References
-
[1]
-
P. Lauterbur,
“Image formation by induced local interactions: Examples employing
nuclear magnetic resonance,”
Nature, vol. 242, pp. 190–191, 1973.
- [2]
-
L. Man, J. Pauly, and M. A.,
“Multifrequency interpolation for fast off-resonance correction,”
Magnetic Resonance in Medicine, vol. 37, no. 5, pp. 785–792,
April 1997.
- [3]
-
K. Pruessmann, M. Weiger, M. Scheidegger, and P. Boesiger,
“SENSE: Sensitivity encoding for fast MRI,”
Magnetic Resonance in Medicine, vol. 42, no. 5, pp. 952–962,
October 1999.
- [4]
-
M. Zaitsev, C. Dold, G. Sakas, J. Hennig, and O. Speck,
“Magnetic resonance imaging of freely moving objects: prospective
real-time motion correction using an external optical motion tracking
system,”
NeuroImage, vol. 31, no. 3, pp. 1038–1050, 2006.
- [5]
-
M. B. Ooi, S. Krueger, W. J. Thomas, S. V. Swaminathan, and T. R. Brown,
“Prospective real-time correction for arbitrary head motion using
active markers,”
Magnetic Resonance in Medicine, vol. 62, no. 4, pp. 943–954,
2009.
- [6]
-
M. Lustig, D. L. Donoho, and J. M. Pauly,
“Sparse MRI: The application of compressed sensing for rapid MR
imaging,”
Magnetic Resonance in Medicine, vol. 58, pp. 1182–1195,
2007.
- [7]
-
B. J. Wilm, C. Barmet, M. Pavan, and K. P. Pruessmann,
“Higher order reconstruction for MRI in the presence of
spatiotemporal field perturbations,”
Magnetic Resonance in Medicine, vol. 65, no. 6, pp.
1690–1701, 2011.
- [8]
-
K. T. Block, M. Uecker, and J. Frahm,
“Undersampled radial MRI with multiple coils. Iterative image
reconstruction using a total variation constraint,”
Magnetic Resonance in Medicine, vol. 57, no. 6, pp.
1086–1098, 2007.
- [9]
-
U. Gamper, P. Boesiger, and S. Kozerke,
“Compressed sensing in dynamic MRI,”
Magnetic Resonance in Medicine, vol. 59, no. 2, pp. 365–373,
2008.
- [10]
-
L. Ying, L. Bo, M. C. Steckner, W. Gaohong, W. Min, and L. Shi-Jiang,
“A statistical approach to SENSE regularization with arbitrary
k-space trajectories,”
Magnetic Resonance in Medicine, vol. 60, pp. 414–421, 2008.
- [11]
-
B. Liu, E. Abdelsalam, J. Sheng, and L. Ying,
“Improved spiral sense reconstruction using a multiscale wavelet
model,”
in Proceedings of ISBI, 2008, pp. 1505–1508.
- [12]
-
B. Liu, K. King, M. Steckner, J. Xie, J. Sheng, and L. Ying,
“Regularized sensitivity encoding (SENSE) reconstruction using
Bregman iterations,”
Magnetic Resonance in Medicine, vol. 61, pp. 145–152,
January 2009.
- [13]
-
L. Chaâri, J.-C. Pesquet, A. Bebazza-Benyahia, and P. Ciuciu,
“Autocalibrated regularized parallel MRI reconstruction in the
wavelet domain,”
in Proceedings of ISBI, Paris, France, May, 14-17 2008, pp.
756–759.
- [14]
-
L. Chaâri, J.-C. Pesquet, A. Benazza-Benyahia, and P. Ciuciu,
“A wavelet-based regularized reconstruction algorithm for SENSE
parallel MRI with applications to neuroimaging,”
Medical Image Analysis Journal, vol. 15, no. 2, pp. 185–201,
April 2011.
- [15]
-
F. Knoll, K. Bredies, T. Pock, and S. R.,
“Second order total generalized variation (TGV) for MRI,”
Magnetic Resonance in Medicine, vol. 65, no. 2, pp. 480–491,
Feb 2011.
