HYR&lt;sup&gt;2&lt;/sup&gt;PICS: Hybrid regularized reconstruction for combined parallel imaging and compressive sensing in MRI

Boyer, Claire; Ciuciu, Philippe; Weiss, Pierre; Mériaux, Sébastien

doi:10.1109/isbi.2012.6235485

Cited by 9 publications

(8 citation statements)

References 17 publications

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“…Moreover we considered a simple MRI model, but our method can be extended to parallel MRI [39], or spread-spectrum techniques [20,40]. 6 We provide Matlab codes to reproduce the proposed experiments here: http://chauffertn.free.fr/codes.html walks and Travelling Salesman Problem. We also compared our solution to classical MRI sampling schemes.…”

Section: Experimental Results In Mrimentioning

confidence: 99%

“…Finally, let us notice that the best empirical convex reconstruction techniques do not rely on the resolution of a simple 1 problem such as (1.1). They are based on regularization with redundant frames and total variation for instance [6]. The signal model, the target density and the reconstruction algorithm should clearly be considered simultaneously to make a substantial leap on reconstruction guarantees.…”

Section: Followsmentioning

confidence: 99%

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Variable Density Sampling with Continuous Trajectories

Chauffert¹,

Ciuciu²,

Kahn³

et al. 2014

SIAM J. Imaging Sci.

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113

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Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse signals by projection on a low-dimensional linear subspace. In this paper, we focus on a setting where the imaging device allows us to sense a fixed set of measurements. We first discuss the choice of an optimal sampling subspace allowing perfect reconstruction of sparse signals. Its design relies on the random drawing of independent measurements. We discuss how to select the drawing distribution and show that a mixed strategy involving partial deterministic sampling and independent drawings can help in breaking the so-called coherence barrier. Unfortunately, independent random sampling is irrelevant for many acquisition devices owing to acquisition constraints. To overcome this limitation, the notion of a variable density sampler (VDS) is introduced and defined as a stochastic process with a prescribed limit empirical measure. It encompasses samplers based on independent measurements or continuous curves. The latter are crucial to extend CS results to actual applications. We propose two original approaches to designing a continuous VDS, one based on random walks over the acquisition space and one based on the travelling salesman problem. Following theoretical considerations and retrospective CS simulations in magnetic resonance imaging, we intend to highlight the key properties of a VDS to ensure accurate sparse reconstructions, namely its limit empirical measure and its mixing time.

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Section: Experimental Results In Mrimentioning

confidence: 99%

Section: Followsmentioning

confidence: 99%

Variable Density Sampling with Continuous Trajectories

Chauffert¹,

Ciuciu²,

Kahn³

et al. 2014

SIAM J. Imaging Sci.

Self Cite

113

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show abstract

“…2D MR image reconstructions were performed by iteratively minimizing a sparsity promoting regularized Compressed Sensing SENsitivity Encoding (CS‐SENSE) criterion introduced in 52–54 . We adopted a synthesis formulation composed of an

ℓ_{2}

‐norm data consistency term and an

ℓ_{1}

‐norm penalty term, which reads as follows:

\overset{true^}{boldz} = \underset{z \in C^{N \times N}}{\arg \min} \frac{1}{2} {false\sum}_{ℓ = 1}^{L} false‖ F_{normalΩ} {boldS}_{ℓ} Ψ z - {boldy}_{ℓ} ‖_{2}^{2} + λ {‖ z ‖}_{1} .

The decomposition (

\overset{z}{true}

) is then transformed back to the image domain using the synthesis operator Ψ :

\overset{true^}{boldx} = Ψ \overset{true^}{boldz}

.…”

Section: Methodsmentioning

confidence: 99%

SPARKLING: variable‐density k‐space filling curves for accelerated T₂^*‐weighted MRI

Lazarus

Weiss

Chauffert

et al. 2019

Magnetic Resonance in Med

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Purpose To present a new optimition‐driven design of optimal k‐space trajectories in the context of compressed sensing: Spreading Projection Algorithm for Rapid K‐space sampLING (SPARKLING). TheoryThe SPARKLING algorithm is a versatile method inspired from stippling techniques that automatically generates optimized sampling patterns compatible with MR hardware constraints on maximum gradient amplitude and slew rate. These non‐Cartesian sampling curves are designed to comply with key criteria for optimal sampling: a controlled distribution of samples (e.g., variable density) and a locally uniform k‐space coverage. MethodsEx vivo and in vivo prospective T2*‐weighted acquisitions were performed on a 7‐Tesla scanner using the SPARKLING trajectories for various setups and target densities. Our method was compared to radial and variable‐density spiral trajectories for high‐resolution imaging. ResultsCombining sampling efficiency with compressed sensing, the proposed sampling patterns allowed up to 20‐fold reductions in MR scan time (compared to fully sampled Cartesian acquisitions) for two‐dimensional T2*‐weighted imaging without deterioration of image quality, as demonstrated by our experimental results at 7 Tesla on in vivo human brains for a high in‐plane resolution of 390 μm. In comparison to existing non‐Cartesian sampling strategies, the proposed technique also yielded superior image quality. ConclusionsThe proposed optimization‐driven design of k‐space trajectories is a versatile framework that is able to enhance MR sampling performance in the context of compressed sensing.

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“…Most of these works were directed to the proposal of reconstruction methods for parallel MRI (PMRI) [7,9,12,31,41]. The objective of PMRI is to reduce the acquisition time while maintaining a good image quality.…”

Section: Introductionmentioning

confidence: 99%

A Majorize-Minimize Memory Gradient method for complex-valued inverse problems

et al. 2014

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Complex-valued data are encountered in many application areas of signal and image processing. In the context of optimization of functions of real variables, subspace algorithms have recently attracted much interest, owing to their efficiency for solving large-size problems while simultaneously offering theoretical convergence guarantees. The goal of this paper is to show how some of these methods can be successfully extended to the complex case. More precisely, we investigate the properties of the proposed complex-valued Majorize-Minimize Memory Gradient (3MG) algorithm. Important practical applications of these results arise in inverse problems. Here, we focus on image reconstruction in Parallel Magnetic Resonance Imaging (PMRI). The linear operator involved in the observation model then includes a subsampling operator over the k-space (spatial Fourier domain) the choice of which is analyzed through our numerical results. In addition, sensitivity matrices associated with the multiple coil channels come into play. Comparisons with existing optimization methods confirm the good performance of the proposed algorithm. * (1) Part of A. Florescu's work was supported by PhD Fellowship "Investitii in cercetare-inovare-dezvoltare pentru viitor (DocInvest)", EC project POS-DRU/107/1.5/S/76813.(2) Corresponding author. (

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HYR<sup>2</sup>PICS: Hybrid regularized reconstruction for combined parallel imaging and compressive sensing in MRI

Cited by 9 publications

References 17 publications

Variable Density Sampling with Continuous Trajectories

Variable Density Sampling with Continuous Trajectories

SPARKLING: variable‐density k‐space filling curves for accelerated T₂^*‐weighted MRI

A Majorize-Minimize Memory Gradient method for complex-valued inverse problems

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HYR<sup>2</sup>PICS: Hybrid regularized reconstruction for combined parallel imaging and compressive sensing in MRI

Cited by 9 publications

References 17 publications

Variable Density Sampling with Continuous Trajectories

Variable Density Sampling with Continuous Trajectories

SPARKLING: variable‐density k‐space filling curves for accelerated T2*‐weighted MRI

A Majorize-Minimize Memory Gradient method for complex-valued inverse problems

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SPARKLING: variable‐density k‐space filling curves for accelerated T₂^*‐weighted MRI