Reference‐free single‐pass EPI <scp>N</scp>yquist ghost correction using annihilating filter‐based low rank <scp>H</scp>ankel matrix (ALOHA)

Lee, Juyoung; Jin, Kyong Hwan; Ye, Jong Chul

doi:10.1002/mrm.26077

Cited by 71 publications

(137 citation statements)

References 42 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%

“…The annihilating filter‐based approach in this paper is also theoretically similar to the recent ALOHA‐based approach introduced in and the SENSE‐LORAKS method introduced in . Specifically, the referenceless Nyquist ghost correction method uses a similar annihilation filter to compensate for the phase between the odd and the even lines of an EPI acquisition. Since this method was primarily intended for data with modest under‐sampling (odd/even), it used independent coil‐by‐coil reconstruction along with a wavelet‐based pyramidal decomposition constraint.…”

Section: Discussionmentioning

confidence: 95%

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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%

Section: Discussionmentioning

confidence: 95%

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

et al. 2016

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show abstract

“…If the kernel block is sufficiently large in the readout direction, the low‐rank relation can be exploited to estimate the full data. This has been exploited to correct the N/2 ghost artifact of echo planar imaging in many previous works …”

Section: Methodsmentioning

confidence: 99%

Technical Note: Interleaved bipolar acquisition and low‐rank reconstruction for water–fat separation in MRI

Cho

Park

2018

Medical Physics

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The water-fat separation using the bipolar acquisition has several benefits including a short echo-spacing time. However, it suffers from bipolar-gradient issues such as strong gradient switching, system imperfection, and eddy current effects. This study demonstrated that accurate water-fat separated images can be obtained using the proposed interleaved bipolar acquisition and low-rank reconstruction by using the benefits of the bipolar acquisition while reducing the bipolar-gradient issues with a short imaging time.

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“…Inspired by auto-calibration techniques in parallel MRI [12]–[15], the extension to recovery of parallel MRI from undersampled measurements is formulated as a structured low-rank matrix recovery problem in [2], [10]. Similar approaches have also been found very effective in auto-calibrated multishot MRI [16] and correction of echo-planar MRI data [17]. The theoretical performance of structured low-rank matrix completion methods has been studied in [3], [18], [19], showing improved statistical performance over standard discrete spatial domain recovery.…”

Section: Introductionmentioning

confidence: 99%

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Ongie

Jacob

2017

IEEE Trans. Comput. Imaging

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Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multi-level generalizations, built from Fourier data of the image should be low-rank. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from a lifting the image data to a large scale matrix. We introduce a fast and memory efficient approach called the Generic Iterative Reweighted Annihilation Filter (GIRAF) algorithm that exploits the convolutional structure of the lifted matrix to work in the original un-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm is considerably faster than previously proposed algorithms, and can accommodate much larger problem sizes than previously studied.

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Reference‐free single‐pass EPI Nyquist ghost correction using annihilating filter‐based low rank Hankel matrix (ALOHA)

Abstract: Owing to the discovery of the annihilating filter relationship from the intrinsic EPI image property, the proposed method successfully suppresses ghost artifacts without a prescan step. Magn Reson Med 76:1775-1789, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Cited by 71 publications

References 42 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)

Technical Note: Interleaved bipolar acquisition and low‐rank reconstruction for water–fat separation in MRI

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

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