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Adaptive Grid Refinement for Discrete Tomography [chapter]

Tristan van Leeuwen, K. Joost Batenburg
2014 Lecture Notes in Computer Science  
Such locally refined grids match well with the domain of discrete tomography as they are optimally suited for representing images containing large homogeneous regions.  ...  The proposed approach can also be used in a non-adaptive manner for region-of-interest tomography.  ...  This work was supported by the Netherlands Organisation for Scientific Research (NWO), programme 639.072.005. Networking support was provided by the EXTREMA COST Action MP1207.  ... 
doi:10.1007/978-3-319-09955-2_25 fatcat:dl4wqxvrhrfppiqsyaop4bwqaq

Implementation of the radiative transfer equation on block-structured grids for modeling fluorescence light propagation in tissue with arbitrary shape

Ludguier D. Montejo, Alexander D. Klose, Andreas H. Hielscher, Bruce J. Tromberg, Arjun G. Yodh, Mamoru Tamura, Eva M. Sevick-Muraca, Robert R. Alfano
2009 Optical Tomography and Spectroscopy of Tissue VIII  
The natural ordering of this grid allows for simplified algorithms.  ...  We developed a method for solving the fluorescence equation of radiative transfer in the frequency domain on blockstructured grids.  ...  system for green fluorescent protein imaging).  ... 
doi:10.1117/12.810067 fatcat:immvflmkynhaldq33ryc7jdaqq

An Adaptive Multigrid method for modeling photon transport through biological tissues in bioluminescence tomography

Kai Liu, Jie Tian, Pu Wang, Dan Liu, Yujie Lv, Min Xu, Chenghu Qin
2008 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society  
In this paper, we develop an Adaptive Multigrid method (AMGM) to model photon transport through biological tissues in bioluminescence tomography.  ...  In our method, the smoothing operation on fine levels and residual correction on coarse levels in V-Cycle offer fast convergence rate for this forward problem.  ...  Secondly, tag the elements of the coarse grids for refinement where the local errors are large. Finally, according to the tags, grids are adaptively refined.  ... 
doi:10.1109/iembs.2008.4649190 pmid:19162693 fatcat:lyhkiuwajrerbghqq4cqjxge6u

Distributed tomography with adaptive mesh refinement in sensor networks

Wen Zhan Song, Goutham Kamath, Lei Shi, Edmond Chow
2017 International Journal of Sensor Networks (IJSNet)  
In this paper, we present a distributed adaptive mesh refinement solution to invert seismic tomography over large dense network, which avoids centralized computation and expensive data collection.  ...  Our approach first discretizes the high fidility data and later filters them using adaptive mesh to make it well-conditioned.  ...  Adaptive mesh in seismic tomography Now we will provide the motivation for using adaptive mesh refinement in seismic tomography with the help of real data.  ... 
doi:10.1504/ijsnet.2017.10001514 fatcat:svnoxk5ot5h2pnnsgmq6usluea

Plane-wave fluorescence tomography with adaptive finite elements

Amit Joshi, Wolfgang Bangerth, Kildong Hwang, John Rasmussen, Eva M. Sevick-Muraca
2006 Optics Letters  
An adaptive finite-element algorithm is used to handle the ill-posed and computationally demanding inverse image reconstruction problem.  ...  Tomographic images of fluorescent targets buried at 1-2 cm depths from the illumination surface demonstrate the feasibility of fluorescence tomography from reflectance tomography in clinically relevant  ...  On the other hand, with the adaptive refinement, this resolution was achieved with only 2584 cells for the 1 cm deep target and 2416 cells for the 2 cm deep target.  ... 
doi:10.1364/ol.31.000193 pmid:16441027 fatcat:bzk2vm6jyrbexngeukazkytngu

Performance evaluation of adaptive meshing algorithms for fluorescence diffuse optical tomography using experimental data

Lu Zhou, Birsen Yazıcı, Angelique B. F. Ale, Vasilis Ntziachristos
2010 Optics Letters  
To address this trade-off, we analyzed the effect of discretization on the accuracy of FDOT imaging and proposed novel adaptive meshing algorithms for FDOT in a series of studies.  ...  Fluorescence diffuse optical tomography (FDOT) is a computationally demanding imaging problem.  ...  The mesh refinement and image reconstruction were performed on a computer with 3:4 GHz dual-core CPU and 2 GB memory, and the reconstruction time including mesh refinement for each image was approximately  ... 
doi:10.1364/ol.35.003727 pmid:21081977 fatcat:xpjswno3fzhctdgdqrgd56rtjq

Adaptive finite element based tomography for fluorescence optical imaging in tissue

Amit Joshi, Wolfgang Bangerth, Eva M. Sevick-Muraca
2004 Optics Express  
Adaptively refined meshes are used to separately discretize maps of the forward/adjoint variables and the unknown parameter of fluorescent yield.  ...  A three-dimensional fluorescence-enhanced optical tomography scheme based upon an adaptive finite element formulation is developed and employed to reconstruct fluorescent targets in turbid media from frequency-domain  ...  R01CA67176) and the Center for Subsurface Modeling at the Institute for Computational Engineering and Sciences, University of Texas at Austin.  ... 
doi:10.1364/opex.12.005402 pmid:19484100 fatcat:5f3n7fhewzfofa4zgtz4ko4r2i

Numerical aspects of the adaptive computational grid in solving the problems of electrical prospecting with direct current

