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## Article Calibrationless Parallel Magnetic Resonance Imaging: A Joint Sparsity Model (2013)

Citations: | 1 - 0 self |

### Citations

535 | Sparse MRI: The application of compressed sensing for rapid mr imaging,”
- Lustig, Donoho, et al.
- 2007
(Show Context)
Citation Context ... of K-space samples forseach coil is less than the size of the image to be reconstructed. Thus, the reconstruction problem issunder-determined. Following the works in CS based MR image reconstruction =-=[12]-=-, one cansreconstruct the individual coil images separately by exploiting their sparsity in some transformsdomain, i.e., each of the images can be reconstructed by solving,s(2)swhere Ψ is the wavelet ... |

360 | Probing the Pareto frontier for basis pursuit solutions
- Berg, Friedlander
(Show Context)
Citation Context ... analysis prior yields better resultssthan the synthesis prior. Both of the analysis and the synthesis prior formulations can either be convexsor non-convex. The Spectral Projected Gradient algorithm =-=[8]-=- can solve the convex synthesis priorsproblem efficiently. There is no efficient algorithm to solve the analysis prior problem. In the past, itshas been found that for both synthesis and analysis prio... |

264 | Sparse solutions to linear inverse problems with multiple measurement vectors
- Cotter, Rao, et al.
- 2005
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Citation Context ... ε is the variance of noise multiplied by the length of the transformsvector and the number of receiver coils (C in our case).sThe values of the inner (l2) and outer (lp) norms have been suggested in =-=[13]-=-. The choice of suchsvalues for the norms can be understood intuitively. The inner l2-norm over the rows enforces non-zerosvalues on all the elements of the row vector whereas the outer lp-norm enforc... |

102 | Simultaneous acquisition of spatial harmonics (SMASH); fast imaging with rf coils,”
- Sodickson, Manning
- 1997
(Show Context)
Citation Context ...ir field of view; these sensitivity profiles are not accurately known beforehand.sIn the past, all pMRI techniques required the sensitivity profile to be estimated either explicitlys(SENSE [1], SMASH =-=[2]-=-) or implicitly (GRAPPA [3,4], SPIRiT [5]). All the aforementioned methodssassume that the sensitivity maps are smooth and hence have a compact support in the Fourier domain.sThus, while acquiring the... |

78 | Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization
- Trzasko, Manduca
(Show Context)
Citation Context ... n n C z z z zX Z z z 2 2, minssubject to ,s0 1 p p FX X Y F X p 2 2, minssubject to ,s0 1 p T p FZ Z Y F Z p TX Z Sensors 2013, 13 16719s=-=(9)-=-sThe analysis and the synthesis priors yield same results for orthogonal transforms but differentsresults for redundant tight-frames.s2.2. Connection with Previous WorkssIn a recent work, a method sim... |

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.
(Show Context)
Citation Context ...ines in the phase encoding direction. This is widely used samplingsmethod for parallel MRI. Radial sampling is one of the fastest sampling methods [28,29] and has beenspreviously used in parallel MRI =-=[30]-=-. For the brain image, the acceleration factor of 4 is used, for thesShepp-Logan phantom, acceleration factor of 6 is used for both Variable Density random sampling andsradial sampling.sFigure 8. (a) ... |

58 | Wavelet theory demystified.
- Unser, Blu
- 2003
(Show Context)
Citation Context ...uch signals, and the vanishing moments of wavelets.sSensors 2013, 13 16721sA precise way of describing this is that the action of any wavelet ψ(t) can be regarded as a ―smoothed‖sderivative operation =-=[21]-=-, namely:s(12)swhere the order of differentiation n is precisely the number of vanishing moments of ψ(t). Here φ(t) isssome low-pass function matched with the wavelet ψ(t). As a result, large wavelet ... |

51 | Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data
- Chartrand
- 2009
(Show Context)
Citation Context ...terations. Sixty iterations were used tosgenerate the final image.sFor our non-convex formulation, we found that the best results were obtained for p = 0.5 (this valuesof p has also been suggested in =-=[11]-=-). The quantitative reconstruction results are shown in Table 1.sNormalized Mean Squared Error (NMSE) is the metric used for evaluation. The best reconstructions(lowest error) results are shown in bol... |

