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## Nuclear norm-regularized SENSE reconstruction (2012)

Venue: | Magnetic Reson Imaging |

Citations: | 4 - 0 self |

### Citations

3609 | Compressed sensing
- Donoho
- 2006
(Show Context)
Citation Context ...tunately this is a NP hard problem and thus can not be solved efficiently. Theoretical studies insCS showed that instead of solving the NP hard l0-norm, its convex envelope, the l1-norm could besused =-=[13, 14]-=-,s1 2 ˆ minssuch thatsx x Wx y RFx s(9)sThis is a convex problem, and can be solved by quadratic programming. As mentioned earlier, theresare state-of-the-art algorithms [7-9] to solve the l1 mi... |

2621 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Candès, Romberg, et al.
- 2006
(Show Context)
Citation Context ...tunately this is a NP hard problem and thus can not be solved efficiently. Theoretical studies insCS showed that instead of solving the NP hard l0-norm, its convex envelope, the l1-norm could besused =-=[13, 14]-=-,s1 2 ˆ minssuch thatsx x Wx y RFx s(9)sThis is a convex problem, and can be solved by quadratic programming. As mentioned earlier, theresare state-of-the-art algorithms [7-9] to solve the l1 mi... |

562 | Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
- Recht, Fazel, et al.
- 2010
(Show Context)
Citation Context ...minimization showedsthat as long as the number of samples is sufficiently large compared to the number of degrees ofsfreedom of the image matrix, it is possible to recover the image matrix accurately =-=[18, 19]-=-.sIn order to recover a matrix by exploiting its rank deficiency, the following optimization problemsneeds to be solved,s2 ˆ mins( ) such thatsx x rank X y RFx s(11)sHere X is the image in matri... |

537 | Sparse MRI: The application of compressed sensing for rapid MR imaging
- Lustig, Donoho, et al.
- 2007
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Citation Context ...g (23%), (c) Gaussian under-sampling (20%)sFor the CS based reconstruction, it is claimed that the best image reconstruction is obtained if ascombination of wavelet and TV regularization (10) is used =-=[11, 6, 17]-=-. When used in the SENSEsframework, the optimization takes the following form,s1 2 ˆ min + ( ) such thatsx x Wx TV x y Ex s(14)sUnfortunately there is no efficient algorithm to solve the constr... |

365 | Probing the Pareto frontier for basis pursuit solutions - Berg, Friedlander - 2008 |

169 | NESTA: A fast and accurate first-order method for sparse recovery
- Becker, Bobin, et al.
(Show Context)
Citation Context ...n. Thus, from the perspective of optimization theory, solving (5) is moresoptimal than solving (4). Fortunately there are state-of-the-art fast algorithms to solve (5) – SPGL1s[7], C-SALSA [8], NESTA =-=[9]-=-.sIn a recent work [10], we showed that instead of reconstructing single coil MR images from partiallyssampled K-space data by CS based methods such as [11, 12], one could reconstruct them by nuclears... |

165 |
Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature
- Lauterbur
- 1973
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Citation Context ...curacy from our proposed method is the same as the l1-normsregularized SENSE, but the advantage of our method is that it is about an order of magnitude faster.s1. INTRODUCTIONsMulti-coil parallel MRI =-=[1]-=- is a hardware based acceleration technique for fast acquisition of K-spacessamples. Instead of employing a single receiver coil for acquiring the full K-space data, multiple coilsspartially sample th... |

78 | Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization
- Trzasko, Manduca
(Show Context)
Citation Context ...to solve (5) – SPGL1s[7], C-SALSA [8], NESTA [9].sIn a recent work [10], we showed that instead of reconstructing single coil MR images from partiallyssampled K-space data by CS based methods such as =-=[11, 12]-=-, one could reconstruct them by nuclearsnorm minimization. The main difference between our previous work and CS based methods is that,swhile the CS based methods utilise the fact that the MR image is ... |

