« Previous
Next »
Medical Image Analysis
Volume 15, Issue 2
, Pages 185-201
, April 2011
A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging
References
- . A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences. 2009;2(1):183–202
- . Nonlinear Programming. second ed.. Belmont, USA: Athena Scientific; 1995;
- . A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Transactions on Image Processing. 2007;16(12):2992–3004
- . SMASH, SENSE, PILS, GRAPPA: how to choose the optimal method. Magnetic Resonance in Medicine. 2004;15(4):223–236
- . Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint. Magnetic Resonance in Medicine. 2007;56(7):1086–1098
- Chaâri, L., Pesquet, J.-C., Benazza-Benyahia, A., Ciuciu, P., 2008. Autocalibrated parallel MRI reconstruction in the wavelet domain. In: IEEE International Symposium on Biomedical Imaging, Paris, France, pp. 756–759.
- . A hierarchical Bayesian model for frame representation. IEEE Transactions on Signal Processing. 2010;18(11):5560–5571
- . Unsupervised deconvolution of sparse spike trains using stochastic approximation. IEEE Transactions on Signal Processing. 1996;44(12):2988–2998
- . Image analysis using a dual-tree M-band wavelet transform. IEEE Transactions on Image Processing. 2006;15(8):2397–2412
- . A variational formulation for frame-based inverse problems. Inverse Problems. 2007;23(4):1495–1518
- . A nonlinear Stein based estimator for multichannel image denoising. IEEE Transactions on Signal Processing. 2008;56(8):3855–3870
- . Nested iterative algorithms for convex constrained image recovery problems. SIAM Journal on Imaging Sciences. 2009;82(2):730–762
- . A half-quadratic block-coordinate descent method for spectral estimation. Signal Processing. 2002;82(7):941–959
- . Regularized estimation of mixed spectra using a circular Gibbs–Markov model. IEE Transactions on Signal Processing. 2001;49(10):2202–2213
- . Unsupervised robust non-parametric estimation of the hemodynamic response function for any fMRI experiment. IEEE Transactions on Medical Imaging. 2003;22(10):1235–1251
- Ciuciu, P., Idier, J., Roche, A., Pallier, C., 2004. Outlier detection for robust region-based estimation of the hemodynamic response function in event-related fMRI. In: IEEE International Symposium on Biomedical Imaging, Arlington, USA, pp. 392–395.
- . Biorthogonal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics. 1992;45(5):485–560
- . Entropy-based algorithms for best basis selection. IEEE Transactions on Information Theory. 1992;38(2):713–718
- . A Douglas–Rachford splitting approach to nonsmooth convex variational signal recovery. IEEE Journal of Selected Topics in Signal Processing. 2007;1(1):564–574
- Combettes, P.L., Pesquet, J.-C., 2009. Proximal splitting methods in signal processing. In: Bauschke, H. H., Burachik, R., Combettes, P.L., Elser, V., Luke, D.R., Wolkowicz, H. (Eds.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, New York. [Chapter 1].
- . Signal recovery by proximal forward–backward splitting. Multiscale Modeling and Simulation. 2005;4(4):1168–1200
- . Diffusion tensor magnetic resonance image regularization. Medical Image Analysis. 2004;8(1):47–67
- . Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics. 1988;41(7):909–996
- . Ten Lectures on Wavelets. Philadelphia, USA: Society for Industrial and Applied Mathematics; 1992;
- . Variational image restoration by means of wavelets: simultaneous decomposition, deblurring and denoising. Applied and Computational Harmonic Analysis. 2005;19(1):1–16
- . An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics. 2004;57(11):1413–1457
- . Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B. 1977;39:1–38
- . Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association. 1995;90(432):1200–1224
- . Convex Analysis and Variational Problems. Philadelphia: Society for Industrial and Applied Mathematics; 1999;
- . Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization. Applied and Computational Harmonic Analysis. 2007;23(3):346–367
- . Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates. Journal of Optimization Theory and Applications. 1987;52(2):209–215
- . Wavelet encoding for 3D gradient-echo MR imaging. Magnetic Resonance in Medicine. 1996;36(4):613–619
- Griesbaum, A., Kaltenbacher, B., Vexler, B., 2008. Efficient computation of the Tikhonov regularization parameter by goal-oriented adaptive discretization. Inverse Problems 24 (2), 20 pp.