- [16]
-
G. Puy, J. Marques, R. Gruetter, J. Thiran, D. Van De Ville, P. Vandergheynst,
and Y. Wiaux,
“Spread spectrum magnetic resonance imaging,”
IEEE Transactions on Medical Imaging, vol. 31, no. 3, pp.
586–598, March 2012.
- [17]
-
M. A. T. Figueiredo and R. D. Nowak,
“An EM algorithm for wavelet-based image restoration,”
IEEE Transactions on Signal Processing, vol. 12, no. 8, pp.
906–916, 2003.
- [18]
-
J. Bect, L. Blanc-Féraud, G. Aubert, and A. Chambolle,
“A ℓ1-unified variational framework for image restoration,”
Lecture Notes in Computer Science, vol. 3024, pp. 1–13, 2004.
- [19]
-
I. Daubechies, M. Defrise, and C. De Mol,
“An iterative thresholding algorithm for linear inverse problems
with a sparsity constraint,”
Communications on Pure and Applied Mathematics, vol. 57, no.
11, pp. 1413–1457, 2004.
- [20]
-
A. Beck and M. Teboulle,
“A fast iterative shrinkage-thresholding algorithm for linear
inverse problems,”
SIAM Journal on Imaging Sciences, vol. 2, no. 1, pp. 183–202,
2009.
- [21]
-
İ. Bayram and I. W. Selesnick,
“A subband adaptive iterative shrinkage/thresholding algorithm,”
IEEE Transactions on Signal Processing, vol. 58, no. 3, pp.
1131–1143, 2010.
- [22]
-
M. E. Haacke, R. W. Brown, M. R. Thompson, and R. Venkatesan,
Magnetic Resonance Imaging: Physical Principles and Sequence
Design,
Wiley-Liss, June 1999.
- [23]
-
Z.-P. Liang and P. C. Lauterbur,
Principles of Magnetic Resonance Imaging: A Signal Processing
Perspective,
Wiley-IEEE Press, October 1999.
- [24]
-
C. Cohen-Tannoudji, B. Diu, and F. Laloë,
Mécanique quantique, vol. I and II,
Hermann, 1973.
- [25]
-
I. I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch,
“A new method of measuring nuclear magnetic moment,”
Physical Review, vol. 53, no. 4, pp. 318, Feb 1938.
- [26]
-
E. M. Purcell, H. C. Torrey, and R. V. Pound,
“Resonance absorption by nuclear magnetic moments in a solid,”
Physical Review, vol. 69, no. 1–2, pp. 37–38, Jan 1946.
- [27]
-
F. Bloch,
“Nuclear induction,”
Physical Review, vol. 70, pp. 460–473, 1946.
- [28]
-
R. V. Damadian,
“Tumor detection by nuclear magnetic resonance,”
Science, vol. 171, pp. 1151–1153, March 1971.
- [29]
-
H. Gach, C. Tanase, and F. Boada,
“2D & 3D Shepp-Logan phantom standards for MRI,”
in 19th International Conference on Systems Engineering, Las
Vegas, NV, USA, Los Alamitos, CA, USA, August 2008, pp. 521–526, IEEE
Computer Society.
- [30]
-
M. Blaimer, F. Breuer, M. Mueller, R. Heidemann, M. Griswold, and P. Jakob,
“SMASH, SENSE, PILS, GRAPPA: how to choose the optimal method.,”
Top. Magn. Reson. Imaging, vol. 15, no. 4, pp. 223–236, 2004.
- [31]
-
D. J. Larkman and R. G. Nunes,
“Parallel magnetic resonance imaging,”
Physics in Medicine and Biology, vol. 52, no. 7, pp. R15–R55,
Apr. 2007.
- [32]
-
D. Sodickson and W. Manning,
“Simultaneous acquisition of spatial harmonics (SMASH): fast
imaging with radiofrequency coil arrays.,”
Magnetic Resonance in Medicine, vol. 38, no. 4, pp. 591–603,
1997.
