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## Sparse Models and Multiple Receivers (2012)

### Citations

7445 | Convex Optimization
- Boyd, Vandenberghe
- 2004
(Show Context)
Citation Context ...is therefore convex. This convex relaxation is popular due to the wide variety of efficient techniques for solving `1-regularized problems, and the global convergence guarantees provided by convexity =-=[10]-=-. A wide variety of nonconvex relaxations exist as well. The `pp (0 < p < 1) “norms” [23] are popular: ‖w‖pp = N−1∑ n=0 |w[n]|p. (3.3) The unit balls for the `0, `1, and ` p p penalty functions are de... |

4202 | Regression shrinkage and selection via the lasso
- Tibshirani
- 1996
(Show Context)
Citation Context ...‖1}. (3.26) This problem is most efficiently solved in the log domain: ŷ = minimize y 1 2σ2 ‖d−Kay‖22 + λ‖Ψy‖1. (3.27) The above formulation is not unlike basis pursuit denoising (BPDN) or the Lasso =-=[89]-=-, and can be solved using any of a wide variety of iterative techniques developed for either framework [61, 92, 101, 36]. The extension to multiple jointly sparse measure54 ment vectors is similar: Ŷ... |

3609 | Compressed sensing
- Donoho
- 1996
(Show Context)
Citation Context ... for the high acceleration levels we would like to attain. Another technique for reconstructing images from undersampled data called compressed sensing (CS) emerged in the signal processing community =-=[18, 16, 20, 27]-=-. Compressed sensing takes advantage of the sparsity or compressibility of an appropriate representation or transform of the desired image. While not specific to MRI, MRI is a widely suitable candidat... |

3310 | Numerical optimization
- Nocedal, Wright
- 2006
(Show Context)
Citation Context ...fter which any unconstrained optimization method can be used. Augmented or penalized Lagrangian methods produce a series of unconstrained problems that asymptotically approach the constrained problem =-=[69]-=-. A similar method, Bregman iteration, has been proposed for compressed sensing and related problems [102]. In this work, we take advantage of the simple form of the observation matrix Ka to re-expres... |

2621 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Candès, Romberg, et al.
- 2006
(Show Context)
Citation Context ... for the high acceleration levels we would like to attain. Another technique for reconstructing images from undersampled data called compressed sensing (CS) emerged in the signal processing community =-=[18, 16, 20, 27]-=-. Compressed sensing takes advantage of the sparsity or compressibility of an appropriate representation or transform of the desired image. While not specific to MRI, MRI is a widely suitable candidat... |

1575 |
Fundamentals of Statistical Signal Processing: Estimation theory. Englewood Cliffs NJ
- Kay
- 1993
(Show Context)
Citation Context ... σ2. Mathematically, d = Kay + n. (3.13) Without additional information about the signal, the minimum mean squared error (MMSE) optimal linear estimator for y is the maximum likelihood (ML) estimator =-=[46]-=-, which is also the least-squares solution of Equation (3.13), ŷ = (KTaKa) −1KTad. (3.14) Now, suppose the signal y is known to be zero-mean, approximately sparse, and uncorrelated with the noise. In... |

1505 | Near optimal signal recovery from random projections: Universal encoding strategies?,”
- Candès, Tao
- 2006
(Show Context)
Citation Context ... for the high acceleration levels we would like to attain. Another technique for reconstructing images from undersampled data called compressed sensing (CS) emerged in the signal processing community =-=[18, 16, 20, 27]-=-. Compressed sensing takes advantage of the sparsity or compressibility of an appropriate representation or transform of the desired image. While not specific to MRI, MRI is a widely suitable candidat... |

1398 | Decoding by linear programming
- Candès, Tao
(Show Context)
Citation Context ...bservation matrices for CS include a random matrix with iid Gaussian entries and a randomly chosen subset of a unitary matrix like a DFT matrix. Conditions like the restricted isometry property (RIP) =-=[19]-=- and mutual coherence bounds [17] on the observation matrix can be used to assess the suitability of the matrix for CS as well as its effect on the quality of the estimated signal. Given a matrix Ka a... |

1364 | Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
- Sturm
- 1999
(Show Context)
Citation Context ...rating the nth coefficient of the sparse vectors for each column of Y. A variety of convex iterative solvers can be applied to second-order cone programs, including interior point methods like SeDuMi =-=[88]-=-. Another family of optimization problems arises when the data is noisy, or there is a least-squares term in the objective. The basis pursuit denoising problem with either the `1 norm for sparsity or ... |

1265 | Ideal spatial adaption by wavelet shrinkage
- Donoho, Johnstone
- 1994
(Show Context)
Citation Context ...l estimates of the signal mean and variance is used [51]. The global noise variance is estimated using the median absolute deviation method with the same fourlevel DWT used as a sparsifying transform =-=[28]-=-. The signal and noise statistics are measured from the combined image, and multi-channel statistics are formed using low-resolution coil sensitivity estimates S formed from the ACS lines apodized wit... |

1136 |
Methods of conjugate gradients for solving linear systems
- Hestenes, Stiefel
- 1952
(Show Context)
Citation Context ...st descent algorithm will typically move in a zigzag pattern. As an alternative, the conjugate gradient method enforces “conjugacy” between descent vectors. Technically, the conjugate gradient method =-=[42, 84]-=- describes an iterative approach to solving the linear system Ax = b for a square, symmetric matrix A with full rank; fortunately, the normal equations AHAx = AHb satisfy these conditions for leastsqu... |

928 | K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
- Aharon, Elad, et al.
- 2006
(Show Context)
Citation Context ...nstruction or during reconstruction from the acquired data [24, 80]. A training set of MR images can be decomposed into small patches, and a sparse dictionary can be learned using a method like K-SVD =-=[1]-=-. A learned dictionary captures details particular to MR images more effectively than generic transforms and preserves those details in the reconstructed image. However, use of learned dictionaries ma... |

874 | The Dantzig selector: statistical estimation when p is much larger than n, The Annals of Statistics 35
- Candes, Tao
- 2007
(Show Context)
Citation Context ...n Equation (3.33) is known as the Lasso [89]. Both of these denoising CS variants are equivalent to the MAP estimation problem with appropriate choices of λ. A related problem is the Dantzig selector =-=[21]-=-: ŷ = minimize y ‖Ψy‖1 s.t. ‖KTa (d−Kay)‖∞ ≤ (1 + t−1)σ √ 2 logN, (3.34) where t > 0 is a scalar parameter connected to the RIP constants of Ka. 3.3.2 Compressed Sensing with Joint Sparsity Compresse... |