- . Generalized autocalibrating partially parallel acquisitions GRAPPA. Magnetic Resonance in Medicine. 2002;47(6):1202–1210
- . Zur theorie der orthogonalen funktionen systeme. Mathematische Annalen. 1910;69:331–371
- Harikumar, G., Bresler, Y., 1996. A new algorithm for computing sparse solutions to linear inverse problems. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, Atlanta, USA, pp. 1331–1334.
- . VD AUTO-SMASH imaging. Magnetic Resonance in Medicine. 2001;45(6):1066–1074
- . Multivariate Bayes wavelet shrinkage and applications. Journal of Applied Statistics. 2005;32(5):529–542
- . A tour of accelerated parallel MR imaging from a linear systems perspective. Concepts in Magnetic Resonance. 2005;27A(1):17–37
- . AUTO-SMASH: a self-calibrating technique for SMASH imaging. Magnetic Resonance Materials in Physics, Biology and Medicine. 1998;7(1):42–54
- Jalobeanu, A., Blanc-Féraud, L., Zerubia, J., 2002. Hyperparameter estimation for satellite image restoration using a MCMC maximum likelihood method. Pattern Recognition 35 (2).
- . Total variation based convex filters for medical imaging. Applied Mathematics and Computation. 2003;139(1):101–119
- . Bayesian wavelet denoising: Besov priors and non-Gaussian noises. Signal Processing. 2001;81(1):55–67
- Liang, Z.P., Bammer, R., Ji, J., Pelc, N.J., Glover, G.H., 2002. Making better SENSE: wavelet denoising, Tikhonov regularization, and total least squares. In: International Society for Magnetic Resonance in Medicine, Hawaı¨, USA, p. 2388.
- . Accelerating sensitivity encoding using compressed sensing. In: IEEE Engineering in Medicine and Biology. Canada: Vancouver; 2008;p. 1667–1670
- . A wavelet-based approximation of surface coil sensitivity profiles for correction of image intensity inhomogeneity and parallel imaging reconstruction. Human Brain Mapping. 2003;19(2):96–111
- . Parallel imaging reconstruction using automatic regularization. Magnetic Resonance in Medicine. 2004;51(3):559–567
- Liu, L.Y.B., Zou, Y.M., 2008. SparseSENSE: application of compressed sensing in parallel MRI. In: IEEE International Conference on Technology and Applications in Biomedicine, Shenzhen, China, pp. 127–130.
- Liu, B., Ying, L., Steckner, M., Xie, J., Sheng, J., 2007. Regularized SENSE reconstruction using iteratively refined total variation method. In: IEEE ISBI, Washington, DC, USA, pp. 121–124.
- . Regularized sensitivity encoding (SENSE) reconstruction using Bregman iterations. Magnetic Resonance in Medicine. 2008;61(1):145–152
- Lustig, M., Donoho, D.L., Pauly, J.M., 2007. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine 58 (6), 1182–1195.
- . Joint detection-estimation of brain activity in functional MRI: a multichannel deconvolution solution. IEEE Transactions on Signal Processing. 2005;53(9):3488–3502
- . A fully Bayesian approach to the parcel-based detection-estimation of brain activity in fMRI. Neuroimage. 2008;41(3):941–969
- . A Wavelet Tour of Signal Processing. New York: Academic Press; 1999;
- . Wavelet-based estimation of a semiparametric generalized linear model of fMRI time-series. IEEE Transactions on Medical Imaging. 2003;22(3):315–322
- . Characterization of visually similar diffuse diseases from B-scan liver images using nonseparable wavelet transform. IEEE Transactions on Medical Imaging. 1998;17(4):541–549
- . Proximité et dualité dans un espace hilbertien. Bulletin de la Société Mathématique de France. 1965;93:273–299
- . MCMC methods in wavelet shrinkage: non-equally spaced regression, density and spectral density estimation. Bayesian Inference in Wavelet-Based Models. 1999;187–202
- Olson, T., 1992. Limited-angle tomography via multiresolution analysis and oversampling. In: IEEE International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, USA, pp. 204–216.
