Realistic Analytical Phantoms for Parallel Magnetic Resonance Imaging

Guerquin-Kern, M.; Lejeune, Laurent; Pruessmann, Klaas P.; Unser, Michaël

doi:10.1109/tmi.2011.2174158

Cited by 205 publications

(169 citation statements)

References 22 publications

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“…Observe also that we may argue exactly as in the proof of Step III (via Proposition 11.1) and regardless of the vector Z j−1 , we may deduce that P(D 2 ) ≤ 1/8 when N and q j are chosen such that 35) for some universal constant C > 0. Thus, for l = 1, .…”

Section: (116)mentioning

confidence: 66%

“…Note that most of the above works describe infinite-dimensional CS approaches for some particular class of problems, and do not address the fundamental problem of reconstructing the coefficients {α j } j∈N of a function f = j∈N α j ϕ j from fixed, but arbitrary, linear samples {ζ j (f )} j∈N (this is precisely the issue in the infinite-dimensional MRI model in [34,35]). Our GS-CS framework does precisely this.…”

Section: Relation To Other Work and Contributions Of The Papermentioning

confidence: 99%

“…Had this data actually been simulated using the discrete Fourier transform, then no such problems would have occurred, and one would have seen a vastly improved reconstruction (in this case, perfect recovery). However, this improvement is artificial and an example of the well-known inverse crime [35]. That is to say, inappropriate simulation of data leads to spuriously good reconstructions, but when applied to real data, such as in the above examples, the reconstruction quality substantially declines.…”

Section: Relation To the Inverse Crimementioning

confidence: 99%

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Generalized Sampling and Infinite-Dimensional Compressed Sensing

2015

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We introduce and analyze an abstract framework, and corresponding method, for compressed sensing in infinite dimensions. This extends the existing theory from signals in finite-dimensional vectors spaces to the case of separable Hilbert spaces. We explain why such a new theory is necessary, and demonstrate that existing finite-dimensional techniques are ill-suited for solving a number of important problems.This work stems from recent developments in generalized sampling theorems for classical (Nyquist rate) sampling that allows for reconstructions in arbitrary bases. The main conclusion of this paper is that one can extend these ideas to allow for significant subsampling of sparse or compressible signals. The key to these developments is the introduction of two new concepts in sampling theory, the stable sampling rate and the balancing property, which specify how to appropriately discretize the fundamentally infinitedimensional reconstruction problem.

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Section: (116)mentioning

confidence: 66%

Section: Relation To Other Work and Contributions Of The Papermentioning

confidence: 99%

Section: Relation To the Inverse Crimementioning

confidence: 99%

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Generalized Sampling and Infinite-Dimensional Compressed Sensing

2015

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“…Conversely, the standard CS is based on a finite-dimensional model. Such a mismatch between the computational and the physical model can lead to critical errors when CS techniques are applied to real data arising from continuous models, or inverse crimes when the data is inappropriately simulated [22,46]. To overcome this issue, a theory of CS in infinite dimensions was recently introduced in [3].…”

Section: Introductionmentioning

confidence: 99%

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Adcock

Hansen

Poon³

et al. 2017

Forum of Mathematics, Sigma

274

461

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This paper presents a framework for compressed sensing that bridges a gap between existing theory and the current use of compressed sensing in many real-world applications. In doing so, it also introduces a new sampling method that yields substantially improved recovery over existing techniques. In many applications of compressed sensing, including medical imaging, the standard principles of incoherence and sparsity are lacking. Whilst compressed sensing is often used successfully in such applications, it is done largely without mathematical explanation. The framework introduced in this paper provides such a justification. It does so by replacing these standard principles with three more general concepts: asymptotic sparsity, asymptotic incoherence and multilevel random subsampling. Moreover, not only does this work provide such a theoretical justification, it explains several key phenomena witnessed in practice. In particular, and unlike the standard theory, this work demonstrates the dependence of optimal sampling strategies on both the incoherence structure of the sampling operator and on the structure of the signal to be recovered. Another key consequence of this framework is the introduction of a new structured sampling method that exploits these phenomena to achieve significant improvements over current state-of-the-art techniques.2010 Mathematics Subject Classification: 94A20, 94A08 (primary); 42C40, 65R32, 92C55 (secondary)

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“…A realistic analytical phantom [70] was used to simulate the T 2 mapping acquisition, reconstruction and parameter estimation process. We represented the grey and white matter by four ROIs with T 2 = 50, 80, 120, and 250 ms. To simulate multiple TEs, 100 parameter encoding states were measured with echo spacing equal to 3 ms.…”

Section: Simulationmentioning

confidence: 99%

Accuracy of Arterial Spin Labeling in Magnetic Resonance Imaging

Li¹

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Cerebral perfusion imaging provides information about the blood supply of tissue. It reveals functional changes of the brain before and after structural changes, which can be used to improve the sensitivity and accuracy of stroke and tumor diagnosis. There has been an increasing interest in developing methods for non-contrast perfusion imaging, because of the risk of nephrogenic systemic fibrosis (NSF) in patients with kidney dysfunction and the need for repeated blood flow measurements in a short period of time for functional studies.Magnetic resonance imaging (MRI) provides a safer option for perfusion imaging without a contrast agent: arterial spin labeling (ASL). In this work, we propose several new techniques to improve the quality and quantification of ASL MRI.Using the water spins of blood as a tracer makes ASL safer than other perfusion imaging methods, but also results in a low signal-noise-ratio (SNR). Conventionally, ASL uses lengthy scan times to improve image quality and compensate for motion. However, this strategy is typically used to measure the perfusion bolus at a single time point, which can limit the accuracy of perfusion quantification, particularly in the setting of disease. Measuring multiple time points, which is called dynamic ASL, can improve quantification of cerebral ii iii blood flow (CBF) and yield additional information, but long scan times may be needed. In this work, we describe the following advances that can be used to improve dynamic ASL:(1) accurate reference T 2 mapping; (2) robust and rapid single-shot data acquisition; (3) dynamic model-based image reconstruction; and (4) optimal experiment design.As a parameter estimation problem, CBF is quantified based on other reference parameters, such as T 1 and T 2 . Here, I introduce a novel T 2 mapping paradigm, which combines the conventional image reconstruction and parameter regression steps into one state tracking step. Using the unscented Kalman filter (UKF), the proposed method uses a T 2 decay model to estimate T 2 information from k-space data directly and efficiently. It achieves accurate estimation up to an undersampling factor of 8, which is comparable to a compressed sensing method with model-based sparsity. This new paradigm can be adapted to Cartesian and non-Cartesian trajectories, and other parameter mapping models.In order to improve ASL image quality, a rapid and robust ASL sequence was developed with a combined parallel and compressed sensing image reconstruction. Pseudo continuous radio frequency (RF) pulses are used to tag the proximal blood. A 3D turbo spin echo sequence with stack-of-spiral readouts [1] is used to acquire k-space data. Additionally, pulsatile motion artifacts are corrected by exploiting the redundancy among multiple receiver coils. A dual-density spiral trajectory is used to achieve single-shot imaging, which improves the SNR and freezes motion. ASL image quality and SNR are further improved by parallel reconstruction with spatial sparsity constraints.Accurate CBF mapping requires dy...

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Realistic Analytical Phantoms for Parallel Magnetic Resonance Imaging

Cited by 205 publications

References 22 publications

Generalized Sampling and Infinite-Dimensional Compressed Sensing

Generalized Sampling and Infinite-Dimensional Compressed Sensing

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Accuracy of Arterial Spin Labeling in Magnetic Resonance Imaging

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