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Electron paramagnetic resonance image reconstruction with total variation and curvelets regularization. (English) Zbl 1381.92055

92C55 Biomedical imaging and signal processing
65R10 Numerical methods for integral transforms
44A12 Radon transform
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[1] Weil J A and Bolton J 2007 Electron Paramagnetic Resonance: Elementary Theory and Practical Applications 2nd edn (New York: Wiley)
[2] Mäder K, Swartz H, Stösser R and Borchert H 1994 The application of EPR spectroscopy in the field of pharmacy Pharmazie49 97-101
[3] Hirata H and Fujii H 2006 Free radicals in living systems: in vivo detection of bioradicals with EPR spectroscopy Curr. Org. Chem.10 521-34
[4] Khan N, Williams B and Swartz H 2006 Clinical applications of in vivo EPR: rationale and initial results Appl. Magn. Reson.30 185-99
[5] Plonka P 2009 Electron paramagnetic resonance as a unique tool for skin and hair research Exp. Dermatol.18 472-84
[6] Frapart Y 2012 In vivo electron paramagnetic resonance and imaging in biomedical science Adv. Bio-Imaging 67-76
[7] Velan S, Spencer R, Zweier J and Kuppusamy P 2000 Electron paramagnetic resonance oxygen mapping (EPROM): direct visualization of oxygen concentration in tissue Magn. Reson. Med.43 804-9
[8] Kuppusamy P and Zweier J 2004 Cardiac applications of EPR imaging NMR Biomed.17 226-39
[9] Blank A, Freed J, Kumar N and Wang C 2006 Electron spin resonance microscopy applied to the study of controlled drug release J. Control. Release111 174-84
[10] Binet L, Gourier D and Derenne S 2008 Potential of EPR imaging to detect traces of primitive life in sedimentary rocks Earth Planet. Sci. Lett.273 359-66
[11] Fujii H, Sato-Akaba H, Kawanishi K and Hirata H 2011 Mapping of redox status in a brain-disease mouse model by three-dimensional EPR imaging Magn. Reson. Med.65 295-303
[12] Sathiya M et al 2015 Electron paramagnetic resonance imaging for real-time monitoring of Li-ion batteries Nat. Commun.6 6276
[13] Radon J 1917 Über die bestimmung von funktionen durch ihre integralwerte längsgewisser mannigfaltigkeiten Berichte Saechsishe Acad. Wissenschaft. Math. Phys., Klass69 262
[14] The Mathematics of Computerized Tomography, Ill-Posedness and Accuracy ch 4
[15] Herman G T 2009 Fundamentals of Computerized Tomography, Image Reconstruction from Projections(Advances in Pattern Recognition) (New York: Springer)
[16] Xepr, version 2.6b.36. Bruker 2009 https://www.bruker.com/products/mr/epr/epr-software/xepr/overview.html
[17] Hayner D A 1983 The missing cone problem in computer tomography and a model for interpolation in synthetic aperture radar PhD Thesis University of Illinois
[18] Pan X, Sidky E and Vannier M 2009 Why do commercial CT scanner still employ traditional, filtered back-projection for image reconstruction? Inverse Problems25 123009
[19] Bezières N 2012 First combined in vivo x-ray tomography and high-resolution molecular electron paramagnetic resonance (EPR) imaging of the mouse knee joint taking into account the disappearance kinetics of the EPR probe Mol. Imaging11 7290-2011
[20] Ahmad R, Clymer B, Vikram D, Deng Y, Hirata H, Zweier J and Kuppusmy P 2007 Enhanced resolution for EPR imaging by two-step deblurring J. Magn. Reson.184 246-57
[21] Johnson C, McGarry D, Cook J, Devashayam N, Mitchell J, Subramanian S and Krishna M 2003 Maximum entropy reconstruction methods in electron paramagnetic resonance imaging Ann. Oper. Res.119 101-18
[22] Tseitlin M, Dhami A, Eaton S and Eaton G 2007 Comparison of maximum entropy and filtered back-projection methods to reconstruct rapid-scan EPR images J. Magn. Reson.184 157-68
[23] Tseitlin M, Czechowski T, Eaton S and Eaton G 2008 Regularized optimization (RO) reconstruction for oximetric EPR imaging J. Magn. Reson.194 212-21
[24] Johnson D, Ahmad R, He G, Samouilov A and Zweier J 2014 Compressed sensing of spatial electron paramagnetic resonance imaging Magn. Reson. Med.72 893-901
[25] Qiao Z, Redler G, Epel B, Qian Y and Halpern H 2015 3D pulse EPR imaging from sparse-view projections via constrained total variation minimization J. Magn. Reson.258 49-57
[26] Feichtinger H, Gröchenig K and Strohmer T 1995 Efficient numerical methods in non-uniform sampling theory Numer. Math.69 423-40
[27] Chambolle A and Pock T 2011 A first-order primal-dual algorithm for convex problems with applications to imaging J. Math. Imaging Vision40 120-45
[28] Palmer J, Potter L, Johnson D, Zweier J and Ahmadb R 2013 Dual-scan acquisition for accelerated continuous-wave EPR oximetry J. Magn. Reson.222 53-8
[29] Ahmad R, Clymer B, Deng Y, He G, Vikram D, Kuppusamy P and Zweier J 2006 Optimization of data acquisition for EPR imaging J. Magn. Reson.179 263-72
[30] Deans S R 2007 The Radon Transform and Some of its Applications (Mineola, NY: Courier Corporation)
[31] Rudin L, Osher S and Fatemi E 1992 Nonlinear total variation based noise removal algorithms Physica D 60 259-68
[32] Meyer Y 1992 Wavelets and Operators(Cambridge Studies in Advanced Mathematics vol 37) (Cambridge: Cambridge University Press)
[33] Vese L and Osher S 2002 Modeling textures with total variation minimization and oscillating patterns in image processing J. Sci. Comput.19 553-72
[34] Aujol J-F and Chambolle A 2005 Dual norms and image decomposition models Int. J. Comput. Vis.63 85-104
[35] Frühauf F, Pontow C and Scherzer O 2011 Texture enhancing based on variational image decomposition Math. Image Process.5 127-40
[36] Chambolle A 2004 An algorithm for total variation minimization and applications J. Math. Imaging Vis.20 89-97
[37] Kostov C 1990 Toeplitz structure in slant-stack inversion SEG Technical Program Expanded Abstracts 1990 (Tulsa, OK: Society of Exploration Geophysicists) pp 1618-21
[38] Candès E, Demanet L, Donoho D and Ying L 2006 Fast discrete curvelet transforms Multiscale Model. & Simul.5 861-99
[39] MATLAB and Image Processing Toolbox Release 2015a The MathWorks, Inc., Natick, MA, United States
[40] Frigo M and Johnson S 2005 The design and implementation of FFTW3 Proc. IEEE93 216-31
[41] Greengard L and Lee J-Y 2004 Accelerating the nonuniform fast Fourier transform Soc. Ind. Appl. Math.46 443-54
[42] Stoll S and Schweiger A 2006 Easyspin, a comprehensive software package for spectral simulation and analysis in EPR J. Magn. Reson.178 42-55
[43] Shepp L and Logan B 1974 The Fourier reconstruction of a head section IEEE Trans. Nucl. Sci.21 21-43
[44] Horé A and Ziou D 2010 Image quality metrics: PSNR versus SSIM Int. Conf. Pattern Recognit. 2366-9
[45] Burger M, Mennucci A CG, Osher S and Rumpf M 2013 A guide to the TV zoo Level Set and PDE Based Reconstruction Methods in Imaging (New York: Springer) pp 1-70
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