697 | Compressive sensing
- Baraniuk
- 2007
(Show Context)
Citation Context ...nt vectors of each subset have to be weighted carefully. This approach can be employed to leverage information like persistence across scales in the wavelet transform representation of natural images =-=[2]-=-. A looser interpretation of joint sparsity, where sparse supports do not necessarily overlap significantly but have some common degree of sparsity, Bayesian multi-task compressed sensing has been app... |

652 | LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
- Paige, Saunders
- 1982
(Show Context)
Citation Context ...ar for approximately solving Equation (4.4) using only a small number of iterations (much less than a million). Since the normal equations also solve the least squares problem Ax = b, the LSQR method =-=[74, 73]-=- can also be used. However, since these iterative methods are terminated early, the LSMR method [33] is used instead because it guarantees a monotonic decrease in both the normal residual ‖AH(b−Ax)‖2,... |

648 | Brain magnetic resonance imaging with contrast dependent on blood oxygenation
- Ogawa, TM, et al.
- 1990
(Show Context)
Citation Context ...ion, increasing costs and reducing availability of the scanner. In addition, compromises in image quality such as resolution reduction are necessary for time-critical applications like functional MRI =-=[71, 6]-=-. MRI acquisition speed is limited by physiological constraints connected to the effects of spatially varying magnetic fields on the body. A spatially-varying applied 17 magnetic field can induce curr... |

537 | Sparse MRI: The application of compressed sensing for rapid MR imaging
- Lustig, Donoho, et al.
- 2007
(Show Context)
Citation Context ...ge. While not specific to MRI, MRI is a widely suitable candidate for CS due to the approximate transform sparsity of many MR images and the ability to use nearly arbitrary (random) sampling patterns =-=[57]-=-. For instance, many MR images have few edges or have simple textures representable using a small number of wavelet coefficients. CS has enabled successful 18 reconstructions of modestly accelerated M... |

513 | The contourlet transform : an efficient directional multiresolution image representation.”
- Do, Vetterli
- 2005
(Show Context)
Citation Context ...en found to be favorable to MR images. Overcomplete transforms like the curvelet, contourlet, and shearlet extend the multiresolution idea of wavelet transforms to incorporate directional information =-=[15, 26, 39]-=-. CS can also accommodate adaptive and learned dictionaries, learning the sparsifying transform using training data prior to reconstruction or during reconstruction from the acquired data [24, 80]. A ... |

481 | An Introduction to Conjugate Gradient Methods without the Agonizing Pain http://www.cs.cmu.edu/∼quake-papers/painlessconjugate-gradient.pdf
- Shewchuk
- 1994
(Show Context)
Citation Context ...st descent algorithm will typically move in a zigzag pattern. As an alternative, the conjugate gradient method enforces “conjugacy” between descent vectors. Technically, the conjugate gradient method =-=[42, 84]-=- describes an iterative approach to solving the linear system Ax = b for a square, symmetric matrix A with full rank; fortunately, the normal equations AHAx = AHb satisfy these conditions for leastsqu... |

412 |
Measuring the thickness of the human cerebral cortex from magnetic resonance images.
- Fischl, AM
- 2016
(Show Context)
Citation Context ...[22]. Moreover, magnetic resonance imaging can be used to distinguish gray and white matter in the brain, observe blood flow, and measure diagnostically valuable quantities such as cortical thickness =-=[13, 47, 32]-=-. Because of its great versatility, MRI has myriad applications in both medical research and diagnostic and perioperative clinical imaging. However, magnetic resonance imaging remains limited by the t... |

371 | Sparse reconstruction by separable approximation
- Wright, Nowak, et al.
- 2009
(Show Context)
Citation Context ...Ψy‖1. (3.27) The above formulation is not unlike basis pursuit denoising (BPDN) or the Lasso [89], and can be solved using any of a wide variety of iterative techniques developed for either framework =-=[61, 92, 101, 36]-=-. The extension to multiple jointly sparse measure54 ment vectors is similar: Ŷ = minimize Y 1 2 ‖ vec(D−KaY)‖2Λ⊗IN×N + λ‖ΨY‖1,2. (3.28) Methods for approximately solving this type of problem include... |

367 |
Constrained restoration and the recovery of discontinuities”,
- Geman, Reynolds
- 1992
(Show Context)
Citation Context ...3.28) Methods for approximately solving this type of problem include iteratively reweighted least squares (IRLS), half-quadratic minimization, and interior point methods for semi-definite programming =-=[43, 34, 104]-=-. 3.3 Compressed Sensing Reconstruction The denoising problem is presented for a complete set of observations; however, accelerated imaging provides an incomplete set of M observations (or an M ×P mat... |

365 | Probing the Pareto frontier for basis pursuit solutions
- Berg, Friedlander
- 2008
(Show Context)
Citation Context ...Ψy‖1. (3.27) The above formulation is not unlike basis pursuit denoising (BPDN) or the Lasso [89], and can be solved using any of a wide variety of iterative techniques developed for either framework =-=[61, 92, 101, 36]-=-. The extension to multiple jointly sparse measure54 ment vectors is similar: Ŷ = minimize Y 1 2 ‖ vec(D−KaY)‖2Λ⊗IN×N + λ‖ΨY‖1,2. (3.28) Methods for approximately solving this type of problem include... |

325 |
Digital image enhancement and noise filtering by use of local statistics”,
- Lee
- 1980
(Show Context)
Citation Context ...iT [98, 99]. Because the signal model statistics (mean and variance) are not known exactly, an adaptive Wiener filter-based approach that forms local estimates of the signal mean and variance is used =-=[51]-=-. The global noise variance is estimated using the median absolute deviation method with the same fourlevel DWT used as a sparsifying transform [28]. The signal and noise statistics are measured from ... |

260 |
Robust regression using iteratively reweighted leastsquares,
- Holland, Welsch
- 1977
(Show Context)
Citation Context ...3.28) Methods for approximately solving this type of problem include iteratively reweighted least squares (IRLS), half-quadratic minimization, and interior point methods for semi-definite programming =-=[43, 34, 104]-=-. 3.3 Compressed Sensing Reconstruction The denoising problem is presented for a complete set of observations; however, accelerated imaging provides an incomplete set of M observations (or an M ×P mat... |

