## BLAST/SENSE (Broad-use Linear Acquisition Speed-up Technique/SENSitivity

### BibTeX

@MISC{Jung_blast/sense(broad-use,

author = {Hong Jung and Jaeseok Park and Jaeheung Yoo and Jong Chul Ye},

title = {BLAST/SENSE (Broad-use Linear Acquisition Speed-up Technique/SENSitivity},

year = {}

}

### OpenURL

### Abstract

A compressed sensing dynamic MR technique called k-t

### Citations

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Citation Context ...s does not satisfy the Nyquist sampling limit, substantial streaking artifacts are often observed. In this paper, we solve this problem by applying compressed sensing. According to compressed sensing =-=(14,16)-=-, very accurate signal reconstruction is possible even from very limited measurements if the signal can be represented sparsely in a modeling basis and the measurement bases are incoherent from the mo... |

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Citation Context ...plicit gridding method where the radial data are transformed to and from a Cartesian grid during the FOCUSS iterations. Similar to Cartesian k-t FOCUSS, after the initial application of FOCUSS, ME/MC =-=(15)-=- using a high-resolution reference frame was applied to the image domain to sparsify the residual image. Our proposed radial k-t FOCUSS is expected to yield the high spatiotemporal resolution without ... |

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Citation Context ...trajectory ¯v j radial , then ¯υradial can be approximated using bilinear interpolation from the surrounding data on the Cartesian grid: ¯v j radial = ∑ i w(i,j) ¯v i cart where ¯v i cart ∈ Vj cart , =-=[10]-=- where w(i,j) are interpolation coefficients between the ith Cartesian data to the jth radial data, as shown in Fig. 1(b). During iterations, we require the adjoint operation S H of S, which can be si... |

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Citation Context ...t since hardwareimplemented ME/MC is already commercially available. For software implementation, various fast search methods such as three-step search (17), four-step search (18), and diamond search =-=(19)-=-, and adaptive rood pattern search (20) have been proposed. This paper employs the adaptive rood pattern search, which significantly reduces searching steps and increases accuracy compared with other ... |

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Citation Context ...m may be lessened somewhat since hardwareimplemented ME/MC is already commercially available. For software implementation, various fast search methods such as three-step search (17), four-step search =-=(18)-=-, and diamond search (19), and adaptive rood pattern search (20) have been proposed. This paper employs the adaptive rood pattern search, which significantly reduces searching steps and increases accu... |

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Citation Context ...pace. If a prediction ρ 0 for ρ is available (12), we can decompose the signal ρ = ρ 0 + �ρ, where �ρ denotes a residual term (12). Then, Eq. [3] can be converted into �υ � υ − MFsRFtρ 0 = MFsRFt�ρ . =-=[4]-=- To enhance temporal resolution, the number of measurements should be limited by skipping some angular sampling. However, if the number of measurements does not satisfy the Nyquist sampling limit, sub... |

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Citation Context ...cted images. The in vivo data with radial k-space sampling trajectories were acquired using electrocardiogram-triggered segmented spoiled GRE sequence with spatial modulation of magnetization tagging =-=(21)-=-. Imaging parameters were as follows: pulse repetition time/echo time was 3.4/2.9 ms, flip angle was 10◦ , imaging FOV was 340 × 340 mm2 , and the slice thickness was 10 mm. The number of views for ea... |

101 |
Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med
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Citation Context ... �ρ. k-t FOCUSS was developed to address the l1 minimization problem using a reweighted quadratic optimization technique (11,12). Accordingly, radial k-t FOCUSS is implemented to find �ρ l+1 = Wl ql, =-=[5]-=- by solving the following l2 optimization problem. minimize ‖ql‖2 subject to ‖υ − MFsRFtWl ql − MFsRFtρ 0‖2 ≤ ɛ, [6] where Wl is a diagonal weighting matrix at the l-th FOCUSS update: Wl+1 = ⎛ |�ρl+1(... |

59 |
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Citation Context ...ique (11,12). Accordingly, radial k-t FOCUSS is implemented to find �ρ l+1 = Wl ql, [5] by solving the following l2 optimization problem. minimize ‖ql‖2 subject to ‖υ − MFsRFtWl ql − MFsRFtρ 0‖2 ≤ ɛ, =-=[6]-=- where Wl is a diagonal weighting matrix at the l-th FOCUSS update: Wl+1 = ⎛ |�ρl+1(1)| ⎜ ⎝ p 0 ··· 0 0 |�ρl+1(2)| p ··· 0 . . . .. . 0 0 ··· |�ρl+1(N)| p ⎞ ⎟ ⎠ , 1/2 ≤ p ≤ 1. [7] Radial k-t FOCUSS it... |

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Citation Context ...l − MFsRFtρ 0‖2 ≤ ɛ, [6] where Wl is a diagonal weighting matrix at the l-th FOCUSS update: Wl+1 = ⎛ |�ρl+1(1)| ⎜ ⎝ p 0 ··· 0 0 |�ρl+1(2)| p ··· 0 . . . .. . 0 0 ··· |�ρl+1(N)| p ⎞ ⎟ ⎠ , 1/2 ≤ p ≤ 1. =-=[7]-=- Radial k-t FOCUSS iteratively solves Eq. [6] and successively updates Wl until the solution �ρ l converges. As previously shown (11), this algorithm solves the l1 minimization problem by setting p = ... |