67 |
Undersampled radial MRI with multiple coils Iterative image reconstruction using a total variation constraint. Magn Reson Med 2007;57:1086–98
- KT, Uecker, et al.
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Citation Context ...d is radial sampling (Fig 3b); it is a non-Cartesian sampling method but is one of thesfastest possible [25]. Radial sampling has been used with SENSE like reconstruction for parallel MRIsin the past =-=[26]-=-. The third method is sampling from a Gaussian distribution (Fig. 3c). In practice itsmay not be efficient to sample points from the K-space following a Gaussian distribution, butsprevious works in CS... |

57 |
SENSE: Sensitivity encoding for fast
- Pruessmann, Weiger, et al.
- 1999
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Citation Context ...chers have proposed a plethora of multi-coil parallel MR imagesreconstruction methods. In the limited scope of this work, it is not possible to discuss them evensbriefly. SENSitivity Encoding (SENSE) =-=[2]-=- is physically and mathematically the most optimalsparallel image reconstruction technique when the sensitivity profiles of the different coils are known.sSENSE is by far the most widely used parallel... |

51 | Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data - Chartrand - 2009 |

49 | An ecient algorithm for compressed mr imaging using total variation and wavelets.
- Ma, Yin, et al.
- 2008
(Show Context)
Citation Context ...ints from the K-space following a Gaussian distribution, butsprevious works in CS based MR image reconstruction have reported results based on samplingstrajectories based on probability distributions =-=[17, 27, 28]-=-.s(a)s(b)s(c)sFig. 3. (a) Periodic under-sampling (26%) , (b) Radial sampling (23%), (c) Gaussian under-sampling (20%)sFor the CS based reconstruction, it is claimed that the best image reconstruction... |

38 |
SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space
- Lustig, Pauly
(Show Context)
Citation Context ...d out on real 8 coil brain data (Fig. 1) and synthesized phantom data (Fig.s2). The data had been obtained from [23]. To find out the parameters used by the scanner, we requeststhe reader to refer to =-=[24]-=-. The complete data consists of fully sampled K-space for all the 8 coils fromswhich the corresponding coil images can be reconstructed by inverse 2D FFT. The images from allsthe coils were combined t... |

36 | Necessary and sufficient conditions for success of the nuclear norm heuristic for rank minimization.
- Recht, Xu, et al.
- 2008
(Show Context)
Citation Context ...minimization showedsthat as long as the number of samples is sufficiently large compared to the number of degrees ofsfreedom of the image matrix, it is possible to recover the image matrix accurately =-=[18, 19]-=-.sIn order to recover a matrix by exploiting its rank deficiency, the following optimization problemsneeds to be solved,s2 ˆ mins( ) such thatsx x rank X y RFx s(11)sHere X is the image in matri... |

21 | Accelerating SENSE using compressed sensing
- Liang, Liu, et al.
- 2009
(Show Context)
Citation Context ...er, from the perspective of optimization theory, the meaning of this free parametersis not readily discernible. A more theoretical approach to SENSE regularization is based onsCompressed Sensing (CS) =-=[6]-=-. Instead of solving an unconstrained optimization problem, it proposessa constrained problem of the following form,s1 2 ˆ minssuch thatsx x Wx y Ex s(5)swhere W represents the wavelet transform... |

17 | Rapid MR imaging with compressed sensing and randomly under-sampled 3DFT trajectories
- Lustig, Donoho, et al.
- 2006
(Show Context)
Citation Context ...ints from the K-space following a Gaussian distribution, butsprevious works in CS based MR image reconstruction have reported results based on samplingstrajectories based on probability distributions =-=[17, 27, 28]-=-.s(a)s(b)s(c)sFig. 3. (a) Periodic under-sampling (26%) , (b) Radial sampling (23%), (c) Gaussian under-sampling (20%)sFor the CS based reconstruction, it is claimed that the best image reconstruction... |