47 | Signal restoration with overcomplete wavelet transforms: Comparison of analysis and synthesis priors
- Selesnick, Figueiredo
- 2009
(Show Context)
Citation Context ...the modulated signals have high valued coefficients at the same positions; but thesactual values at these positions are varying.s4. Optimization AlgorithmssThe Majorization-Minimization (MM) approach =-=[23]-=- is employed to derive solution to thesfollowing problems:sSynthesis:s(14a)sAnalysis:s(14b)sFor the synthesis prior X = Z, H = FΩΨ and for analysis prior, A = Ψ and H = FΩ.sInstead of solving the afor... |

38 |
SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space
- Lustig, Pauly
(Show Context)
Citation Context ...les are not accurately known beforehand.sIn the past, all pMRI techniques required the sensitivity profile to be estimated either explicitlys(SENSE [1], SMASH [2]) or implicitly (GRAPPA [3,4], SPIRiT =-=[5]-=-). All the aforementioned methodssassume that the sensitivity maps are smooth and hence have a compact support in the Fourier domain.sThus, while acquiring the MRI scan, the centre of the K-space is d... |

25 | Joint image reconstruction and sensitivity estimation in SENSE (JSENSE). Magn Reson Med 2007; 57: 1196–1202
- Ying, Sheng
(Show Context)
Citation Context ...latedssignal m(t)f(t).sFor parallel MRI reconstruction, the sensitivity map modulates the underlying signal (MR image).sThe sensitivity maps are assumed to be smooth and can be modeled as polynomials =-=[22]-=-. The design ofsthe scanner ensures that there are no singularities in the sensitivity maps; physically this ensures thatseach receiver coil has information about the full image. Based on the discussi... |

21 | Accelerating SENSE using compressed sensing
- Liang, Liu, et al.
- 2009
(Show Context)
Citation Context ...nscombined by the sum-of-squares approach (used in GRAPPA and SPIRiT). We compare our methodswith state-of-the-art parallel MRI reconstruction methods; two of these are calibrated techniques—CSsSENSE =-=[7]-=- and SPIRiT and the other two are calibration free methods—DCS and SAKE. Oursproposed method outperforms all of them.sMathematically the sensitivity encoding of MR images is a modulation operation whe... |

17 | Combination of compressed sensing and parallel imaging for highly accelerated first-pass cardiac perfusion - Otazo, Kim, et al. - 2010 |

13 | New insights into one-norm solvers from the pareto curve
- Hennenfent, Berg, et al.
- 2008
(Show Context)
Citation Context ...constrained problem by iteratively solving a series of unconstrained problems withsdecreasing values of λ. Such cooling techniques are successful since the Pareto curve for the saidsproblem is smooth =-=[24]-=-; similar cooling algorithms have been successfully used in the past for solvingsCompressed Sensing problems [24–26].s4.1. Solving the Unconstrained ProblemssWe solve this problem by the Majorization-... |

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 ...he K-space is sparselyssampled by randomly omitting lines in the phase encoding direction. This is widely used samplingsmethod for parallel MRI. Radial sampling is one of the fastest sampling methods =-=[28,29]-=- and has beenspreviously used in parallel MRI [30]. For the brain image, the acceleration factor of 4 is used, for thesShepp-Logan phantom, acceleration factor of 6 is used for both Variable Density r... |

11 | An algorithm for sparse MRI reconstruction by Schatten p-norm minimization. Magn Reson Imaging 2011;29:408–17 - Majumdar, RK |

7 |
sensitivity encoding for fast
- Med
- 1999
(Show Context)
Citation Context ...ding onstheir field of view; these sensitivity profiles are not accurately known beforehand.sIn the past, all pMRI techniques required the sensitivity profile to be estimated either explicitlys(SENSE =-=[1]-=-, SMASH [2]) or implicitly (GRAPPA [3,4], SPIRiT [5]). All the aforementioned methodssassume that the sensitivity maps are smooth and hence have a compact support in the Fourier domain.sThus, while ac... |

6 | Ying L. Accelerating SENSE using distributed compressed sensing - Liang, KF, et al. - 2008 |

4 |
The effect of reconstruction and acquisition parameters for GRAPPA-based parallel imaging on the image quality,” Magn
- Bauer, Markl, et al.
- 2011
(Show Context)
Citation Context ...uned and the best results aresreported. The GRAPPA formulation has been studied in detail, and there is a study which claims tosoffer insights regarding the choice of GRAPPA reconstruction parameters =-=[6]-=-; however for otherstechniques such as SPIRiT and CS SENSE, there are no detailed studies on parameter tuning.sIn this work, we improve upon our previous work on calibration free reconstruction (seesS... |