42 | Adaptive sensitivity encoding incorporating temporal filtering (TSENSE). Magn Reson Med 2001;45: 846–852
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Citation Context ... ‖υ − MSFxFy FtWl ql − Fρ0‖2 ≤ ɛ, where Fx and Fy are the Fourier transform along x-direction and y-direction, respectively, and S is the resampling operator. Compared to Eq. [6], the relation in Eq. =-=[8]-=- does not include the computationally expensive projection operation. Instead, the resampling operator can be represented by [8] ¯υradial = S ¯υcart, [9]70 Jung et al. FIG. 1. (a) Radial sampling on ... |

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Citation Context ...ator. Compared to Eq. [6], the relation in Eq. [8] does not include the computationally expensive projection operation. Instead, the resampling operator can be represented by [8] ¯υradial = S ¯υcart, =-=[9]-=-70 Jung et al. FIG. 1. (a) Radial sampling on Cartesian grid and (b) bilinear interpolation from Cartesian to polar, and (c) its adjoint operation. where ¯υradial and ¯υcart are interpolated values o... |

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Citation Context ...ready commercially available. For software implementation, various fast search methods such as three-step search (17), four-step search (18), and diamond search (19), and adaptive rood pattern search =-=(20)-=- have been proposed. This paper employs the adaptive rood pattern search, which significantly reduces searching steps and increases accuracy compared with other methods. Residual Encoding So far, we h... |

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Citation Context ...y of ME/MC in Dynamic MRI For our Cartesian k-t FOCUSS implementation (12), we introduced two efficient prediction methods: twodimensional reduced-encoding imaging by generalizedseries reconstruction =-=(12,27)-=- and ME/MC (15). However, the application of reduced-encoding imaging by generalized-series reconstruction to radial trajectories is not well established due to the difficulty involved with generalize... |

13 |
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Citation Context ... the improvements quantitatively, we calculated the normalized MSE within the full FOV and the ROI in Fig. 3. The normalized MSE is calculated as follows: normalized MSE = ‖ρ − ρTrue‖ 2 2 ‖ρTrue‖ 2 , =-=[14]-=- 2 where ρ True is the assumed reference result obtained from an inverse radon transform of 192 views. SW shows the smallest MSE between the 12th and 15th frames. Note that that period corresponds to ... |

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Citation Context ... to reconstruct residual images. Recall that the updated estimate at (l + 1)-th iteration can be derived from Eq. [8] as follows: ρ l+1 = ρ 0 + �ρ l+1 = ρ 0 + �l ˆF H ( ˆF�l ˆF H + λI) −1 (υ − Fρ 0), =-=[13]-=- where F = MFsRFt, ˆF = MSFxFy Ft, and �l = WlW H l , respectively. From Eq. [13], two important issues must be addressed for successful implementation of our algorithm. One is that the predicted imag... |

11 |
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Citation Context ...a moving heart, we can apply a Fourier transform in the temporal direction to make the signal sparse. In this case, Eq. [1] becomes ∫∫ υ(R, θ, t) = ρ(x, y, f )e j2πR(x cos θ+y sin θ) e j2πft dxdydf , =-=[2]-=- where ρ(x, y, f ) is the temporal Fourier transform of σ (x, y, t). We now write Eq. [2] in matrix form: υ = MFsRFtρ, [3] where ρ represents the stacked vector of the pixel values of unknown x-f spec... |

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Citation Context ... trajectory that are affected by ¯v j we have ∑ = v j cart i cart during a resampling operation. Then, w(j,i) ¯v i radial where ¯v i radial where v j cart corresponds to Cartesian data. ∈ Vj radial . =-=[11]-=- Prediction Using ME/MC Recall that the (l + 1)-th update of our k-t FOCUSS framework can be summarized as follows: ρl+1 = ρ0 }{{} + �ρl+1 } {{ } . [12] prediction residual encoding As demonstrated fo... |

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Citation Context ...HEORY Compressed Sensing Formulation In radial trajectory acquisition, an MR scanner acquires data on polar coordinates of k-space as follows: ∫∫ υ(R, θ, t) = σ (x, y, t)e j2πR(x cos θ+y sin θ) dxdy, =-=[1]-=- where σ (x, y, t) is the image content resulting from tissue property and sequence parameters at position (x, y) and time t, and υ(R, θ, t) is the measurement on the polar coordinate (R, θ) ofk-space... |

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Citation Context ...] becomes ∫∫ υ(R, θ, t) = ρ(x, y, f )e j2πR(x cos θ+y sin θ) e j2πft dxdydf , [2] where ρ(x, y, f ) is the temporal Fourier transform of σ (x, y, t). We now write Eq. [2] in matrix form: υ = MFsRFtρ, =-=[3]-=- where ρ represents the stacked vector of the pixel values of unknown x-f spectrum of dynamic images and υ represents measurements in k-t space; Ft, R, and Fs imply a Fourier transform along the tempo... |

2 |
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Citation Context ...rt corresponds to Cartesian data. ∈ Vj radial . [11] Prediction Using ME/MC Recall that the (l + 1)-th update of our k-t FOCUSS framework can be summarized as follows: ρl+1 = ρ0 }{{} + �ρl+1 } {{ } . =-=[12]-=- prediction residual encoding As demonstrated for Cartesian trajectories (12), ME/MC prediction further improves the image quality via high spatiotemporal resolution by making the residual image very ... |

2 |
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Citation Context ... expensive. This problem may be lessened somewhat since hardwareimplemented ME/MC is already commercially available. For software implementation, various fast search methods such as three-step search =-=(17)-=-, four-step search (18), and diamond search (19), and adaptive rood pattern search (20) have been proposed. This paper employs the adaptive rood pattern search, which significantly reduces searching s... |