- [33]
-
P. Jakob, M. Griswold, R. Edelman, and D. Sodickson,
“AUTO-SMASH: a self-calibrating technique for SMASH imaging.
SiMultaneous Acquisition of Spatial Harmonics.,”
MAGMA, vol. 7, no. 1, pp. 42–54, 1998.
- [34]
-
R. Heidemann, M. Griswold, A. Haase, and P. Jakob,
“VD-AUTO-SMASH imaging.,”
Magnetic Resonance in Medicine, vol. 45, no. 6, pp.
1066–1074, 2001.
- [35]
-
M. A. Griswold, P. M. Jackob, R. M. Heidemann, M. Nittka, V. Jellus, J. Wang,
B. Kiefer, and A. Haase,
“Generalized autocalibrating partially parallel acquisition
(GRAPPA),”
Magnetic Resonance in Medicine, vol. 47, no. 6, pp.
1002–1010, 2002.
- [36]
-
M. Griswold, P. Jakob, M. Nittka, J. Goldfarb, and A. Haase,
“Partially parallel imaging with localized sensitivities
(PILS).,”
Magnetic Resonance in Medicine, vol. 44, no. 4, pp. 602–609,
2000.
- [37]
-
K. P. Pruessmann, M. Weiger, P. Börnert, and P. Boesiger,
“Advances in sensitivity encoding with arbitrary k-space
trajectories,”
Magnetic Resonance in Medicine, vol. 46, no. 4, pp. 638–651,
2001.
- [38]
-
B. P. Sutton, D. C. Noll, and J. A. Fessler,
“Fast, iterative image reconstruction for MRI in the presence of
field inhomogeneities,”
IEEE Transactions on Medical Imaging, vol. 22, no. 2, pp.
178–188, 2003.
- [39]
-
B. Delattre, J.-N. Hyacinthe, J.-P. Vallée, and D. Van De Ville,
“Spline-based variational reconstruction of variable density spiral
k-space data with automatic parameter adjustment,”
in Proceedings of ISMRM 17th Annual Meeting, Hawai’i, USA,
2009, p. 2066.
- [40]
-
M. Guerquin-Kern, M. Häberlin, K. P. Pruessmann, and M. Unser,
“A fast wavelet-based reconstruction method for magnetic resonance
imaging,”
IEEE Transactions on Medical Imaging, vol. 30, no. 9, pp.
1649–1660, September 2011.
- [41]
-
M. Unser and T. Blu,
“Wavelet theory demystified,”
IEEE Transactions on Signal Processing, vol. 51, no. 2, pp.
470–483, 2003.
- [42]
-
S. Mallat,
A wavelet tour of signal processing,
Academic Press, 1999.
- [43]
-
D. L. Phillips,
“A technique for the numerical solution of certain integral
equations of the first kind,”
J. ACM, vol. 9, no. 1, pp. 84–97, Jan. 1962.
- [44]
-
S. Twomey,
“On the numerical solution of Fredholm integral equations of the
first kind by the inversion of the linear system produced by quadrature,”
J. ACM, vol. 10, no. 1, pp. 97–101, Jan. 1963.
- [45]
-
A. Tikhonov and V. Arsenin,
Solutions of Ill-Posed Problems,
Winston, Washington, D.C., 1977.
- [46]
-
C. Barmet, M. Haeberlin, and K. P. Pruessmann,
“A Robust Alternative to Regularization in Parallel Imaging
Reconstruction,”
in Proceedings of ISMRM, 2007.
- [47]
-
L. Rudin, S. Osher, and E. Fatemi,
“Nonlinear total variation based noise removal algorithms,”
Physica D, vol. 60, pp. 259–268, 1992.
- [48]
-
J. A. Fessler and B. P. Sutton,
“Nonuniform fast Fourier transforms using min-max interpolation,”
IEEE Transactions on Signal Processing, vol. 51, pp.
560–574, 2003.
