Compressive imaging using approximate message passing and a Markov-tree prior

Som,; Potter,; Schniter, Philip

doi:10.1109/acssc.2010.5757509

Cited by 66 publications

(158 citation statements)

References 15 publications

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“…Most existing tree-based compressed sensing algorithms directly replace the standard sparsity with tree sparsity [25][26][27][28]37,38]. However, for practical MR images, the wavelet coefficients cannot perfectly match the theoretical assumption of tree sparsity.…”

Section: Algorithmmentioning

confidence: 99%

“…All experiments are conducted on a laptop with 2.4GHz Intel core i5 2430 M CPU in MATLAB 2009 (MathWorks, Natick, MA). We first compare our algorithm with the classical CG method [6] and three of the fastest MR image reconstruction algorithms: TVCMRI [12], RecPF [13], FCSA [14,15], and then with general tree based algorithms or solvers: AMP [28], VB [27], YALL1 [38], and SLEP [37]. For fair comparisons, all codes are downloaded from the Websites of the corresponding authors.…”

Section: Experiments Setupmentioning

confidence: 99%

“…For fair comparisons, all codes are downloaded from the Websites of the corresponding authors. We do not include MCMC [26] in experiments because it has ultra-slow execution speed and untractable convergence [27,28]. OGL [25] solves its model by SpaRSA [11] with only O 1=n ð Þ convergence rate, which cannot be competitive with recent FISTA [10,16] algorithms with O 1=n 2 À Á convergence rate.…”

Section: Experiments Setupmentioning

confidence: 99%

“…Markov Chain Monte Carlo (MCMC) [26] and Variational Bayesian (VB) [27] are applied to solve the hierarchical Bayesian models. For approximate message passing (AMP) algorithm [28], the wavelet coefficients are modeled as conditionally Gaussian with variances that depend on the values of hidden Markov tree (HMT) states. Therefore the beliefs (about both coefficients and states) on the corresponding factor graph are propagated.…”

Section: Tree Based Imaging Algorithmsmentioning

confidence: 99%

“…m r i j o u r n a l . c o m greedy algorithms [20,21,24], convex programming [25] and Bayesian learning [26][27][28]. Although these algorithms provide better reconstruction accuracy than those with standard sparsity, they are slow in general due to the intricate tree structure.…”

Section: Contents Lists Available At Sciencedirectmentioning

confidence: 99%

See 4 more Smart Citations

Exploiting the wavelet structure in compressed sensing MRI

Chen¹,

Huang²

2014

Magnetic Resonance Imaging

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Section: Algorithmmentioning

confidence: 99%

Section: Experiments Setupmentioning

confidence: 99%

Section: Experiments Setupmentioning

confidence: 99%

Section: Tree Based Imaging Algorithmsmentioning

confidence: 99%

Section: Contents Lists Available At Sciencedirectmentioning

confidence: 99%

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Exploiting the wavelet structure in compressed sensing MRI

Chen¹,

Huang²

2014

Magnetic Resonance Imaging

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Variable density incoherent spatiotemporal acquisition (VISTA) for highly accelerated cardiac MRI

Ahmad

Xue

Giri

et al. 2014

Magnetic Resonance in Med

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Purpose For the application of compressive sensing to parallel MRI, Poisson disk sampling (PDS) has been shown to generate superior results compared with random sampling methods. However, due to its limited flexibility to incorporate additional constraints, PDS is not readily extendible to dynamic applications. Here, we propose and validate a pseudo-random sampling technique that allows incorporating constraints specific to dynamic imaging. Methods The proposed sampling scheme, called variable density incoherent spatiotemporal acquisition (VISTA), is based on constrained minimization of Riesz energy on a spatiotemporal grid. Data from both a digital phantom and real-time cine were used to compare VISTA with uniform interleaved sampling (UIS) and variable density random sampling (VRS). The image quality was assessed qualitatively and quantitatively. Results VISTA improved the trade-off between noise and sharpness. Also, VISTA produced diagnostic quality images at an acceleration rate of 15, whereas UIS and VRS images degraded below the diagnostic threshold at lower acceleration rates. Conclusions VISTA generates spatiotemporal sampling patterns with high levels of uniformity and incoherence, while maintaining a constant temporal resolution. Using a small pilot study, VISTA was shown to produce diagnostic quality images at acceleration rates up to 15.

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A Bayesian model for highly accelerated phase-contrast MRI

Rich

Potter

Jin³

et al. 2015

Magn. Reson. Med.

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Purpose Phase-contrast magnetic resonance imaging (PC-MRI) is a noninvasive tool to assess cardiovascular disease by quantifying blood flow; however, low data acquisition efficiency limits the spatial and temporal resolutions, real-time application, and extensions to 4D flow imaging in clinical settings. We propose a new data processing approach called Reconstructing Velocity Encoded MRI with Approximate message passing aLgorithms (ReVEAL) that accelerates the acquisition by exploiting data structure unique to PC-MRI. Theory and Methods ReVEAL models physical correlations across space, time, and velocity encodings. The proposed Bayesian approach exploits the relationships in both magnitude and phase among velocity encodings. A fast iterative recovery algorithm is introduced based on message passing. For validation, prospectively undersampled data are processed from a pulsatile flow phantom and five healthy volunteers. Results ReVEAL is in good agreement, quantified by peak velocity and stroke volume (SV), with reference data for acceleration rates R ≤ 10. For SV, Pearson r ≥ 0.996 for phantom imaging (n = 24) and r ≥ 0.956 for prospectively accelerated in vivo imaging (n = 10) for R ≤ 10. Conclusion ReVEAL enables accurate quantification of blood flow from highly undersampled data. The technique is extensible to 4D flow imaging, where higher acceleration may be possible due to additional redundancy.

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Compressive imaging using approximate message passing and a Markov-tree prior

Cited by 66 publications

References 15 publications

Exploiting the wavelet structure in compressed sensing MRI

Exploiting the wavelet structure in compressed sensing MRI

Variable density incoherent spatiotemporal acquisition (VISTA) for highly accelerated cardiac MRI

A Bayesian model for highly accelerated phase-contrast MRI

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