Accelerated High-Dimensional MR Imaging With Sparse Sampling Using Low-Rank Tensors

He, Jingfei; Liu, Qiegen; Christodoulou, Anthony G.; Ma, Chao; Lam, Fan; Liang, Zhi‐Pei

doi:10.1109/tmi.2016.2550204

Cited by 124 publications

(109 citation statements)

References 55 publications

(57 reference statements)

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“…Our feasibility studies fell into this scenario. If a more general (

boldk

, f , T )‐space sampling pattern is used to acquire

D_{2}

, e.g., for higher frame rate, the joint estimation of

{{bold-italicθ}_{l}}_{l = 1}^{L}

and

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

in can be used for image reconstruction, where the proposed method can be used to obtain the initial guess of

{{bold-italicθ}_{l}}_{l = 1}^{L}

and

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

.…”

Section: Discussionmentioning

confidence: 99%

“…Denoting the estimated spectral and temporal bases as

{{\overset{ϕ}{true}}_{m}}_{m = 1}^{M}

and

{\overset{truê}{ψ_{n}}}_{n = 1}^{N}, ρ

in Equation is reconstructed by determining the model coefficients

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

and spatial basis

{{bold-italicθ}_{l}}_{l = 1}^{L}

via fitting the “imaging” data in

D_{2}

min_{_{{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}, {{bold-italicθ}_{l}}_{l = 1}^{L}}} | | d_{2} - Ω F_{B} {\sum_{l = 1}^{L} \sum_{m = 1}^{M} \sum_{n = 1}^{N} c_{l, m, n} θ_{l} ○ {\overset{truê}{bold-italicϕ}}_{m} ○ {\overset{truê}{bold-italicψ}}_{n}} {| |}_{2}^{2} + R ({{bold-italicθ}_{l}}_{l = 1}^{L}),

where

…”

Section: Theorymentioning

confidence: 99%

“…While the optimization problem in Equation can be solved by updating

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

and

{{bold-italicθ}_{l}}_{l = 1}^{L}

in an alternating scheme as described in Ref. , we propose to solve the problem using the following algorithm because of its computational efficiency: Estimate an MRSI image (denoted as

ρ_{r}^{false(1 false)} = {ρ_{p, q, r}^{false(1 false)})}_{p, q = 1}^{P, Q false)}

at each time point T r ,

r = 1, \dots, R

by solving the following optimization problem:

{{\overset{truê}{bolda}}_{m, r}}_{m = 1}^{M} = \underset{_{{a_{m, r}}_{m = 1}^{M}}}{arg min} | | {boldd}_{2, r} - {normalΩ}_{r} {scriptF}_{B} {true \sum_{m = 1}^{M} {bolda}_{m, r} ○ {\overset{ϕ}{true}}_{m}} {| |}_{2}^{2} + R false({a_{m, r}}_{m = 1}^{M} false),

where

d_{2, r}

denotes a vector concatenating the k‐space samples in

D_{2}

at T r ,

…”

Section: Theorymentioning

confidence: 99%

See 2 more Smart Citations

High-resolution dynamic³¹P-MRSI using a low-rank tensor model

Clifford

Liu

et al. 2017

Magn. Reson. Med.

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Purpose To develop a rapid 31P-MRSI method with high spatiospectral resolution using low-rank tensor-based data acquisition and image reconstruction. Methods The multidimensional image function of 31P-MRSI is represented by a low-rank tensor to capture the spatial–spectral–temporal correlations of data. A hybrid data acquisition scheme is used for sparse sampling, which consists of a set of “training” data with limited k-space coverage to capture the subspace structure of the image function, and a set of sparsely sampled “imaging” data for high-resolution image reconstruction. An explicit subspace pursuit approach is used for image reconstruction, which estimates the bases of the subspace from the “training” data and then reconstructs a high-resolution image function from the “imaging” data. Results We have validated the feasibility of the proposed method using phantom and in vivo studies on a 3T whole-body scanner and a 9.4T preclinical scanner. The proposed method produced high-resolution static 31P-MRSI images (i.e., 6.9×6.9×10 mm3 nominal resolution in a 15-min acquisition at 3T) and high-resolution, high-frame-rate dynamic 31P-MRSI images (i.e., 1.5 × 1.5 × 1.6 mm3 nominal resolution, 30 s/frame at 9.4T). Conclusions Dynamic spatiospectral variations of 31P-MRSI signals can be efficiently represented by a low-rank tensor. Exploiting this mathematical structure for data acquisition and image reconstruction can lead to fast 31P-MRSI with high resolution, frame-rate, and SNR.