- [49]
-
F. T. W. A. Wajer and K. P. Pruessmann,
“Major speedup of reconstruction for sensitivity encoding with
arbitrary trajectories,”
in Proceedings of ISMRM 9th Annual Meeting, Glasgow, United
Kingdom, 2001, p. 625.
- [50]
-
M. R. Hestenes and E. Stiefel,
“Methods of conjugate gradients for solving linear systems,”
Journal of Research of the National Bureau of Standards, vol.
49, pp. 409–436, Dec. 1952.
- [51]
-
D. Geman and C. Yang,
“Nonlinear image recovery with half-quadratic regularization,”
IEEE Transactions on Image Processing, vol. 4, no. 7, pp.
932–946, July 1995.
- [52]
-
J.-C. Baritaux, K. Hassler, M. Bucher, S. Sanyal, and M. Unser,
“Sparsity-driven reconstruction for FDOT with anatomical priors,”
IEEE Transactions on Medical Imaging, vol. 30, no. 5, pp.
1143–1153, May 2011.
- [53]
-
B. Wohlberg and P. Rodríguez,
“An iteratively reweighted norm algorithm for minimization of total
variation functionals,”
IEEE Signal Processing Letters, vol. 14, no. 12, pp.
948–951, Dec. 2007.
- [54]
-
A. Chambolle and T. Pock,
“A first-order primal-dual algorithm for convex problems with
applications to imaging,”
Journal of Mathematical Imaging and Vision, vol. 40, pp.
120–145, May 2011.
- [55]
-
M. J. Fadili and G. Peyré,
“Total variation projection with first order schemes,”
IEEE Transactions on Image Processing, vol. 20, no. 3, pp.
657–669, March 2011.
- [56]
-
A. Chambolle, R. A. DeVore, N.-Y. Lee, and B. J. Lucier,
“Nonlinear wavelet image processing: Variational problems,
compression, and noise removal through wavelet shrinkage,”
IEEE Transactions on Signal Processing, vol. 7, no. 3, pp.
319–335, 1998.
- [57]
-
M. Guerquin-Kern, L. Lejeune, K. P. Pruessmann, and M. Unser,
“Realistic analytical phantoms for parallel magnetic resonance
imaging,”
IEEE Transactions on Medical Imaging, vol. 31, no. 3, pp.
626–636, March 2012.
- [58]
-
A. Ribés and F. Schmitt,
“Linear inverse problems in imaging,”
IEEE Signal Processing Magazine, vol. 25, no. 4, pp. 84–99,
July 2008.
- [59]
-
L. Shepp and B. Logan,
“The Fourier reconstruction of a head section,”
IEEE Transactions on Nuclear Science, vol. 21, pp. 21–43,
June 1974.
- [60]
-
M. Smith, L. Chen, Y. Hui, T. Mathews, J. Yang, and X. Zeng,
“Alternatives to the use of the DFT in MRI and spectroscopic
reconstructions,”
International Journal of Imaging Systems and Technology, vol.
8, no. 6, pp. 558–564, December 1997.
- [61]
-
R. Van de Walle, H. Barrett, K. Myers, M. Aitbach, B. Desplanques, A. Gmitro,
J. Cornelis, and I. Lemahieu,
“Reconstruction of MR images from data acquired on a general
nonregular grid by pseudoinverse calculation,”
IEEE Transactions on Medical Imaging, vol. 19, no. 12, pp.
1160–1167, December 2000.
- [62]
-
C. Koay, J. Sarlls, and E. Ãzarslan,
“Three-dimensional analytical magnetic resonance imaging phantom in
the Fourier domain,”
Magnetic Resonance in Medicine, vol. 58, no. 2, pp. 430–436,
August 2007.
- [63]
-
L. Greengard and C. Stucchio,
“Spectral edge detection in two dimensions using wavefronts,”
Applied and Computational Harmonic Analysis, vol. 30, no. 1,
pp. 69–95, 2011.