B. Mukanova, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan, T. Mirgalikyzy, M. Turarova, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
2018 International Journal of Mathematics and Physics  
The purpose of this work is to determine the acceptable parameters of various algorithms for constructing a computational grid for computing electrical tomography curves associated with the ground surface  ...  This paper is devoted to the numerical aspects of the adaptive computational grid in solving the problems of electrical prospecting with direct current.  ...  resistivity are taken with different algorithms of grid's construction: 1 -by grid adapted to source electrode, 2 -by grid with triangulation adapted to measuring line Numerical aspects of the adaptive  ... 
doi:10.26577/ijmph.2018.v9i2.259 fatcat:ldx5l4bjhfd7pbowjtr5fn2twe

3-D electrical resistivity tomography using adaptive wavelet parameter grids

A. Plattner, H. R. Maurer, J. Vorloeper, M. Blome
2012 Geophysical Journal International  
We present a novel adaptive model parametrization strategy for the 3-D electrical resistivity tomography problem and demonstrate its capabilities with a series of numerical examples.  ...  Because our approach is not tightly coupled to electrical resistivity tomography, it should be straightforward to adapt it to other data types.  ...  A C K N O W L E D G M E N T S We thank Stewart Greenhalgh, Thomas Günther, the editor Mark Everett and an anonymous reviewer for their helpful comments that improved the quality of the paper.  ... 
doi:10.1111/j.1365-246x.2012.05374.x fatcat:a4vjeauaife4pmwv57rvgxapm4

A source reconstruction algorithm based on adaptive hp-FEM for bioluminescence tomography

Runqiang Han, Jimin Liang, Xiaochao Qu, Yanbin Hou, Nunu Ren, Jingjing Mao, Jie Tian
2009 Optics Express  
In this paper, a new algorithm is presented for BLT source reconstruction based on adaptive hp-finite element method.  ...  Using adaptive mesh refinement strategy and intelligent permissible source region, we can obtain more accurate information about the location and density of sources, with the robustness, stability and  ...  The purpose is to compare the results of global refinement (FEM on a fine grid) and local adaptive refinement (hp-FEM) in the condition of similar small mesh size.  ... 
doi:10.1364/oe.17.014481 pmid:19687926 fatcat:7sbpyqbbxndfnkiaci23fbtd5m

Adaptive finite element methods for nonlinear inverse problems

Wolfgang Bangerth, Amit Joshi
2009 Proceedings of the 2009 ACM symposium on Applied Computing - SAC '09  
In this contribution, we outline such an adaptive algorithm and demonstrate results using a realistic example from optical tomography.  ...  As a consequence, in realistic, threedimensional cases, they become extraordinarily expensive to solve numerically, and advanced methods like adaptive mesh refinement become indispensible.  ...  Our implementation therefore works as follows: Starting with uniformly refined, relatively coarse meshes for each of the M + 1 grids, we discretize and solve several iterations of the Gauss-Newton system  ... 
doi:10.1145/1529282.1529500 dblp:conf/sac/BangerthJ09 fatcat:ro2fyamoejechel2kkikcgiku4

Optimal imaging with adaptive mesh refinement in electrical impedance tomography

Marc Molinari, Barry H Blott, Simon J Cox, Geoffrey J Daniell
2002 Physiological Measurement  
In this paper we introduce the idea of adaptive mesh refinement to the 2D problem so that the local scale of the mesh is always matched to the scale of the image structures.  ...  Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-tonoise ratios of 60 to 80 dB, one or two refinement stages  ...  Acknowledgment MM is grateful to EPSRC for financial support.  ... 
doi:10.1088/0967-3334/23/1/311 pmid:11876225 fatcat:asavioelx5fjrep3usjabwpv2a

On Bow Shock Source of Cusp Energetic Ions [chapter]

Shen-Wu Chang, Karlheinz J. Trattner
2013 Geophysical Monograph Series  
Two examples of adaptive tomography in non-seismic problems suggest that the gradual refinement of the parameterization may be an effective way to regularize the inverse problem.  ...  Some recent implementations of tomography are discussed where the parameterization is refined during the course of the inversion process.  ...  We are grateful to Todd Nicholson and Eric Debayle for use of Plate 1 and Figure 6 , and Alexei Gorbatov for his tomographic models used in Figure 1 and Plate 1.  ... 
doi:10.1029/156gm04 fatcat:bkz7n5eombhqrnvlphfemdcd6q

Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: I

Murat Guven, Birsen Yazici, Kiwoon Kwon, Eldar Giladi, Xavier Intes
2007 Inverse Problems  
The proposed discretization schemes lead to adaptively refined composite meshes that yield the desired level of imaging accuracy while reducing the size of the discretized forward and inverse problems.  ...  In this work, based on the analysis presented in part I, we develop new adaptive discretization schemes for the forward and inverse problems in order to reduce the error in the reconstructed images resulting  ...  In the same study, an adaptive refinement scheme was proposed for the inverse problem discretization, but no adaptive refinement was considered for the solution of the forward problem.  ... 
doi:10.1088/0266-5611/23/3/017 fatcat:p5dukhwumnhaniikvpu6jl4mcm

Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: II

Murat Guven, Birsen Yazici, Kiwoon Kwon, Eldar Giladi, Xavier Intes
2007 Inverse Problems  
The proposed discretization schemes lead to adaptively refined composite meshes that yield the desired level of imaging accuracy while reducing the size of the discretized forward and inverse problems.  ...  In this work, based on the analysis presented in part I, we develop new adaptive discretization schemes for the forward and inverse problems in order to reduce the error in the reconstructed images resulting  ...  In the same study, an adaptive refinement scheme was proposed for the inverse problem discretization, but no adaptive refinement was considered for the solution of the forward problem.  ... 
doi:10.1088/0266-5611/23/3/018 fatcat:bcbk5mrch5gwzd4h64m4jkhoxy
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