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Greedy approximate projection for magnetic resonance fingerprinting with partial volumes. (English) Zbl 1453.92157
92C55 Biomedical imaging and signal processing
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[1] Jara H 2013 Theory of Quantitative Magnetic Resonance Imaging (Singapore: World Scientific)
[2] Ma D, Gulani V, Seibelich N, Liu K, Duerk J L and Griswold M A 2013 Magnetic resonance fingerprinting Nature465 187-92
[3] Donoho D L 2006 Compressed sensing IEEE Trans. Inform. Theory52 1289-306 · Zbl 1288.94016
[4] Doneva M, Brnert P, Eggers H, Stehning C, Sngas J and Mertins A 2010 Compressed sensing reconstruction for magnetic resonance parameter mapping Magn. Reson. Med.64 1114-20
[5] Davies M, Puy G, Vandergheynst P and Wiaux Y 2014 A compressed sensing framework for magnetic resonance fingerprinting SIAM J. Imaging Sci.7 2623 · Zbl 1309.65012
[6] Beck A and Teboulle M 2009 A fast iterative shrinkage-thresholding algorithm for linear inverse problems SIAM J. Imaging Sci.2 183-202 · Zbl 1175.94009
[7] Tseng P 2000 A modified forward-backward splitting method for maximal monotone mappings SIAM J. Control Optim.38 431-46 · Zbl 0997.90062
[8] Pierre E Y, Ma D, Chen Y, Badve C and Griswold M A 2016 Multiscale reconstruction for mr fingerprinting Magn. Reson. Med.75 2481-92
[9] Zhao B, Setsompop K, Ye H, Cauley S F and Wald L L 2016 Maximum likelihood reconstruction for magnetic resonance fingerprinting IEEE Trans. Med. Imaging35 1812-23
[10] Zhao B, Setsompop K, Adalsteinsson E, Gagoski B, Ye H, Ma D, Jiang Y, Ellen Grant P, Griswold M A and Wald L L 2017 Improved magnetic resonance fingerprinting reconstruction with low-rank and subspace modeling Magn. Reson. Med.79 933-42
[11] Doneva M, Amthor T, Koken P, Sommer K and Brnert P 2017 Matrix completion-based reconstruction for undersampled magnetic resonance fingerprinting data Magn. Reson. Imaging41 41-52
[12] Mazor G, Weizman L, Tal A and Eldar Y C 2018 Low-rank magnetic resonance fingerprinting Med. Phys.45 4066-84
[13] McGivney D F, Pierre E, Ma D, Jiang Y, Saybasili H, Gulani V and Griswold M A 2014 Svd compression for magnetic resonance fingerprinting in the time domain IEEE Trans. Med. Imaging33 2311-22
[14] Tohka J 2014 Partial volume effect modeling for segmentation and tissue classification of brain magnetic resonance images: a review World J. Radiol.6 855-64
[15] Deshmane A, McGivney D F, Ma D, Jiang Y, Badve C, Gulani V, Seiberlich N and Griswold M A 2019 Partial volume mapping using magnetic resonance fingerprinting NMR Biomed.32 e4082
[16] McGivney D, Deshmane A, Jiang Y, Ma D, Badve C, Sloan A, Gulani V and Griswold M 2018 Bayesian estimation of multicomponent relaxation parameters in magnetic resonance fingerprinting Magn. Reson. Med.80 159-70
[17] Tang S, Fernandez-Granda C, Lannuzel S, Bernstein B, Lattanzi R, Cloos M, Knoll F and Assländer J 2018 Multicompartment magnetic resonance fingerprinting Inverse Problems34 094005 · Zbl 1397.78054
[18] Bertsekas D P 1999 Nonlinear Programming (Belmont, MA: Athena Scientific) · Zbl 1015.90077
[19] Tseng P 2001 Convergence of a block coordinate descent method for nondifferentiable minimization J. Optim. Theory Appl.109 475-94 · Zbl 1006.65062
[20] Bolte J, Sabach S and Teboulle M 2014 Proximal alternating linearized minimization for nonconvex and nonsmooth problems Math. Program.146 459-94 · Zbl 1297.90125
[21] Frankel P, Garrigos G and Peypouquet J 2015 Splitting methods with variable metric for Kurdyka-Łojasiewicz functions and general convergence rates J. Optim. Theory Appl.165 874-900 · Zbl 1316.49039
[22] Chouzenoux E, Pesquet J-C and Repetti A 2016 A block coordinate variable metric forward-backward algorithm J. Global Optim.66 457-85 · Zbl 1351.90128
[23] Bauschke H and Combettes P L 2017 Convex Analysis and Monotone Operator Theory in Hilbert Spaces (New York: Springer) · Zbl 1359.26003
[24] Rockafellar R T and Wets R J B 2009 Variational Analysis vol 317 (New York: Springer)
[25] Weigel M 2015 Extended phase graphs: dephasing, RF pulses, and echoes-pure and simple J. Magn. Reson. Imaging41 266-95
[26] Candes E J, Romberg J and Tao T 2006 Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information IEEE Trans. Inform. Theory52 489-509 · Zbl 1231.94017