4 |
Under-determined non-Cartesian MR reconstruction
- Majumdar, Ward
(Show Context)
Citation Context ...2.2. Connection with Previous WorkssIn a recent work, a method similar to ours has been proposed [14]. The individual coil images weresreconstructed by the solving the following optimization problem:s=-=(10)-=-sThis is actually the unconstrained version of our prior analysis problem Equation (6) with p = 1.sThe algorithm proposed in [14] to solve Equation (10) is ad hoc and is not derived from anysoptimizat... |

4 | Distributed compressed sensing for accelerated MRI - Otazo, Sodickson - 2009 |

4 | On NUFFT-based gridding for non-Cartesian MRI
- Fessler
- 2007
(Show Context)
Citation Context ... two calibration freestechniques DCS [14] and SAKE [19]. For our proposed method, the mapping from non-CartesiansK-space to the Cartesian image space is the Non-Uniform Fast Fourier Transform (NUFFT) =-=[31,32]-=-.sFor CS SENSE the sensitivity profiles are estimated in the fashion shown in [30]. A Kaiser-Besselswindow at the center of the K-space is densely sampled, from which a low resolution image for eachsc... |

3 |
Calibration-less multi-coil MR image reconstruction. Magn Reson Imag 2012;30:1032–1045
- Majumdar, RK
(Show Context)
Citation Context ...refore are notscalibration free techniques. The approach proposed here and those in the aforementioned studiessare different.sPrior to this work, we proposed a naive version of the CaLM MRI technique =-=[18]-=-. There in, insteadsof stacking the coil images/transform coefficients as columns of a MMV matrix (as done here), weresconcatenated to a long vector, i.e., instead of Equation (4) the data acquisition... |

3 | Compressive Color Imaging with Group Sparsity on Analysis - Majumdar, Ward - 2010 |

3 |
Mr coronary vessel wall imaging: comparison between radial and spiral k-space sampling
- Katoh, Spuentrup, et al.
(Show Context)
Citation Context ...he K-space is sparselyssampled by randomly omitting lines in the phase encoding direction. This is widely used samplingsmethod for parallel MRI. Radial sampling is one of the fastest sampling methods =-=[28,29]-=- and has beenspreviously used in parallel MRI [30]. For the brain image, the acceleration factor of 4 is used, for thesShepp-Logan phantom, acceleration factor of 6 is used for both Variable Density r... |

2 |
Accelerated noncontrast-enhanced pulmonary vein MRA with distributed compressed sensing
- Akcakaya, Hu, et al.
(Show Context)
Citation Context ... priors yield same results for orthogonal transforms but differentsresults for redundant tight-frames.s2.2. Connection with Previous WorkssIn a recent work, a method similar to ours has been proposed =-=[14]-=-. The individual coil images weresreconstructed by the solving the following optimization problem:s(10)sThis is actually the unconstrained version of our prior analysis problem Equation (6) with p = 1... |

2 | On the choice of compressed sensing priors: an experimental study,” - Majumdar, Ward - 2012 |

1 |
Calibrationless parallel MRI using CLEAR
- Trzasko, Manduca
(Show Context)
Citation Context ...s work issa more generalized, thorough and in-depth extension to the prior studies.sDuring the review, one of the reviewers pointed out to a few recent studies that do not require ascalibration stage =-=[19,20]-=-. The formulation in [19] can be understood from the following diagrams(Figure 3)—overlapping blocks from all the channels are vectorized and stacked as columns of asHankel matrix A.sFigure 3. Formati... |

1 |
Iterative image reconstruction for PROPELLER-MRI using the nonuniform fast fourier transform
- Tamhane, Anastasio, et al.
(Show Context)
Citation Context ... two calibration freestechniques DCS [14] and SAKE [19]. For our proposed method, the mapping from non-CartesiansK-space to the Cartesian image space is the Non-Uniform Fast Fourier Transform (NUFFT) =-=[31,32]-=-.sFor CS SENSE the sensitivity profiles are estimated in the fashion shown in [30]. A Kaiser-Besselswindow at the center of the K-space is densely sampled, from which a low resolution image for eachsc... |