- . A review of wavelet denoising in MRI and ultrasound brain imaging. Current Medical Imaging Reviews. 2006;2(2):247–260
- . SENSE: sensitivity encoding for fast MRI. Magnetic Resonance in Medicine. 1999;42(5):952–962
- . Advances in sensitivity encoding with arbitrary k-space trajectories. Magnetic Resonance in Medicine. 2001;46(4):638–651
- . High temporal resolution functional MRI using parallel echo volume imaging. Magnetic Resonance Imaging. 2008;27(4):744–753
- . Fast and stable Bayesian image expansion using sparse edge priors. IEEE Transactions on Image Processing. 2007;16(4):1073–1084
- . Bayesian parallel imaging with edge-preserving priors. Magnetic Resonance in Medicine. 2007;57(1):8–21
- . Monte-Carlo SURE: a black-box optimization of regularization parameters for general denoising algorithms. IEEE Transactions on Image Processing. 2008;17(9):1540–1554
- . Linear inverse problems in imaging. IEEE Signal Processing Magazine. 2008;25(2):84–99
- Risser, L., Vincent, T., Forbes, F., Idier, J., Ciuciu, P., 2010. Min–max extrapolation scheme for fast estimation of 3D Potts field partition functions. Application to the joint detection-estimation of brain activity in fMRI. Journal of Signal Processing Systems 60 (1).
- . Statistical analysis of functional MRI data in the wavelet domain. IEEE Transactions on Medical Imaging. 1998;17(2):142–154
- . ML parameter estimation for Markov random fields with applications to Bayesian tomography. IEEE Transactions on Image Processing. 1998;7(7):1029–1044
- . Image Analysis and Mathematical Morphology. London: Academic Press; 1982;
- . Automatic estimation of the noise variance from the histogram of a magnetic resonance image. Physics in Medicine and Biology. 2007;52(5):1335–1348
- . Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magnetic Resonance in Medicine. 1999;38(4):591–603
- . Theory of regular M-band wavelet bases. IEEE Transactions on Signal Processing. 1993;41(12):3497–3511
- . Tikhonov regularization of incorrectly posed problems. Soviet Mathematics Doklady. 1963;4:1624–1627
- . Just relax: convex programming methods for identifying sparse signals in noise. IEEE Transactions on Information Theory. 2006;52(3):1030–1051
- . Integrated wavelet processing and spatial statistical testing of fMRI data. Neuroimage. 2004;23(4):1472–1485
- . Surfing the brain – an overview of wavelet-based techniques for fMRI data analysis. IEEE Engineering in Medicine and Biology Magazine. 2006;25(2):65–78
- . Spatially adaptive mixture modeling for analysis of fMRI time series. IEEE Transactions on Medical Imaging. 2010;29(4):1059–1074
- . A fast thresholded Landweber algorithm for wavelet-regularized multidimensional deconvolutions. IEEE Transactions on Image Processing. 2008;17(4):539–549
- Wang, Y., Haomin, Z., 2006. Total variation wavelet-based medical image denoising. International Journal of Biomedical Imaging 2006, 1–6.
- . Filtering noise from images with wavelet transforms. Magnetic Resonance in Medicine. 1991;21(2):288–295
- . Cardiac real-time imaging using SENSE. Magnetic Resonance in Medicine. 2000;43(2):177–184
- . Specific coil design for SENSE: a six-element cardiac array. Magnetic Resonance in Medicine. 2001;45(3):495–504
- . Dynamic tracking in interventional MRI using wavelet-encoded gradient-echo sequences. IEEE Transactions on Medical Imaging. 1998;17(5):803–809
- Ying, L., Xu, D., Liang, Z.-P., 2004. On Tikhonov regularization for image reconstruction in parallel MRI. In: IEEE Engineering in Medicine and Biology Society, San Francisco, USA, pp. 1056–1059.
- . A statistical approach to SENSE reconstruction with arbitrary trajectories. Magnetic Resonance in Medicine. 2008;60(2):414–421
- . Highly parallel volumetric imaging with a 32-element RF coil array. Magnetic Resonance in Medicine. 2004;52(4):869–877
- . Compressed sensing with quantized measurements. IEEE Signal Processing Letters. 2009;17(2):149–152
☆ Part of this work was presented at the ISBI conference in 2008 (Chaâri et al., 2008).
PII: S1361-8415(10)00105-2
doi: 10.1016/j.media.2010.08.001
© 2010 Elsevier B.V. All rights reserved.
« Previous
Next »
Medical Image Analysis
Volume 15, Issue 2
, Pages 185-201
, April 2011