236 | Sparsity and incoherence in compressive sampling
- Candès, Romberg
- 2007
(Show Context)
Citation Context ...e a random matrix with iid Gaussian entries and a randomly chosen subset of a unitary matrix like a DFT matrix. Conditions like the restricted isometry property (RIP) [19] and mutual coherence bounds =-=[17]-=- on the observation matrix can be used to assess the suitability of the matrix for CS as well as its effect on the quality of the estimated signal. Given a matrix Ka and sparsity level K ≤ N , the RIP... |

209 | Nonlinear image recovery with half-quadratic regularization,”
- Geman, Yang
- 1995
(Show Context)
Citation Context ...and superlinear (approaching quadratic as p → 0) convergence behavior for `1- and `p-regularized least-squares problems, respectively [25]. The closely-related approach of half-quadratic minimization =-=[34, 35]-=- actually refers to two different methods for approximating with quadratic functions separable regularizers of the form λ ∑ n φ(xn). The core idea of the first method, which is used extensively in thi... |

192 | SENSE: sensitivity encoding for fast MRI,
- Pruessmann, Weiger, et al.
- 1999
(Show Context)
Citation Context ...sing to recover complete images from fewer samples. Parallel imaging had already been used effectively to mitigate noise, and now, accelerated parallel imaging methods also enable faster acquisitions =-=[82, 87, 76, 38]-=-. Whereas conventional receiver coils have a single channel with spatially uniform sensitivity to magnetization, parallel receiver coils have multiple channels with different non-uniform magnetic sens... |

187 | Exact reconstruction of sparse signals via nonconvex minimization
- Chartrand
(Show Context)
Citation Context ...nt techniques for solving `1-regularized problems, and the global convergence guarantees provided by convexity [10]. A wide variety of nonconvex relaxations exist as well. The `pp (0 < p < 1) “norms” =-=[23]-=- are popular: ‖w‖pp = N−1∑ n=0 |w[n]|p. (3.3) The unit balls for the `0, `1, and ` p p penalty functions are depicted in two dimensions in Figure 3.1. The `0 and `p unit balls are nonconvex, while the... |

184 | Structured Variable Selection with Sparsity-Inducing Norms,” Arxiv preprint arXiv:0904.3523
- Jenatton, Audibert, et al.
- 2009
(Show Context)
Citation Context ...onal CS reconstruction problem [64]. Similar to joint sparsity, structured group sparsity accounts for knowledge of shared support across particular subsets of the set of multiple measurement vectors =-=[45]-=-. These subsets may overlap, in which case the component vectors of each subset have to be weighted carefully. This approach can be employed to leverage information like persistence across scales in t... |

181 | Quantitative robust uncertainty principles and optimally sparse decompositions
- Candes, Romberg
- 2006
(Show Context)
Citation Context |

175 | D.Donoho, and L.Ying, “Fast discrete curvelet transforms,”
- Candes
- 2006
(Show Context)
Citation Context ...en found to be favorable to MR images. Overcomplete transforms like the curvelet, contourlet, and shearlet extend the multiresolution idea of wavelet transforms to incorporate directional information =-=[15, 26, 39]-=-. CS can also accommodate adaptive and learned dictionaries, learning the sparsifying transform using training data prior to reconstruction or during reconstruction from the acquired data [24, 80]. A ... |

157 |
Messagepassing algorithms for compressed sensing
- Donoho, Maleki, et al.
- 2009
(Show Context)
Citation Context ...sed sensing-type problems utilizes a Bayesian interpretation of the compressed sensing framework and uses belief propagation over the graph of the problem to converge to a solution rather efficiently =-=[4, 29, 78]-=-. These methods rely on the large scale limiting behavior of the associated 139 graphical models to reduce the CS reconstruction problem to iterating simple scalar estimators. Thus, they scale well to... |

156 | Iteratively reweighted least squares minimization for sparse recovery
- Daubechies, DeVore, et al.
- 2010
(Show Context)
Citation Context ...evious iteration’s estimate of x. The IRLS method exhibits linear and superlinear (approaching quadratic as p → 0) convergence behavior for `1- and `p-regularized least-squares problems, respectively =-=[25]-=-. The closely-related approach of half-quadratic minimization [34, 35] actually refers to two different methods for approximating with quadratic functions separable regularizers of the form λ ∑ n φ(xn... |

138 |
Multi-planar image formation using NMR spin echoes
- Mansfield
(Show Context)
Citation Context ...econstruction methods [9, 70]. Fast MRI acquisition techniques also can use multiple echoes to reduce imaging time while reducing contrast or increasing susceptibility to magnetic field inhomogeneity =-=[62, 41, 30]-=-. A different approach for accelerating MRI uses multiple receivers in parallel and post-processing to recover complete images from fewer samples. Parallel imaging had already been used effectively to... |

125 | Bayesian compressive sensing via belief propagation
- Baron, Sarvotham, et al.
- 2010
(Show Context)
Citation Context ...sed sensing-type problems utilizes a Bayesian interpretation of the compressed sensing framework and uses belief propagation over the graph of the problem to converge to a solution rather efficiently =-=[4, 29, 78]-=-. These methods rely on the large scale limiting behavior of the associated 139 graphical models to reduce the CS reconstruction problem to iterating simple scalar estimators. Thus, they scale well to... |

123 | Generalized approximate message passing for estimation with random linear mixing,” in
- Rangan
- 2011
(Show Context)
Citation Context ...sed sensing-type problems utilizes a Bayesian interpretation of the compressed sensing framework and uses belief propagation over the graph of the problem to converge to a solution rather efficiently =-=[4, 29, 78]-=-. These methods rely on the large scale limiting behavior of the associated 139 graphical models to reduce the CS reconstruction problem to iterating simple scalar estimators. Thus, they scale well to... |

118 |
Generalized autocalibrating partially parallel acquisitions (grappa),”
- Griswold, Jakob, et al.
- 2008
(Show Context)
Citation Context ...sing to recover complete images from fewer samples. Parallel imaging had already been used effectively to mitigate noise, and now, accelerated parallel imaging methods also enable faster acquisitions =-=[82, 87, 76, 38]-=-. Whereas conventional receiver coils have a single channel with spatially uniform sensitivity to magnetization, parallel receiver coils have multiple channels with different non-uniform magnetic sens... |

108 |
Algorithm 583. LSQR: Sparse linear equations and least squares problems
- Paige, Saunders
- 1982
(Show Context)
Citation Context ...ar for approximately solving Equation (4.4) using only a small number of iterations (much less than a million). Since the normal equations also solve the least squares problem Ax = b, the LSQR method =-=[74, 73]-=- can also be used. However, since these iterative methods are terminated early, the LSMR method [33] is used instead because it guarantees a monotonic decrease in both the normal residual ‖AH(b−Ax)‖2,... |

