Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint

Block, Kai Tobias; Uecker, Martin; Frahm, Jens

doi:10.1002/mrm.21236

Cited by 686 publications

(734 citation statements)

References 20 publications

(33 reference statements)

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“…For comparison, SparseSENSE and two other competing methods were also used for reconstruction. One approach was VD-SENSE (25) with ᐉ 2 regularization, whose regularization function is defined as ʈ⌬fʈ 2 ϭ ⌺͉⌬ x f ͉ 2 ϩ ͉⌬ y f ͉ 2 as in Block et al (11) and Ying et al (26), and the other used SparseMRI for a full FOV image in each channel and a SoS combination. The latter approach is similar to Marinelli et al (27), except that the joint sparsity was not employed here due to its inhibitive computational requirement.…”

Section: Phantom Experimentsmentioning

confidence: 99%

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Accelerating SENSE using compressed sensing

Liang

Liu

Wang

et al. 2009

Magnetic Resonance in Med

397

388

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Both parallel MRI and compressed sensing (CS) are emerging techniques to accelerate conventional MRI by reducing the number of acquired data. The combination of parallel MRI and CS for further acceleration is of great interest. In this paper, we propose a novel method to combine sensitivity encoding (SENSE), one of the standard methods for parallel MRI, and compressed sensing for rapid MR imaging (SparseMRI), a recently proposed method for applying CS in MR imaging with Cartesian trajectories. The proposed method, named CS-SENSE, sequentially reconstructs a set of aliased reducedfield-of-view images in each channel using SparseMRI and then reconstructs the final image from the aliased images using Cartesian SENSE. The results from simulations and phantom and in vivo experiments demonstrate that CS-SENSE can achieve a reduction factor higher than those achieved by SparseMRI and SENSE individually and outperform the existing method that combines parallel MRI and CS. Magn Reson Med 62:1574 -1584, 2009.

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Section: Phantom Experimentsmentioning

confidence: 99%

“…Therefore, the MR images can be reconstructed using a nonlinear convex program from data sampled at a rate close to their intrinsic information rate, which is well below the Nyquist rate. CS-MRI methods include SparseMRI for Cartesian trajectories (10) and methods for other trajectories (11,12).…”

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confidence: 99%

Accelerating SENSE using compressed sensing

Liang

Liu

Wang

et al. 2009

Magnetic Resonance in Med

397

388

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“…These reconstruction algorithms are generally in the state-of-the-art compressive sensing (CS) framework, utilizing prior knowledge effectively and permitting accurate and stable reconstruction from a more limited amount of raw data than requested by the classic Shannon sampling theory. CS-inspired reconstruction algorithms can be roughly categorized into the following stages (Wang et al , 2011): (1) The 1st stage: Candes’ total variation (TV) minimization method and variants (initially used for MRI and later on tried out for CT) (Li and Santosa, ’96; Jonsson et al , ’98; Candes and Tao, 2005; Landi and Piccolomini, 2005; Yu et al , 2005; Candes et al , 2006, 2008; Block et al , 2007; Landi et al , 2008; Sidky and Pan, 2008; Yu and Wang, 2009); (2) the 2nd stage: Soft-thresholding method adapted for X-ray CT to guarantee the convergence (Daubechies et al , 2004; Yu and Wang, 2010; Liu et al , 2011; Yu et al , 2011); and (3) the 3rd stage: Dictionary learning (DL) and non-local mean methods being actively developed by our group and others (Kreutz-Delgado et al , 2003; Gao et al , 2011; Lu et al , 2012; Xu et al , 2012; Zhao et al , 2012a,b). …”

Section: Introductionmentioning

confidence: 99%

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Liu

Verbridge

et al. 2014

Scanning

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Summary Electron tomography usually suffers from so-called “missing wedge” artifacts caused by limited tilt angle range. An equally sloped tomography (EST) acquisition scheme (which should be called the linogram sampling scheme) was recently applied to achieve 2.4-angstrom resolution. On the other hand, a compressive sensing inspired reconstruction algorithm, known as adaptive dictionary based statistical iterative reconstruction (ADSIR), has been reported for X-ray computed tomography. In this paper, we evaluate the EST, ADSIR, and an ordered-subset simultaneous algebraic reconstruction technique (OS-SART), and compare the ES and equally angled (EA) data acquisition modes. Our results show that OS-SART is comparable to EST, and the ADSIR outperforms EST and OS-SART. Furthermore, the equally sloped projection data acquisition mode has no advantage over the conventional equally angled mode in this context.

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“…To overcome this problem, a method was proposed (19) that first compensates for the missing negative spatial frequencies in the region [Àu h , Àu 1 ] using phase correction and Hermitian symmetry property and then recovers the nonacquired k-space data beyond the region [Àu h , u h ] by means of a mathematical model based on singularity function analysis (SFA). Another approach, called the total variation (TV) method, which is mainly used in computerized tomography (CT) reconstruction, was also employed for reconstructing MR images from undersampled k-space (20). The TV method aims to find a solution that optimizes the total variance of the reconstructed image.…”

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confidence: 99%

MRI reconstruction from 2D truncated k‐space

Luo¹,

Zhu²,

Li³

et al. 2011

Magnetic Resonance Imaging

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Purpose: To shorten acquisition time by means of both partial scanning and partial echo acquisition and to reconstruct images from such 2D partial k-space acquisitions. Materials and Methods:We propose an approach to reconstructing magnetic resonance images from 2D truncated k-space in which the k-space is truncated in both phase-and frequency-encoding directions. Unlike conventional reconstruction techniques, the proposed approach is based on a newly developed 2D singularity function analysis (SFA) model and a sparse representation of an image whose parameters can be estimated from the 2D partial k-space data. Such a sparse representation leads to an accurate recovery of the missing k-space data and, hence, an accurate reconstruction of the image.Results: The proposed approach can reconstruct an image from as little as 20%-30% of the k-space data and the quality of the reconstructed image is comparable to the reference image that is reconstructed from the complete k-space data. Conclusion:Despite the high asymmetry of a 2D truncated k-space, the proposed approach allows for accurate reconstruction without the need of phase correction and, thus, overcomes the assumption of slow phase variations that is usually required by the existing reconstruction methods. It provides a new way of fast imaging for applications that require a significant reduction of the acquisition time.

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Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint

Cited by 686 publications

References 20 publications

Accelerating SENSE using compressed sensing

Accelerating SENSE using compressed sensing

Issue Information

MRI reconstruction from 2D truncated k‐space

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