14 | A fast algorithm for the constrained formulation of compressive image reconstruction and other linear inverse problems,” Submitted, Available at http://arxiv.org/abs/0909.3947v1
- Afonso, Bioucas-Dias, et al.
- 2009
(Show Context)
Citation Context ...ise is known. Thus, from the perspective of optimization theory, solving (5) is moresoptimal than solving (4). Fortunately there are state-of-the-art fast algorithms to solve (5) – SPGL1s[7], C-SALSA =-=[8]-=-, NESTA [9].sIn a recent work [10], we showed that instead of reconstructing single coil MR images from partiallyssampled K-space data by CS based methods such as [11, 12], one could reconstruct them ... |

12 |
Magnetic resonance imaging in real time: advances using radial FLASH. J Magn Reson Imaging 2010;31:101–109
- Zhang, KT, et al.
(Show Context)
Citation Context ...s the traditionally the most widely used method in multi-coil data acquisition. Ourssecond method is radial sampling (Fig 3b); it is a non-Cartesian sampling method but is one of thesfastest possible =-=[25]-=-. Radial sampling has been used with SENSE like reconstruction for parallel MRIsin the past [26]. The third method is sampling from a Gaussian distribution (Fig. 3c). In practice itsmay not be efficie... |

11 |
An algorithm for sparse MRI reconstruction by Schatten p-norm minimization. Magn Reson Imaging 2011;29:408–17
- Majumdar, RK
(Show Context)
Citation Context ...pective of optimization theory, solving (5) is moresoptimal than solving (4). Fortunately there are state-of-the-art fast algorithms to solve (5) – SPGL1s[7], C-SALSA [8], NESTA [9].sIn a recent work =-=[10]-=-, we showed that instead of reconstructing single coil MR images from partiallyssampled K-space data by CS based methods such as [11, 12], one could reconstruct them by nuclearsnorm minimization. The ... |

7 |
2007, ‘Noise distribution in SENSE- and GRAPPAreconstructed images: a computer simulation study’. Magnetic Resonance Imaging 25
- Thunberg, Zetterberg
- 1956
(Show Context)
Citation Context ...ed on solving a least-squares problem (3). It is easysto see that the least-squares problem does not have any inherent denoising capability. Images obtainedsby the traditional SENSE method were noisy =-=[21]-=-. Regularised SENSE reconstruction (4) yieldssbetter reconstruction results. This is because the regularization term incorporates some priorsinformation regarding the image, e.g. in TV regularization ... |

6 | Nonconvex compressive sensing and reconstruction of gradient-sparse images: random vs. tomographic Fourier sampling
- Chartrand
- 2008
(Show Context)
Citation Context ...ints from the K-space following a Gaussian distribution, butsprevious works in CS based MR image reconstruction have reported results based on samplingstrajectories based on probability distributions =-=[17, 27, 28]-=-.s(a)s(b)s(c)sFig. 3. (a) Periodic under-sampling (26%) , (b) Radial sampling (23%), (c) Gaussian under-sampling (20%)sFor the CS based reconstruction, it is claimed that the best image reconstruction... |

4 | On NUFFT-based gridding for non-Cartesian MRI
- Fessler
- 2007
(Show Context)
Citation Context ...econstruction. The best results were obtained for ComplexsDualtree wavelets. For non-Cartesian radial sampling, the mapping from the image space to thesFrequency space is performed by Non Uniform FFT =-=[29]-=-.sQuantitatively the reconstruction accuracy is determined in terms of Normalized Mean Squared Errors(NMSE). The NMSE’s for various sampling schemes are shown in Table 1.sTable 1. NMSE from SparSENSE ... |

2 |
Compressed extrapolation
- Lin, Herrmann
- 2007
(Show Context)
Citation Context ...nner loop solves (13).sThe outer loop progressively reduces the value of λ till the solution converges tos2 y Ex . Suchsa cooling technique is guaranteed to converge and has been used previously =-=[22]-=- to solve l1sminimization in geophysical CS problems.s4. EXPERIMENTAL EVALUATIONsThe experiments were carried out on real 8 coil brain data (Fig. 1) and synthesized phantom data (Fig.s2). The data had... |

1 | Three dimension double inversion recovery gray matter imaging using compressed sensing - Ghoa, Nama, et al. - 2010 |