107 |
Functional mapping of the human visual cortex by magnetic resonance imaging
- Belliveau, Kennedy, et al.
- 1991
(Show Context)
Citation Context ...ion, increasing costs and reducing availability of the scanner. In addition, compromises in image quality such as resolution reduction are necessary for time-critical applications like functional MRI =-=[71, 6]-=-. MRI acquisition speed is limited by physiological constraints connected to the effects of spatially varying magnetic fields on the body. A spatially-varying applied 17 magnetic field can induce curr... |

102 | Optimally sparse multidimensional representation using shearlets
- Guo, Labate
(Show Context)
Citation Context ...en found to be favorable to MR images. Overcomplete transforms like the curvelet, contourlet, and shearlet extend the multiresolution idea of wavelet transforms to incorporate directional information =-=[15, 26, 39]-=-. CS can also accommodate adaptive and learned dictionaries, learning the sparsifying transform using training data prior to reconstruction or during reconstruction from the acquired data [24, 80]. A ... |

102 | Simultaneous acquisition of spatial harmonics (SMASH); fast imaging with rf coils,”
- Sodickson, Manning
- 1997
(Show Context)
Citation Context ...sing to recover complete images from fewer samples. Parallel imaging had already been used effectively to mitigate noise, and now, accelerated parallel imaging methods also enable faster acquisitions =-=[82, 87, 76, 38]-=-. Whereas conventional receiver coils have a single channel with spatially uniform sensitivity to magnetization, parallel receiver coils have multiple channels with different non-uniform magnetic sens... |

93 | Reduce and boost: Recovering arbitrary sets of jointly sparse vectors
- Mishali, Eldar
- 2008
(Show Context)
Citation Context ...t vectors with common sparse support. Alternatively, the reduce-and-boost method can be applied to transform the joint sparsity CS reconstruction problem into a conventional CS reconstruction problem =-=[64]-=-. Similar to joint sparsity, structured group sparsity accounts for knowledge of shared support across particular subsets of the set of multiple measurement vectors [45]. These subsets may overlap, in... |

81 |
Homotopy Continuation for Sparse Signal Representation
- Malioutov, Cetin, et al.
(Show Context)
Citation Context ...Ψy‖1. (3.27) The above formulation is not unlike basis pursuit denoising (BPDN) or the Lasso [89], and can be solved using any of a wide variety of iterative techniques developed for either framework =-=[61, 92, 101, 36]-=-. The extension to multiple jointly sparse measure54 ment vectors is similar: Ŷ = minimize Y 1 2 ‖ vec(D−KaY)‖2Λ⊗IN×N + λ‖ΨY‖1,2. (3.28) Methods for approximately solving this type of problem include... |

78 | Highly undersampled magnetic resonance image reconstruction via homotopic l0-minimization
- Trzasko, Manduca
(Show Context)
Citation Context ... has reached that line. Although the `pp measures of sparsity are not convex, they are monotonic and concave on R+, and convergence guarantees for such functions are possible under certain conditions =-=[91]-=-. The graphs of `pp penalty functions are compared against that of the `1 norm in Figure 3.2. The Laplace penalty function ‖w‖L(α), the Welsch penalty function ‖w‖W (α), and 49 0 0.5 1 1.5 2 0 0.5 1 1... |

77 | Asymptotic analysis of MAP estimation via the replica method and applications to compressed sensing. arXiv preprint arXiv:0906.3234v3
- Rangan, Fletcher, et al.
- 2009
(Show Context)
Citation Context ...ators relies on the Replica method to simplify a complex optimization problem into a scalar estimation problem, enabling precise error and support recovery analysis in a computationally tractable way =-=[79]-=-. While these theoretical results are useful when the sparsity level is known, empirical methods like cross validation may be useful to ascertain reconstruction quality when the image sparsity is unkn... |

70 |
Bregman iterative algorithms for `1-minimization with applications to compressed sensing.
- Yin, Osher, et al.
- 2008
(Show Context)
Citation Context ...roduce a series of unconstrained problems that asymptotically approach the constrained problem [69]. A similar method, Bregman iteration, has been proposed for compressed sensing and related problems =-=[102]-=-. In this work, we take advantage of the simple form of the observation matrix Ka to re-express the optimization as an unconstrained problem operating in the nullspace of Ka. Since Ka is a simple subs... |

52 | Analysis of halfquadratic minimization methods for signal and image recovery,”
- Nikolova, Ng
- 2005
(Show Context)
Citation Context ...d of a multiplicative rescaling of the quadratic to approximate the regularizer. This approximation replaces φ(xn) with (xn−s)2, where s(xn) = cxn−φ′(xn), and the optimal choice of c is supxn φ′′(xn) =-=[67]-=-. The optimal value of c is equal to φ′′(0+) for the regularizers in Table A.1. In Equation (A.12), the reweighting matrix ∆(i−1) can be specified according to half-quadratic minimization. Let w = Cx(... |

45 |
Principles of Magnetic Resonance Imaging.
- Nishimura
- 2010
(Show Context)
Citation Context ...ern detection of the magnetization of these particles and allow us to reconstruct an image of the magnetic properties of the bulk material. A concise, thorough treatment of these concepts is given in =-=[68]-=-. A summary of pertinent information from this reference is provided here. 25 2.1.1 Magnetic Moments At a high level, MRI involves exciting particles in the test subject using a combination of several... |

42 |
MR image reconstruction from highly undersampled k-space data by dictionary learning
- Ravishankar, Bresler
- 2011
(Show Context)
Citation Context ...[15, 26, 39]. CS can also accommodate adaptive and learned dictionaries, learning the sparsifying transform using training data prior to reconstruction or during reconstruction from the acquired data =-=[24, 80]-=-. A training set of MR images can be decomposed into small patches, and a sparse dictionary can be learned using a method like K-SVD [1]. A learned dictionary captures details particular to MR images ... |

38 |
SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space
- Lustig, Pauly
(Show Context)
Citation Context ... expect high quality reconstructions from data collected with even greater undersampling. Linear system inversion techniques for accelerated parallel imaging reconstruction like SENSE [76] and SPIRiT =-=[59]-=- can be directly combined with the compressed sensing reconstruction framework. Methods like SparseSENSE [52] and L1 SPIRiT [56] follow this approach, yielding a sparsitypromoting regularized reconstr... |