- [64]
-
T. M. Ngo, G. S. Fung, B. M. Tsui, E. McVeigh, and H. D. A.,
“Three dimensional digital polyhedral phantom framework with
analytical fourier transform and application in cardiac imaging,”
in Proceedings of ISMRM, 2011, p. 1310.
- [65]
-
W. Segars, D. Lalush, and B. Tsui,
“A realistic spline-based dynamic heart phantom,”
IEEE Transactions on Nuclear Science, vol. 46, no. 3, pp.
503–506, June 1999.
- [66]
-
S. Vembu,
“Fourier transformation of the n-dimensional radial delta
function,”
The Quarterly Journal of Mathematics, vol. 12, no. 1, pp.
165–168, 1961.
- [67]
-
E. Sorets,
“Fast Fourier transforms of piecewise constant functions,”
Journal of Computational Physics, vol. 116, no. 2, pp.
369–379, 1995.
- [68]
-
M. Jacob, T. Blu, and M. Unser,
“An exact method for computing the area moments of wavelet and
spline curves,”
IEEE Transactions on Pattern Analysis and Machine
Intelligence, vol. 23, no. 6, pp. 633–642, June 2001.
- [69]
-
W. Gautschi,
“Computational aspects of three-term recurrence relations,”
SIAM review, vol. 9, pp. 24–82, January 1967.
- [70]
-
F. Champagnat and J. Idier,
“A connection between half-quadratic criteria and EM algorithms,”
IEEE Signal Processing Letters, vol. 11, no. 9, pp. 709–712,
September 2004.
- [71]
-
R. Archibald and A. Gelb,
“A method to reduce the Gibbs ringing artifact in MRI scans
while keeping tissue boundary integrity,”
IEEE Transactions on Medical Imaging, vol. 21, no. 4, pp.
305–319, April 2002.
- [72]
-
M. Guerquin-Kern, J.-C. Baritaux, and M. Unser,
“Efficient image reconstruction under sparsity constraints with
application to MRI and bioluminescence tomography,”
in Proceedings of the Thirty-Sixth IEEE International
Conference on Acoustics, Speech, and Signal Processing (ICASSP’11),
Prague, Czech Republic, May 22-27 2011, pp. 5760–5763.
- [73]
-
M. Lustig, J. H. Lee, D. L. Donoho, and J. M. Pauly,
“Faster imaging with randomly perturbed, undersampled spirals and
|L|1 reconstruction,”
in Proceedings of ISMRM, 2005.
- [74]
-
M. Guerquin-Kern, D. Van De Ville, C. Vonesch, J.-C. Baritaux, K. P.
Pruessmann, and M. Unser,
“Wavelet-regularized reconstruction for rapid MRI,”
in Proceedings of ISBI, 2009, pp. 193–196.
- [75]
-
J. M. Bioucas-Dias and M. A. T. Figueiredo,
“A new TwIST: Two-step iterative shrinkage/thresholding algorithms
for image restoration,”
IEEE Transactions on Image Processing, vol. 16, no. 12, pp.
2992–3004, 2007.
- [76]
-
Y. E. Nestorov,
“Gradient methods for minimizing composite objective function,”
Tech. Rep., CORE report, 2007.
- [77]
-
P. Weiss,
Algorithmes rapides d’optimisation convexe. Application à
la restoration d’images et à la détection de changements,
Ph.D. thesis, Université de Nice, Dec. 2008.
- [78]
-
S. Becker, J. Bobin, and E. J. Candès,
“NESTA: A fast and accurate first-order method for sparse
recovery,”
Tech. Rep., California Institute of Technology, 2009.
- [79]
-
A. Beck and M. Teboulle,
“Fast gradient-based algorithms for constrained total variation
image denoising and deblurring problems,”
IEEE Transactions on Image Processing, vol. 18, pp.
2419–2434, 2009.
- [80]
-
C. Vonesch and M. Unser,
“A fast thresholded Landweber algorithm for wavelet-regularized
multidimensional deconvolution,”
IEEE Transactions on Image Processing, vol. 17, no. 4, pp.
539–549, 2008.