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“…Our feasibility studies fell into this scenario. If a more general (

boldk

, f , T )‐space sampling pattern is used to acquire

D_{2}

, e.g., for higher frame rate, the joint estimation of

{{bold-italicθ}_{l}}_{l = 1}^{L}

and

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

in can be used for image reconstruction, where the proposed method can be used to obtain the initial guess of

{{bold-italicθ}_{l}}_{l = 1}^{L}

and

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

.…”

Section: Discussionmentioning

confidence: 99%

“…Denoting the estimated spectral and temporal bases as

{{\overset{ϕ}{true}}_{m}}_{m = 1}^{M}

and

{\overset{truê}{ψ_{n}}}_{n = 1}^{N}, ρ

in Equation is reconstructed by determining the model coefficients

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

and spatial basis

{{bold-italicθ}_{l}}_{l = 1}^{L}

via fitting the “imaging” data in

D_{2}

min_{_{{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}, {{bold-italicθ}_{l}}_{l = 1}^{L}}} | | d_{2} - Ω F_{B} {\sum_{l = 1}^{L} \sum_{m = 1}^{M} \sum_{n = 1}^{N} c_{l, m, n} θ_{l} ○ {\overset{truê}{bold-italicϕ}}_{m} ○ {\overset{truê}{bold-italicψ}}_{n}} {| |}_{2}^{2} + R ({{bold-italicθ}_{l}}_{l = 1}^{L}),

where

…”

Section: Theorymentioning

confidence: 99%

“…While the optimization problem in Equation can be solved by updating

{c_{l, m, n}}_{l, m, n = 1}^{L, M, N}

and

{{bold-italicθ}_{l}}_{l = 1}^{L}

in an alternating scheme as described in Ref. , we propose to solve the problem using the following algorithm because of its computational efficiency: Estimate an MRSI image (denoted as

ρ_{r}^{false(1 false)} = {ρ_{p, q, r}^{false(1 false)})}_{p, q = 1}^{P, Q false)}

at each time point T r ,

r = 1, \dots, R

by solving the following optimization problem:

{{\overset{truê}{bolda}}_{m, r}}_{m = 1}^{M} = \underset{_{{a_{m, r}}_{m = 1}^{M}}}{arg min} | | {boldd}_{2, r} - {normalΩ}_{r} {scriptF}_{B} {true \sum_{m = 1}^{M} {bolda}_{m, r} ○ {\overset{ϕ}{true}}_{m}} {| |}_{2}^{2} + R false({a_{m, r}}_{m = 1}^{M} false),

where

d_{2, r}

denotes a vector concatenating the k‐space samples in

D_{2}

at T r ,

…”

Section: Theorymentioning

confidence: 99%

See 1 more Smart Citation

High-resolution dynamic³¹P-MRSI using a low-rank tensor model

Clifford

Liu

et al. 2017

Magn. Reson. Med.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This regularization term could be used to enforce additional complementary image properties, for example in the form of a weighted ℓ 2 penalty term or sparsity-promoting ℓ 1 penalty term. This would provide an avenue for exploiting additional signal properties [28] or for controlling model order [32, 42], at the expense of additional computational time.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, we propose a sparse sampling method exploiting low-rank tensor properties [26, 30– 32] of EPR oxygen images. This approach specifically exploits both the partial separability of space and time in EPR oxygen images (i.e., the correlation between images at different times) [21] and the partial separability of space and sequence parameters (i.e., the correlation between images with different contrast weightings) [33, 34].…”

Section: Introductionmentioning

confidence: 99%

Fast dynamic electron paramagnetic resonance (EPR) oxygen imaging using low-rank tensors