36 |
Homodyne detection in magnetic resonance imaging,”
- Noll, Nishimura, et al.
- 1991
(Show Context)
Citation Context ...l these methods have their advantages and disadvantages. Adjusting the sampling pattern often means reducing resolution, losing phase information, or requiring more complicated reconstruction methods =-=[9, 70]-=-. Fast MRI acquisition techniques also can use multiple echoes to reduce imaging time while reducing contrast or increasing susceptibility to magnetic field inhomogeneity [62, 41, 30]. A different app... |

30 |
The NMR phased array.
- Roemer, Edelstein, et al.
- 1990
(Show Context)
Citation Context |

28 |
LSMR: an iterative algorithm for sparse least-squares problems,”
- Fong, Saunders
- 2011
(Show Context)
Citation Context ...llion). Since the normal equations also solve the least squares problem Ax = b, the LSQR method [74, 73] can also be used. However, since these iterative methods are terminated early, the LSMR method =-=[33]-=- is used instead because it guarantees a monotonic decrease in both the normal residual ‖AH(b−Ax)‖2, like the CG method, and the least-squares residual ‖b−Ax‖2, like LSQR. These iterative least-square... |

27 |
Parallel imaging reconstruction using automatic regularization. Magn Reson Med 2004; 51: 559–567
- Lin, KK, et al.
(Show Context)
Citation Context ...lly, so gfactors are usually computed for each voxel in the full field of view. To reduce noise amplification and aliasing artifacts, the SENSE method can be regularized using Tikhonov regularization =-=[90, 54]-=-, a sparsity-promoting `1 norm, or a low rank matrix prior using the nuclear norm [60]. 2.5.2 SMASH SMASH, the SiMultaneous Acquisition of Spatial Harmonics, is an early method for accelerated paralle... |

27 |
Keyhole method for accelerating imaging of contrast agent uptake.
- Vaals, ME, et al.
- 1993
(Show Context)
Citation Context ...ecome popular for accelerating Cartesian MRI. Keyhole and partial Fourier imaging reduce the extent of k-space that is sampled and use side information to recover the missing regions. Keyhole imaging =-=[93]-=- is a time-series imaging technique used primarily for contrast-enhanced imaging or cardiac imaging, where multiple volumes are collected, and changes of interest are primarily in the low spatial freq... |

26 | An information-theoretic approach to distributed compressed sensing,” in
- Baron, Duarte, et al.
- 2005
(Show Context)
Citation Context ...ndencies between multiple measurement vectors. Joint sparsity, described previously to capture shared support across all the measurement vectors, has an analogue in CS: distributed compressed sensing =-=[3]-=-. Using a joint sparsity model and an `1 norm-based reconstruction, results demonstrated a reduction in the number of observations necessary to reach the same distortion level for multiple measurement... |

25 |
Parallel MR image reconstruction using augmented Lagrangian methods,” Medical Imaging,
- Ramani, Fessler
- 2011
(Show Context)
Citation Context ...tigates Poisson disc sampling, which incorporates randomness while guaranteeing that samples are not clustered too close and gaps between samples are not too large, in accelerated parallel MR imaging =-=[56, 77, 95]-=-. Avoiding large gaps is especially useful for parallel imaging reconstruction methods like GRAPPA, since GRAPPA-like methods have difficulty approximating large frequency shifts with linear combinati... |

25 | Compressed sensing with cross validation
- Ward
(Show Context)
Citation Context ...ile these theoretical results are useful when the sparsity level is known, empirical methods like cross validation may be useful to ascertain reconstruction quality when the image sparsity is unknown =-=[94]-=-. Now, we go back to the optimization problem used for reconstruction. The CS framework is more general than the MAP estimator in Equation (3.27). If the observations are exact (no additive noise), we... |

25 | Joint image reconstruction and sensitivity estimation in SENSE (JSENSE). Magn Reson Med 2007; 57: 1196–1202
- Ying, Sheng
(Show Context)
Citation Context ...use SENSE to improperly un-alias the reduced-FOV images, yielding a combined image with visible aliasing artifacts. To reduce the effect of coil sensitivity errors on the SENSE reconstruction, JSENSE =-=[103]-=- jointly estimates and refines the sensitivities and the image, using a low-degree polynomial basis for the sensitivities. In addition, the noise in the result may be amplified in the combined un-alia... |

22 |
AUTOSMASH: a self-calibrating technique for SMASH imaging.
- PM, MA, et al.
- 1998
(Show Context)
Citation Context ...tion data called ACS lines that have frequency spacing corresponding to the full field of view; these lines are used to fit the interpolation weights as is done in the SMASH variant called AUTO-SMASH =-=[44]-=-. The ACS lines are usually chosen to be at the center of k-space, or in a region known to have high SNR, to minimize the effect of observation noise on the fit. Rather than form a single combined ima... |

21 | Accelerating SENSE using compressed sensing
- Liang, Liu, et al.
- 2009
(Show Context)
Citation Context ...sion techniques for accelerated parallel imaging reconstruction like SENSE [76] and SPIRiT [59] can be directly combined with the compressed sensing reconstruction framework. Methods like SparseSENSE =-=[52]-=- and L1 SPIRiT [56] follow this approach, yielding a sparsitypromoting regularized reconstruction method that can recover high quality images from moderate accelerations with random undersampling. Wit... |

19 |
RARE imaging: A fast imaging method for clinical
- Hennig, Nauerth, et al.
- 1986
(Show Context)
Citation Context ...econstruction methods [9, 70]. Fast MRI acquisition techniques also can use multiple echoes to reduce imaging time while reducing contrast or increasing susceptibility to magnetic field inhomogeneity =-=[62, 41, 30]-=-. A different approach for accelerating MRI uses multiple receivers in parallel and post-processing to recover complete images from fewer samples. Parallel imaging had already been used effectively to... |

13 |
General formulation for quantitative G-factor calculation
- Breuer, Kannengiesser, et al.
- 2009
(Show Context)
Citation Context ...d parallel imaging reconstruction methods, the noise amplification can be significant. GRAPPA g-factors can be computed analytically by considering interpolation as multiplication in the image domain =-=[12]-=-. When an analytical expression for the g-factors does not exist or is computationally expensive, the multiple replica method, which consists of taking multiple full- and reduced-FOV acquisitions and ... |

