ◽  
S. Lefantzi ◽  
A. M. Michalak ◽  
...  
Keyword(s):  
Inverse Problems ◽  
Random Field ◽  
Matching Pursuit ◽  
Computational Cost ◽  
Sparse Reconstruction ◽  
Reconstruction Method ◽  
Flow Measurements ◽  
Linear Inverse Problems ◽  
Reconstruction Scheme ◽  
Atmospheric Inversion

Abstract. We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP to impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO2 (ffCO2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.

scholarly journals A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

2015 ◽  
Vol 8 (4) ◽  
pp. 1259-1273 ◽  
Author(s):  
J. Ray ◽  
J. Lee ◽  
V. Yadav ◽  
S. Lefantzi ◽  
A. M. Michalak ◽  
...  
Keyword(s):  
Field Model ◽  
Computational Cost ◽  
Estimation Method ◽  
Sparse Reconstruction ◽  
Model Parameters ◽  
Reconstruction Method ◽  
Reconstruction Procedure ◽  
Reconstruction Methods ◽  
Atmospheric Inversion ◽  
Atmospheric Inversions

Abstract. Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO2 (ffCO2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO2 emissions and synthetic observations of ffCO2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.

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 The Sparsity Adaptive Reconstruction Algorithm Based on Simulated Annealing for Compressed Sensing

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Yangyang Li ◽  
Jianping Zhang ◽  
Guiling Sun ◽  
Dongxue Lu
Keyword(s):  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Matching Pursuit ◽  
Optimal Solution ◽  
Sparse Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Adaptive Simulated Annealing ◽  
Annealing Algorithm ◽  
Adaptive Simulated Annealing Algorithm

This paper proposes a novel sparsity adaptive simulated annealing algorithm to solve the issue of sparse recovery. This algorithm combines the advantage of the sparsity adaptive matching pursuit (SAMP) algorithm and the simulated annealing method in global searching for the recovery of the sparse signal. First, we calculate the sparsity and the initial support collection as the initial search points of the proposed optimization algorithm by using the idea of SAMP. Then, we design a two-cycle reconstruction method to find the support sets efficiently and accurately by updating the optimization direction. Finally, we take advantage of the sparsity adaptive simulated annealing algorithm in global optimization to guide the sparse reconstruction. The proposed sparsity adaptive greedy pursuit model has a simple geometric structure, it can get the global optimal solution, and it is better than the greedy algorithm in terms of recovery quality. Our experimental results validate that the proposed algorithm outperforms existing state-of-the-art sparse reconstruction algorithms.

An Upwind-Biased Transport Scheme Using a Quadratic Reconstruction on Spherical Icosahedral Grids

2013 ◽  
Vol 141 (2) ◽  
pp. 832-847 ◽  
Author(s):  
Hiroaki Miura ◽  
William C. Skamarock
Keyword(s):  
Fourth Order ◽  
Piecewise Linear ◽  
Computational Cost ◽  
Second Order ◽  
Quadratic Approximation ◽  
Piecewise Linear Approximation ◽  
Reconstruction Method ◽  
Reconstruction Scheme ◽  
Order Reconstruction ◽  
Least Squares Fit

Abstract Several transport schemes developed for spherical icosahedral grids are based on the piecewise linear approximation. The simplest one among them uses an algorithm where the tracer distribution in the upwind side of a cell face is reconstructed using a linear surface. Recently, it was demonstrated that using second- or fourth-order reconstructions instead of the linear one produces better results. The computational cost of the second-order reconstruction method was not much larger than the linear one, while that of the fourth-order one was significantly larger. In this work, the authors propose another second-order reconstruction scheme on the spherical icosahedral grids, motivated by some ideas from the piecewise parabolic method. The second-order profile of a tracer is reconstructed under two constraints: (i) the area integral of the profile is equal to the cell-averaged value times the cell area and (ii) the profile is the least squares fit to the cell-vertex values. The new scheme [the second upwind-biased quadratic approximation (UQA-2)] is more accurate than the preceding second-order reconstruction scheme [the first upwind-biased quadratic approximation (UQA-1)] in most of the tests in this work. Solutions of UQA-2 are sharper than those of UQA-1, although with slightly larger phase errors. The computational cost of UQA-2 is comparable to UQA-1.

3D RECONSTRUCTION OF BREAST CANCER FROM MAMMOGRAMS USING VOLUME RENDERING TECHNIQUES

2015 ◽  
Vol 75 (2) ◽  
Author(s):  
Ho Wei Yong ◽  
Abdullah Bade ◽  
Rajesh Kumar Muniandy
Keyword(s):  
Breast Cancer ◽  
3D Reconstruction ◽  
Computational Cost ◽  
Reconstruction Method ◽  
Cancer Model ◽  
Volume Reconstruction ◽  
The Past ◽  
Breast Cancer Model ◽  
Reconstruction Software ◽  
To Come

Over the past thirty years, a number of researchers have investigated on 3D organ reconstruction from medical images and there are a few 3D reconstruction software available on the market. However, not many researcheshave focused on3D reconstruction of breast cancer’s tumours. Due to the method complexity, most 3D breast cancer’s tumours reconstruction were done based on MRI slices dataeven though mammogram is the current clinical practice for breast cancer screening. Therefore, this research will investigate the process of creating a method that will be able to reconstruct 3D breast cancer’s tumours from mammograms effectively.  Several steps were proposed for this research which includes data acquisition, volume reconstruction, andvolume rendering. The expected output from this research is the 3D breast cancer’s tumours model that is generated from correctly registered mammograms. The main purpose of this research is to come up with a 3D reconstruction method that can produce good breast cancer model from mammograms while using minimal computational cost.

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