- [81]
-
C. Vonesch and M. Unser,
“A fast multilevel algorithm for wavelet-regularized image
restoration,”
IEEE Transactions on Image Processing, vol. 18, no. 3, pp.
509–523, 2009.
- [82]
-
J. A. Fessler, S. Lee, V. T. Olafsson, H. R. Shi, and D. C. Noll,
“Toeplitz-based iterative image reconstruction for MRI with
correction for magnetic field inhomogeneity,”
IEEE Transactions on Signal Processing, vol. 53, pp.
3393–3402, 2005.
- [83]
-
W. C. Karl,
“Regularization in image restoration and reconstruction,”
in Handbook of image and video processing, A. C. Bovik, Ed.,
pp. 183–202. Elsevier Science & Technology, 2005.
- [84]
-
G. H. Glover,
“Simple analytic spiral k-space algorithm,”
Magnetic Resonance in Medicine, vol. 42, no. 2, pp. 412–415,
1999.
- [85]
-
D.-H. Kim, E. Adalsteinsson, and D. M. Spielman,
“Simple analytic variable density spiral design,”
Magnetic Resonance in Medicine, vol. 50, no. 1, pp. 214–219,
2003.
- [86]
-
C. Barmet, N. De Zanche, B. J. Wilm, and K. P. Pruessmann,
“A transmit/receive system for magnetic field monitoring of in
vivo MRI,”
Magnetic Resonance in Medicine, vol. 62, no. 1, pp. 269–276,
July 2009.
- [87]
-
M. Guerquin-Kern, F. I. Karahanoğlu, D. Van De Ville, K. P. Pruessmann, and
M. Unser,
“Analytical form of Shepp-Logan phantom for parallel MRI,”
in Proceedings of ISBI, Rotterdam, The Netherlands, April
14-17 2010, pp. 261–264.
- [88]
-
G. H. Golub, M. Heath, and G. Wahba,
“Generalized cross-validation as a method for choosing a good ridge
parameter,”
Technometrics, vol. 21, no. 2, pp. 215–223, 1979.
- [89]
-
P. C. Hansen,
“Analysis of discrete ill-posed problems by means of the
L-curve,”
SIAM Review, vol. 34, pp. 561–580, December 1992.
- [90]
-
S. Ramani, T. Blu, and M. Unser,
“Monte-carlo SURE: A black-box optimization of regularization
parameters for general denoising algorithms,”
IEEE Transactions on Image Processing, vol. 17, no. 9, pp.
1540–1554, 2008.
- [91]
-
S. Ramani, Z. Liu, J. Rosen, J.-F. Nielsen, and J. A. Fessler,
“Regularization parameter selection for nonlinear iterative image
restoration and MRI reconstruction using GCV and SURE-based methods,”
to appear in IEEE Transactions on Image Processing, 2012.
- [92]
-
F. Knoll, M. Unger, C. Diwoky, C. Clason, T. Pock, and R. Stollberger,
“Fast reduction of undersampling artifacts in radial MR
angiography with 3D total variation on graphics hardware,”
Magnetic Resonance Materials in Physics, Biology and Medicine,
vol. 23, pp. 103–114, 2010.
- [93]
-
S. S. Vasanawala, M. J. Murphy, M. T. Alley, P. Lai, K. Keutzer, J. M. Pauly,
and M. Lustig,
“Practical parallel imaging compressed sensing MRI: Summary of two
years of experience in accelerating body MRI of pediatric patients,”
in Proceedings of ISBI, 2011.
- [94]
-
H. Pan and T. Blu,
“Sparse image restoration using iterated linear expansion of
thresholds,”
in Proceedings of the 2011 IEEE International Conference on
Image Processing (ICIP’11), 11–14 September 2011, pp. 1905–1908.
- [95]
-
M. Haeberlin, B. Wilm, C. Barmet, S. Kozerke, G. Katsikatsos, and K. P.
Pruessmann,
“Sinusoidal perturbations improve the noise behavior of parallel
EPI,”
in Proceedings of ISMRM, 2010.