12 | SparseSENSE: randomly-sampled parallel imaging using compressed sensing
- Liu, FM, et al.
(Show Context)
Citation Context ...ng and Parallel Imaging Recent developments in accelerated MR image reconstruction include various combinations of accelerated parallel imaging methods and sparsity or compressed sensing. SparseSENSE =-=[55]-=- and CS-SENSE [52] combine CS with the SENSE parallel imaging method. SparseSENSE is a direct extension of the SparseMRI [57] framework to SENSE reconstruction: x̂ = minimize x ‖Ψx‖1 + α‖x‖TV s.t. ‖D−... |

10 |
Comparison of reconstruction accuracy and efficiency among autocalibrating data-driven parallel imaging methods
- Brau, Beatty, et al.
- 2008
(Show Context)
Citation Context ...ularization of the least-squares fit may be required. Regularized calibration will be discussed in detail in Chapter 5. GRAPPA can be extended to two- or three-dimensional subsampling in several ways =-=[11]-=-. In this work, we leverage the fact that the 3-D acquisition is only subsampled in two phase-encode dimensions, so we inverse Fourier transform the acquisition in the frequency-encoded direction and ... |

10 |
A novel method and fast algorithm for MR image reconstruction with significantly under-sampled data. Inverse Probl Imag 2010
- Chen, Ye, et al.
(Show Context)
Citation Context ...[15, 26, 39]. CS can also accommodate adaptive and learned dictionaries, learning the sparsifying transform using training data prior to reconstruction or during reconstruction from the acquired data =-=[24, 80]-=-. A training set of MR images can be decomposed into small patches, and a sparse dictionary can be learned using a method like K-SVD [1]. A learned dictionary captures details particular to MR images ... |

10 |
GRASE (gradient- and spin-echo) MR imaging: a new fast clinical imaging technique. Radiology
- Feinberg, Oshio
- 1991
(Show Context)
Citation Context ...econstruction methods [9, 70]. Fast MRI acquisition techniques also can use multiple echoes to reduce imaging time while reducing contrast or increasing susceptibility to magnetic field inhomogeneity =-=[62, 41, 30]-=-. A different approach for accelerating MRI uses multiple receivers in parallel and post-processing to recover complete images from fewer samples. Parallel imaging had already been used effectively to... |

9 |
The in-crowd algorithm for fast basis pursuit denoising
- Gill, Wang, et al.
- 2011
(Show Context)
Citation Context |

9 |
Non-Cartesian data reconstruction using GRAPPA operator gridding (GROG). Magnetic Resonance in Medicine
- Seiberlich, Breuer, et al.
(Show Context)
Citation Context ...ent with the acquired data [58]. GRAPPA can also be extended to non-Cartesian k-space trajectories using re-gridding, followed by conventional or non-uniform GRAPPA, or using the hybrid GROG approach =-=[83]-=-. As with other accelerated parallel imaging reconstruction methods, the noise amplification can be significant. GRAPPA g-factors can be computed analytically by considering interpolation as multiplic... |

8 | Multi-contrast reconstruction with Bayesian compressed sensing
- Bilgic, Goyal, et al.
- 2011
(Show Context)
Citation Context ...y but have some common degree of sparsity, Bayesian multi-task compressed sensing has been applied to the joint reconstruction of several different types of MRI images (e.g. T1- and T2-weighted data) =-=[8]-=-. This hierarchical Bayesian model shares information across images via a single hyperparameter common to the sparsity-promoting prior distributions of all the images. 58 3.4 Compressed Sensing for MR... |

7 |
Echo-volumar imaging (EVI) of the brain at 3.0 T: First normal volunteer and functional imaging results
- Mansfield, Coxon, et al.
- 1995
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Citation Context ... assuming the image is real-valued. A variety of echo train pulse sequences can be used to yield very fast acquisitions. Echo planar imaging (EPI) [62] and its 3-D analogue echo volumar imaging (EVI) =-=[63]-=- utilize a train of gradient echoes to acquire a complete slice using only a single excitation. Other echo train pulse sequences combining gradient and/or spin echoes like GRASE [30] and RARE [41] als... |

7 |
Clinically feasible reconstruction time for L1-SPIRiT parallel imaging and compressed sensing MRI
- Murphy, Keutzer, et al.
- 2010
(Show Context)
Citation Context ...led T1-weighted image #1 with four level ‘9-7’ DWT sparsifying transform. and IRLS are used together to solve the joint sparsity version of basis pursuit. The parallelized implementation of L1 SPIRiT =-=[66]-=- used for performance comparisons is available online from [65]. After running preliminary simulations, a 7 × 7 SPIRiT kernel size is chosen (the SPIRiT kernel size refers to the number of points in f... |

6 |
A nonlinear regularization strategy for GRAPPA calibration
- Bydder, Jung
- 2009
(Show Context)
Citation Context ...case, Γ is a finite differences transform, and G0 = 0. An alternative approach to regularizing GRAPPA kernel calibration is to utilize the frequency-shift operator interpretation of the GRAPPA kernel =-=[14]-=-. For the GRAPPA kernel G that performs a frequency shift by one over the full field of view, applying the kernel Ry or Rz times should yield the original data shifted in the y94 or z-direction. This ... |

6 |
L1 SPIRiT: Autocalibrating parallel imaging compressed sensing
- Lustig, Alley, et al.
- 2009
(Show Context)
Citation Context ... accelerated parallel imaging reconstruction like SENSE [76] and SPIRiT [59] can be directly combined with the compressed sensing reconstruction framework. Methods like SparseSENSE [52] and L1 SPIRiT =-=[56]-=- follow this approach, yielding a sparsitypromoting regularized reconstruction method that can recover high quality images from moderate accelerations with random undersampling. With conventional unif... |

6 |
Comprehensive quantification of signal-to-noise ratio and g-factor for image-based and k-space-based parallel imaging reconstructions
- Robson, Grant, et al.
- 2008
(Show Context)
Citation Context ...d using the pseudo multiple replica method, which uses only one set of reduced-FOV data and performs Monte Carlo simulations with synthetic additive noise to approximate the multiple replica estimate =-=[81]-=-. Suppose Ŷ is the accelerated parallel imaging reconstructed k-space from the acquired data D. Then, each Monte Carlo repetition consists of adding complex Gaussian noise N with covariance Λ to the ... |

