Acceleration of MR parameter mapping using annihilating filter‐based low rank hankel matrix (ALOHA)

Lee, Dongwook; Jin, Kyong Hwan; Kim, Eung Yeop; Park, Sung‐Hong; Ye, Jong Chul

doi:10.1002/mrm.26081

Cited by 103 publications

(143 citation statements)

References 48 publications

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“…Multiplying Equation by

ϕ_{i} (x)

and Equation by

ϕ_{l} (x)

, we can write

m_{l} (x) ϕ_{i} (x) - m_{i} (x) ϕ_{l} (x) = 0; \forall x,

which leads to annihilation relations in the image domain, similar to those introduced in . Taking the Fourier transform on both sides of (3), we obtain

\overset{m_{l}}{true} [k] * \overset{ϕ_{i}}{true} [k] - \overset{m_{i}}{true} [k] * \overset{ϕ_{l}}{true} [k] = 0; \forall k,

which leads to annihilation relation in the frequency domain as discussed in . Here,

\overset{m_{l}}{true} [k]

and

\overset{ϕ_{l}}{true} [k]

denote the Fourier coefficients of

m_{l} (x)

and

ϕ_{l} (x)

, respectively for

l = 1

…”

Section: Theorymentioning

confidence: 80%

Multi-shot sensitivity-encoded diffusion data recovery using structured low-rank matrix completion (MUSSELS)

et al. 2016

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Purpose To introduce a novel method for the recovery of multi-shot diffusion weighted (MS-DW) images from echo-planar imaging (EPI) acquisitions. Methods Current EPI-based MS-DW reconstruction methods rely on the explicit estimation of the motion-induced phase maps to recover artifact-free images. In the new formulation, the k-space data of the artifact-free DWI is recovered using a structured low-rank matrix completion scheme, which does not require explicit estimation of the phase maps. The structured matrix is obtained as the lifting of the multi-shot data. The smooth phase-modulations between shots manifest as null-space vectors of this matrix, which implies that the structured matrix is low-rank. The missing entries of the structured matrix are filled in using a nuclear-norm minimization algorithm subject to the data-consistency. The formulation enables the natural introduction of smoothness regularization, thus enabling implicit motion-compensated recovery of the MS-DW data. Results Our experiments on in-vivo data show effective removal of artifacts arising from inter-shot motion using the proposed method. The method is shown to achieve better reconstruction than the conventional phase-based methods. Conclusion We demonstrate the utility of the proposed method to effectively recover artifact-free images from Cartesian fully/under-sampled and partial Fourier acquired data without the use of explicit phase estimates.

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“…Multiplying Equation by

ϕ_{i} (x)

and Equation by

ϕ_{l} (x)

, we can write

m_{l} (x) ϕ_{i} (x) - m_{i} (x) ϕ_{l} (x) = 0; \forall x,

which leads to annihilation relations in the image domain, similar to those introduced in . Taking the Fourier transform on both sides of (3), we obtain

\overset{m_{l}}{true} [k] * \overset{ϕ_{i}}{true} [k] - \overset{m_{i}}{true} [k] * \overset{ϕ_{l}}{true} [k] = 0; \forall k,

which leads to annihilation relation in the frequency domain as discussed in . Here,

\overset{m_{l}}{true} [k]

and

\overset{ϕ_{l}}{true} [k]

denote the Fourier coefficients of

m_{l} (x)

and

ϕ_{l} (x)

, respectively for

l = 1

…”

Section: Theorymentioning

confidence: 80%

Multi-shot sensitivity-encoded diffusion data recovery using structured low-rank matrix completion (MUSSELS)

et al. 2016

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show abstract

“…The first one is wavelet-based pyramidal decomposition approach and the second one is a generalization for multichannel parallel MRI. Note that these are particular instances of the ALOHA algorithm and other variations of ALOHA may be possible for various scenarios as demonstrated in recent applications [32]- [34].…”

Section: Aloha For Accelerated Mrimentioning

confidence: 99%

“…Note that the wavelet decomposition is performed only along the spatial domain, so the pyramidal decomposition is only performed along k y direction. This construction of Hankel matrix is due to the observation that the dynamic signal is sparse in spatial wavelet and temporal Fourier transform domain [32]. See more details in our recent work [32].…”

Section: Reconstruction Flowmentioning

confidence: 99%

“…This construction of Hankel matrix is due to the observation that the dynamic signal is sparse in spatial wavelet and temporal Fourier transform domain [32]. See more details in our recent work [32].…”

Section: Reconstruction Flowmentioning

confidence: 99%

“…For the case of dynamic imaging in Fig. 3(b), one dimensional weighting along the phase encoding direction was applied as explained in detail in [32]. Finally, after the k-space interpolation, the k-space unweighting is done in k-space pixel-by-pixel by dividing the reconstructed value with (66).…”

Section: Reconstruction Flowmentioning

confidence: 99%

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A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Jin

Lee

2016

IEEE Trans. Comput. Imaging

Self Cite

216

325

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Abstract-Parallel MRI (pMRI) and compressed sensing MRI (CS-MRI) have been considered as two distinct reconstruction problems. Inspired by recent k-space interpolation methods, an annihilating filter-based low-rank Hankel matrix approach is proposed as a general framework for sparsity-driven k-space interpolation method which unifies pMRI and CS-MRI. Specifically, our framework is based on a novel observation that the transform domain sparsity in the primary space implies the low-rankness of weighted Hankel matrix in the reciprocal space. This converts pMRI and CS-MRI to a k-space interpolation problem using a structured matrix completion. Experimental results using in vivo data for single/multicoil imaging as well as dynamic imaging confirmed that the proposed method outperforms the state-of-the-art pMRI and CS-MRI.Index Terms-Annihilating filter, cardinal spline, compressed sensing, parallel MRI, pyramidal representation, structured low rank block Hankel matrix completion, wavelets.

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Rapid compositional mapping of knee cartilage with compressed sensing MRI

Zibetti

Baboli

Chang

et al. 2018

Magnetic Resonance Imaging

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More than one decade after the introduction of compressed sensing (CS) in MRI, researchers are still working on ways to translate it into different research and clinical applications. The greatest advantage of CS in MRI is the reduced amount of k-space data needed to reconstruct images, which can be exploited to reduce scan time or to improve spatial resolution and volumetric coverage. Efficient data acquisition using CS is extremely important for compositional mapping of the musculoskeletal system in general and knee cartilage mapping techniques in particular. High-resolution quantitative information about tissue biochemical composition could be obtained in just a few minutes using CS MRI. However, in order to make this goal a reality, some issues still need to be addressed. In this paper, we review the current state of the art of CS methods for rapid compositional mapping of knee cartilage. Specifically, data acquisition strategies, image reconstruction algorithms, and data fitting models are discussed. Different CS studies for T2 and T1ρ mapping of knee cartilage are reviewed, with illustrative results. Future directions, opportunities, and challenges of rapid compositional mapping techniques are also discussed.

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Acceleration of MR parameter mapping using annihilating filter‐based low rank hankel matrix (ALOHA)

Cited by 103 publications

References 48 publications

Multi-shot sensitivity-encoded diffusion data recovery using structured low-rank matrix completion (MUSSELS)

Multi-shot sensitivity-encoded diffusion data recovery using structured low-rank matrix completion (MUSSELS)

A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Rapid compositional mapping of knee cartilage with compressed sensing MRI

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