Christodoulou

Redler

Clifford

et al. 2016

Journal of Magnetic Resonance

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Hypoxic tumors are resistant to radiotherapy, motivating the development of tools to image local oxygen concentrations. It is generally believed that stable or chronic hypoxia is the source of resistance, but more recent work suggests a role for transient hypoxia. Conventional EPR imaging (EPRI) is capable of imaging tissue pO2 in vivo, with high pO2 resolution and 1 mm spatial resolution but low imaging speed (10 min temporal resolution for T1-based pO2 mapping), which makes it difficult to investigate the oxygen changes, e.g. transient hypoxia. Here we describe a new imaging method which accelerates dynamic EPR oxygen imaging, allowing 3D imaging at 2 frames per minute, fast enough to image transient hypoxia at the “speed limit” of observed pO2 change. The method centers on a low-rank tensor model that decouples the tradeoff between imaging speed, spatial coverage/resolution, and number of inversion times (pO2 accuracy). We present a specialized sparse sampling strategy and image reconstruction algorithm for use with this model. The quality and utility of the method is demonstrated in simulations and in vivo experiments in tumor bearing mice.

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Principal component reconstruction (PCR) for cine CBCT with motion learning from 2D fluoroscopy

et al. 2017

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Purpose: This work aims to generate cine CT images (i.e., 4D images with high-temporal resolution) based on a novel principal component reconstruction (PCR) technique with motion learning from 2D fluoroscopic training images. Methods: In the proposed PCR method, the matrix factorization is utilized as an explicit low-rank regularization of 4D images that are represented as a product of spatial principal components and temporal motion coefficients. The key hypothesis of PCR is that temporal coefficients from 4D images can be reasonably approximated by temporal coefficients learned from 2D fluoroscopic training projections. For this purpose, we can acquire fluoroscopic training projections for a few breathing periods at fixed gantry angles that are free from geometric distortion due to gantry rotation, that is, fluoroscopy-based motion learning. Such training projections can provide an effective characterization of the breathing motion. The temporal coefficients can be extracted from these training projections and used as priors for PCR, even though principal components from training projections are certainly not the same for these 4D images to be reconstructed. For this purpose, training data are synchronized with reconstruction data using identical real-time breathing position intervals for projection binning. In terms of image reconstruction, with a priori temporal coefficients, the data fidelity for PCR changes from nonlinear to linear, and consequently, the PCR method is robust and can be solved efficiently. PCR is formulated as a convex optimization problem with the sum of linear data fidelity with respect to spatial principal components and spatiotemporal total variation regularization imposed on 4D image phases. The solution algorithm of PCR is developed based on alternating direction method of multipliers. Results: The implementation is fully parallelized on GPU with NVIDIA CUDA toolbox and each reconstruction takes about a few minutes. The proposed PCR method is validated and compared with a state-of-art method, that is, PICCS, using both simulation and experimental data with the on-board cone-beam CT setting. The results demonstrated the feasibility of PCR for cine CBCT and significantly improved reconstruction quality of PCR from PICCS for cine CBCT. Conclusion: With a priori estimated temporal motion coefficients using fluoroscopic training projections, the PCR method can accurately reconstruct spatial principal components, and then generate cine CT images as a product of temporal motion coefficients and spatial principal components.

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Accelerated High-Dimensional MR Imaging With Sparse Sampling Using Low-Rank Tensors

Cited by 124 publications

References 55 publications

High-resolution dynamic³¹P-MRSI using a low-rank tensor model

High-resolution dynamic³¹P-MRSI using a low-rank tensor model

Fast dynamic electron paramagnetic resonance (EPR) oxygen imaging using low-rank tensors

Principal component reconstruction (PCR) for cine CBCT with motion learning from 2D fluoroscopy

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Accelerated High-Dimensional MR Imaging With Sparse Sampling Using Low-Rank Tensors

Cited by 124 publications

References 55 publications

High-resolution dynamic31P-MRSI using a low-rank tensor model

High-resolution dynamic31P-MRSI using a low-rank tensor model

Fast dynamic electron paramagnetic resonance (EPR) oxygen imaging using low-rank tensors

Principal component reconstruction (PCR) for cine CBCT with motion learning from 2D fluoroscopy

Contact Info

Product

Resources

About

High-resolution dynamic³¹P-MRSI using a low-rank tensor model

High-resolution dynamic³¹P-MRSI using a low-rank tensor model