Variable Density Sampling with Continuous Trajectories

Chauffert, Nicolas; Ciuciu, Philippe; Kahn, Jonas; Weiss, Pierre

doi:10.1137/130946642

Cited by 113 publications

(90 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the initial preprint of this work, there have been several other applications and extensions inspired by the first version which we now mention for the reader's benefit. First, the multilevel sampling strategies we introduced have been extended to block sampling strategies [10,12,20,21], which are more practical for applications such as MRI. A type of multilevel subsampling has also be considered in [49,50] in the context of practical compressive imaging architectures, with application to single-pixel [37,78] and lensless imaging [86].…”

Section: Relation To Other Workmentioning

confidence: 99%

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Adcock

Hansen

Poon³

et al. 2017

Forum of Mathematics, Sigma

269

461

View full text Add to dashboard Cite

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)

show abstract

Section: Relation To Other Workmentioning

confidence: 99%

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Adcock

Hansen

Poon³

et al. 2017

Forum of Mathematics, Sigma

269

461

View full text Add to dashboard Cite

show abstract

“…The selection of a proper target density ρ is critical to obtain good reconstructions in the compressed sensing regime. This question is non‐trivial and currently subject to active research 14,41–44 . In particular, it should depend on the reconstruction algorithm and on the type of images probed.…”

Section: Theorymentioning

confidence: 99%

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

Lazarus

Weiss

Chauffert

et al. 2019

Magnetic Resonance in Med

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…[8][9][10][11][12][13]. Three imaging cases (cardiac cine, brain, and angiography) are compared and R = 6 in each case.…”

Section: B Comparison Of Image Reconstructionmentioning

confidence: 99%

Compressed Sensing MRI via Two-stage Reconstruction

Yang

et al. 2015

IEEE Trans. Biomed. Eng.

View full text Add to dashboard Cite

Compressed sensing (CS) has been applied to magnetic resonance imaging for the acceleration of data collection. However, existing CS techniques usually produce images with residual artifacts, particularly at high reduction factors. In this paper, we propose a novel, two-stage reconstruction scheme, which takes advantage of the properties of k-space data and under-sampling patterns that are useful in CS. In this algorithm, the under-sampled k-space data is segmented into low-frequency and high-frequency domains. Then, in stage one, using dense measurements, the low-frequency region of k-space data is faithfully reconstructed. The fully reconstituted low-frequency k-space data from the first stage is then combined with the high-frequency k-space data to complete the second stage reconstruction of the whole of k-space. With this two-stage approach, each reconstruction inherently incorporates a lower data under-sampling rate and more homogeneous signal magnitudes than conventional approaches. Because the restricted isometric property is easier to satisfy, the reconstruction consequently produces lower residual errors at each step. Compared with a conventional CS reconstruction, for the cases of cardiac cine, brain and angiogram imaging, the proposed method achieves a more accurate reconstruction with an improvement of 2-4 dB in peak signal-to-noise ratio respectively, using reduction factors of up to 6.

show abstract

Variable Density Sampling with Continuous Trajectories

Cited by 113 publications

References 52 publications

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

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

Compressed Sensing MRI via Two-stage Reconstruction

Contact Info

Product

Resources

About

Variable Density Sampling with Continuous Trajectories

Cited by 113 publications

References 52 publications

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

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

Compressed Sensing MRI via Two-stage Reconstruction

Contact Info

Product

Resources

About

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