6 |
96-Channel receive-only head coil for 3 Tesla: Design optimization and evaluation
- Wiggins, Polimeni, et al.
- 2009
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Citation Context ...red effects of the induced fields of one coil affecting the others, and as an end result, the noise is correlated to a small degree. Multi-channel receive coil arrays such as the 96-channel head coil =-=[100]-=- shown in Figure 2.5 are now widely available for a multitude of imaging applications. To understand how parallel imaging can be useful for accelerated imaging with reduced-FOV data, we return to the ... |

5 |
Plewes, “Limitations of the keyhole technique for quantitative dynamic contrast-enhanced breast MRI
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Citation Context ...l these methods have their advantages and disadvantages. Adjusting the sampling pattern often means reducing resolution, losing phase information, or requiring more complicated reconstruction methods =-=[9, 70]-=-. Fast MRI acquisition techniques also can use multiple echoes to reduce imaging time while reducing contrast or increasing susceptibility to magnetic field inhomogeneity [62, 41, 30]. A different app... |

5 |
Magnetic Resonance Imaging Versus Computed Tomography in the Evaluation of Soft Tissue Tumors of the Extremities. Ann Surg
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Citation Context ... researchers for its ability to produce high quality images non-invasively without the side effects of ionizing X-ray radiation. MRI is used extensively to image soft tissue throughout the whole body =-=[22]-=-. Moreover, magnetic resonance imaging can be used to distinguish gray and white matter in the brain, observe blood flow, and measure diagnostically valuable quantities such as cortical thickness [13,... |

4 |
Clinical NMR imaging of the brain: 140 cases
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Citation Context ...[22]. Moreover, magnetic resonance imaging can be used to distinguish gray and white matter in the brain, observe blood flow, and measure diagnostically valuable quantities such as cortical thickness =-=[13, 47, 32]-=-. Because of its great versatility, MRI has myriad applications in both medical research and diagnostic and perioperative clinical imaging. However, magnetic resonance imaging remains limited by the t... |

4 |
Nullspace compressed sensing for accelerated imaging
- Grady, Polimeni
- 2009
(Show Context)
Citation Context ...hy (α = 103)L0 "norm" Figure 3.3: The Cauchy penalty function is plotted for different values of α. The `0 “norm” is included for comparison. the Cauchy penalty function ‖w‖C(α) also promote sparsity =-=[91, 37, 85, 96, 99]-=-: ‖w‖L(α) = N−1∑ n=0 1− e−α|w[n]|. (3.4) ‖w‖W (α) = N−1∑ n=0 1− e−α|w[n]|2 . (3.5) ‖w‖C(α) = 1 log(1 + α) N−1∑ n=0 log(1 + α|w[n]|2). (3.6) These nonconvex penalty functions all converge to the `0 “no... |

4 |
Improving compressed sensing parallel imaging using autocalibrating parallel imaging initialization with variable density tiled random k-space sampling
- Lai, Zhang, et al.
- 2011
(Show Context)
Citation Context ... upper bound on the gap size while producing a PSF very similar to uniformly distributed random sampling. Combinations of Poisson disc, variable density sampling, and tiled sampling are also possible =-=[50]-=-. Examples of these 2-D undersampling patterns, with their image domain PSFs, are shown in Figure 3.4. 60 3.4.1 Compressed Sensing and Parallel Imaging Recent developments in accelerated MR image reco... |

4 |
Iterative GRAPPA: a general solution for the GRAPPA reconstruction from arbitrary k-space sampling
- Lustig, Pauly
- 2007
(Show Context)
Citation Context ... squares solution that is consistent with the GRAPPA reconstruction from the “source” points of the full k-space result with the “target” points of the result and is consistent with the acquired data =-=[58]-=-. GRAPPA can also be extended to non-Cartesian k-space trajectories using re-gridding, followed by conventional or non-uniform GRAPPA, or using the hybrid GROG approach [83]. As with other accelerated... |

4 | Nuclear norm-regularized SENSE reconstruction
- Majumdar, Ward
- 2012
(Show Context)
Citation Context ...noise amplification and aliasing artifacts, the SENSE method can be regularized using Tikhonov regularization [90, 54], a sparsity-promoting `1 norm, or a low rank matrix prior using the nuclear norm =-=[60]-=-. 2.5.2 SMASH SMASH, the SiMultaneous Acquisition of Spatial Harmonics, is an early method for accelerated parallel imaging that attempts to interpolate the missing frequencies in reduced-FOV k-space ... |

4 |
Solutions of Ill-Posed Problems. Winston; distributed solely by
- Tikhonov, Arsenin
- 1977
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Citation Context ...lly, so gfactors are usually computed for each voxel in the full field of view. To reduce noise amplification and aliasing artifacts, the SENSE method can be regularized using Tikhonov regularization =-=[90, 54]-=-, a sparsity-promoting `1 norm, or a low rank matrix prior using the nuclear norm [60]. 2.5.2 SMASH SMASH, the SiMultaneous Acquisition of Spatial Harmonics, is an early method for accelerated paralle... |

4 | Evaluating sparsity penalty functions for combined compressed sensing and parallel MRI
- Weller, Polimeni, et al.
- 2011
(Show Context)
Citation Context ...hy (α = 103)L0 "norm" Figure 3.3: The Cauchy penalty function is plotted for different values of α. The `0 “norm” is included for comparison. the Cauchy penalty function ‖w‖C(α) also promote sparsity =-=[91, 37, 85, 96, 99]-=-: ‖w‖L(α) = N−1∑ n=0 1− e−α|w[n]|. (3.4) ‖w‖W (α) = N−1∑ n=0 1− e−α|w[n]|2 . (3.5) ‖w‖C(α) = 1 log(1 + α) N−1∑ n=0 log(1 + α|w[n]|2). (3.6) These nonconvex penalty functions all converge to the `0 “no... |

4 | Regularizing grappa using simultaneous sparsity to recover denoised images
- Weller, Polimeni, et al.
- 2011
(Show Context)
Citation Context ...sparsifying transform for these images. We begin by investigating the effects of regularization in three regimes marked by the relative number of ACS fit equations to source points (across all coils) =-=[97]-=-. When the number of fits Nfit is much greater than the number of source points ByBzP , we expect regularization not to have a significant effect on image quality, as the calibration is already fairly... |

4 |
Denoising sparse images from GRAPPA using the nullspace method
- Weller, Polimeni, et al.
(Show Context)
Citation Context ...hy (α = 103)L0 "norm" Figure 3.3: The Cauchy penalty function is plotted for different values of α. The `0 “norm” is included for comparison. the Cauchy penalty function ‖w‖C(α) also promote sparsity =-=[91, 37, 85, 96, 99]-=-: ‖w‖L(α) = N−1∑ n=0 1− e−α|w[n]|. (3.4) ‖w‖W (α) = N−1∑ n=0 1− e−α|w[n]|2 . (3.5) ‖w‖C(α) = 1 log(1 + α) N−1∑ n=0 log(1 + α|w[n]|2). (3.6) These nonconvex penalty functions all converge to the `0 “no... |