[27] Donoho D L and Huo X 2001 Uncertainty principles and ideal atomic decomposition IEEE Trans. Inf. Theory47 2845-62 · Zbl 1019.94503
[28] Donoho D L and Elad M 2003 Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization Proc. Natl Acad. Sci.100 2197-202 · Zbl 1064.94011
[29] Davenport M A, Needell D and Wakin M B 2013 Signal space cosamp for sparse recovery with redundant dictionaries IEEE Trans. Inf. Theory59 6820-9 · Zbl 1364.94119
[30] Giryes R and Elad M 2013 Iterative hard thresholding with near optimal projection for signal recovery 10th Int. Conf. on Sampling Theory and Applications
[31] Chen S, Donoho D and Saunders M A 1998 Atomic decomposition by basis pursuit SIAM J. Sci. Comput.20 33-61 · Zbl 0919.94002
[32] Candes E J, Eldar Y C, Needell D and Randall P 2011 Compressed sensing with coherent and redundant dictionaries Appl. Comput. Harmon. Anal.31 59-73 · Zbl 1215.94026
[33] Blumensath T 2011 Sampling and reconstructing signals from a union of linear subspaces IEEE Trans. Inf. Theory57 4660-71 · Zbl 1365.94173
[34] Blumensath T and Davies M E 2010 Normalized iterative hard thresholding: guaranteed stability and performance IEEE J. Sel. Top. Signal Process.4 298-309
[35] Golbabaee M, Chen D, Gómez P A, Menzel M I and Davies M E 2018 A deep learning approach for magnetic resonance fingerprinting CoRR (arXiv:abs/1809.01749)
[36] Cohen O, Zhu B and Rosen M S 2018 MR fingerprinting deep reconstruction network (drone) Magn. Reson. Med.80 885-94
[37] Hoppe E, Körzdörfer G, Würfl T, Wetzl J, Lugauer F, Pfeuffer J and Maier A K 2017 Deep learning for magnetic resonance fingerprinting: a new approach for predicting quantitative parameter values from time series GMDS pp 202-6
[38] Virtue P, Stella X Y and Lustig M 2017 Better than real: complex-valued neural nets for mri fingerprinting IEEE Int. Conf. on Image Processing pp 3953-7
[39] Chen G H G and Rockafellar R T 1997 Convergence rates in forward-backward splitting SIAM J. Optim.7 421-44 · Zbl 0876.49009
[40] Combettes P L and Wajs V R 2005 Signal recovery by proximal forward-backward splitting Multiscale Model. Simul.4 1168-200 · Zbl 1179.94031
[41] Lawson C L and Hanson R J 1995 Solving Least Squares Problems vol 15 (Philadelphia, PA: SIAM)
[42] Canny J 1986 A computational approach to edge detection IEEE Trans. Pattern Anal. Mach. Int.PAMI-8 679-98
[43] Lloyd S 1982 Least squares quantization in PCM IEEE Trans. Inf. Theory28 129-37 · Zbl 0504.94015
[44] Rieger B, Zimmer F, Zapp J, Weingärtner S and Schad L R 2017 Magnetic resonance fingerprinting using echo-planar imaging: joint quantification of T1 and T2* relaxation times Magn. Reson. Med.78 1724-33
[45] Rieger B, Akçakaya M, Pariente J C, Llufriu S, Martinez-Heras E, Weingärtner S and Schad L R 2018 Time efficient whole-brain coverage with mr fingerprinting using slice-interleaved echo-planar-imaging Sci. Rep.8 6667
[46] Collins D L, Zijdenbos A P, Kollokian V, Sled J G, Kabani N J, Holmes C J and Evans A C 1998 Design and construction of a realistic digital brain phantom IEEE Trans. Med. Imaging17 463-8
[47] Benjamin A, Gómez P, Golbabaee M, Mahbub Z, Sprenger T, Menzel M, Davies M and Marshall I 2018 Balanced multi-shot EPI for accelerated cartesian MR fingerprinting: an alternative to spiral MR fingerprinting Proc. Int. Society for Magnetic Resonance in Medicine p 4265
[48] Jiang Y, Ma D, Seiberlich N, Gulani V and Griswold M A 2015 MR fingerprinting using fast imaging with steady state precession (FISP) with spiral readout Magn. Reson. Med.74 1621-31
[49] Cline C C, Chen X, Mailhe B, Wang Q, Pfeuffer J, Nittka M, Griswold M A, Speier P and Nadar M S 2017 AIR-MRF: accelerated iterative reconstruction for magnetic resonance fingerprinting Magn. Reson. Imaging41 29-40
[50] Gómez P A, Bounincontri G, Molina-Romero M, Sperl J I, Menzel M I and Menze B H 2017 Accelerated parameter mapping with compressed sensing: an alternative to MR fingerprinting Proc. Int. Society for Magnetic Resonance in Medicine
[51] Bojorquez J Z, Bricq S, Acquitter C, Brunotte F, Walker P M and Lalande A 2017 What are normal relaxation times of tissues at 3T? Magn. Reson. Imaging35 69-80
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