3 |
A combination of nonconvex compressed sensing and
- Fischer, Seiberlich, et al.
- 2009
(Show Context)
Citation Context ...e coil sensitivities to optimally un-alias the image. Distributed CS can be used to improve the coil sensitivities’ estimates and SparseSENSE or CS-SENSE to perform the reconstruction [75]. CS-GRAPPA =-=[31]-=- alternates nonconvex coil-by-coil CS and GRAPPA reconstruction steps on radially acquired data, re-inserting the gridded acquired data between each step, and iterating until convergence. This method ... |

3 |
Quantification of regional blood flow by monitoring of exogenous tracer via nuclear magnetic resonance spectroscopy. Magnetic Resonance in Medicine
- Kim, Ackerman
- 1990
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Citation Context ...[22]. Moreover, magnetic resonance imaging can be used to distinguish gray and white matter in the brain, observe blood flow, and measure diagnostically valuable quantities such as cortical thickness =-=[13, 47, 32]-=-. Because of its great versatility, MRI has myriad applications in both medical research and diagnostic and perioperative clinical imaging. However, magnetic resonance imaging remains limited by the t... |

3 |
Evaluation of continuous approximation functions for the l0-norm for compressed sensing
- Sing-Long, Tejos, et al.
(Show Context)
Citation Context |

3 |
Non-sparse phantom for compressed sensing MRI reconstruction
- Smith, Welch
- 2011
(Show Context)
Citation Context ...method. Simulated data consists of the Shepp-Logan phantom (available through the MATLAB phantom function) and contrast and resolution phantoms based on a compressed sensing phantom in the literature =-=[86]-=-. Multi-channel simulated data is synthesized from these datasets using the Biot-Savart Law-based B1 simulator available online at [53]. The real data presented was previously acquired using a Siemens... |

3 | SpRING: Sparse reconstruction of images using the nullspace method and GRAPPA
- Weller, Polimeni, et al.
- 2011
(Show Context)
Citation Context ... Comparisons The performance of the DESIGN denoising method is compared against a conventional multi-channel Wiener filter-based denoising method, multi-channel compressed sensing [37], and L1 SPIRiT =-=[98, 99]-=-. Because the signal model statistics (mean and variance) are not known exactly, an adaptive Wiener filter-based approach that forms local estimates of the signal mean and variance is used [51]. The g... |

2 |
Sequential application of parallel imaging and compressed sensing
- Beatty, King, et al.
- 2009
(Show Context)
Citation Context ...r sequential combination of CS and accelerated parallel imaging uses a GRAPPA-like reconstruction method to interpolate uniformly undersampled parts of k-space and CS to fill in the remaining k-space =-=[5]-=-. This iterative combination of GRAPPA and compressed sensing may not 61 be as effective as a joint combination of GRAPPA and compressed sensing. The L1 SPIRiT [56] method regularizes the SPIRiT metho... |

2 |
Peripheral nerve stimulation during MRI: Effects of high gradient amplitudes and switching
- Ham, Engels, et al.
- 1997
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Citation Context ...the body. A spatially-varying applied 17 magnetic field can induce currents in the nervous system; at high enough rates, these currents can stimulate the nerves, irritating or distressing the subject =-=[40]-=-. As the fields used to encode the spatial information for Fourier coefficients are spatially varying, this constraint essentially limits the rate we can collect MRI data. Past efforts in accelerating... |

2 |
Faster L1SPIRiT reconstruction with parallel imaging initialization
- Lai, Lustig, et al.
- 2009
(Show Context)
Citation Context ...educing the number of kernels is to tile the sampling pattern with a limited set of small randomly generated patches, so there are only a few different types of blocks that need interpolation kernels =-=[49]-=-. More recent work investigates Poisson disc sampling, which incorporates randomness while guaranteeing that samples are not clustered too close and gaps between samples are not too large, in accelera... |

2 |
B1 simulator : Simulate B1 field for MRI RF coils. http://www. nmr .mgh.harvard. edu/-fhlin/tool_b.htm
- Lin
- 2005
(Show Context)
Citation Context ...ion of the current flow, and r is the vector from the coil element to the spatial point in question. A simulator for estimating sensitivities of arbitrary coil array geometries can be downloaded from =-=[53]-=-. Note that neither the Biot-Savart law nor this simulator account for the 36 Figure 2.7: Magnitude coil sensitivities for 32-channel head coil array computed from acquired data using 32-channel array... |

2 |
11-SPIRiT MRI reconstruction. http://www.cs.berkeley.edu/ ~mjmurphy/11spirit .html
- Murphy
- 2010
(Show Context)
Citation Context ...transform. and IRLS are used together to solve the joint sparsity version of basis pursuit. The parallelized implementation of L1 SPIRiT [66] used for performance comparisons is available online from =-=[65]-=-. After running preliminary simulations, a 7 × 7 SPIRiT kernel size is chosen (the SPIRiT kernel size refers to the number of points in full-FOV k-space). The regularization parameter for the `1 term ... |

2 |
Autocalibrated approach for the combination of compressed sensing and SENSE
- Prieto, Knowles, et al.
- 2010
(Show Context)
Citation Context ...asurements of the coil sensitivities to optimally un-alias the image. Distributed CS can be used to improve the coil sensitivities’ estimates and SparseSENSE or CS-SENSE to perform the reconstruction =-=[75]-=-. CS-GRAPPA [31] alternates nonconvex coil-by-coil CS and GRAPPA reconstruction steps on radially acquired data, re-inserting the gridded acquired data between each step, and iterating until convergen... |

2 | Combined compressed sensing and parallel MRI compared for uniform and random cartesian undersampling of k-space
- Weller, Polimeni, et al.
- 2011
(Show Context)
Citation Context ...tigates Poisson disc sampling, which incorporates randomness while guaranteeing that samples are not clustered too close and gaps between samples are not too large, in accelerated parallel MR imaging =-=[56, 77, 95]-=-. Avoiding large gaps is especially useful for parallel imaging reconstruction methods like GRAPPA, since GRAPPA-like methods have difficulty approximating large frequency shifts with linear combinati... |