Low-Rank Modeling of Local &lt;formula formulatype="inline"&gt; &lt;tex Notation="TeX"&gt;$k$&lt;/tex&gt;&lt;/formula&gt;-Space Neighborhoods (LORAKS) for Constrained MRI

Haldar, Justin P.

doi:10.1109/tmi.2013.2293974

Cited by 256 publications

(76 citation statements)

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“…Low-rank modeling of local k-space neighborhoods (LORAKS) works by reconstructing k-space data using low rank matrix completion [135,136]. The reconstruction attempts to find a solution that is both consistent with the undersampled data and also satisfies two special properties.…”

Section: Phase-constrained Parallel Imagingmentioning

confidence: 99%

Recent advances in parallel imaging for MRI

Hamilton

Franson

Seiberlich

2017

Progress in Nuclear Magnetic Resonance Spectroscopy

181

125

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Magnetic Resonance Imaging (MRI) is an essential technology in modern medicine. However, one of its main drawbacks is the long scan time needed to localize the MR signal in space to generate an image. This review article summarizes some basic principles and recent developments in parallel imaging, a class of image reconstruction techniques for shortening scan time. First, the fundamentals of MRI data acquisition are covered, including the concepts of k-space, undersampling, and aliasing. It is demonstrated that scan time can be reduced by sampling a smaller number of phase encoding lines in k-space; however, without further processing, the resulting images will be degraded by aliasing artifacts. Nearly all modern clinical scanners acquire data from multiple independent receiver coil arrays. Parallel imaging methods exploit properties of these coil arrays to separate aliased pixels in the image domain or to estimate missing k-space data using knowledge of nearby acquired k-space points. Three parallel imaging methods—SENSE, GRAPPA, and SPIRiT—are described in detail, since they are employed clinically and form the foundation for more advanced methods. These techniques can be extended to non-Cartesian sampling patterns, where the collected k-space points do not fall on a rectangular grid. Non-Cartesian acquisitions have several beneficial properties, the most important being the appearance of incoherent aliasing artifacts. Recent advances in simultaneous multi-slice imaging are presented next, which use parallel imaging to disentangle images of several slices that have been acquired at once. Parallel imaging can also be employed to accelerate 3D MRI, in which a contiguous volume is scanned rather than sequential slices. Another class of phase-constrained parallel imaging methods takes advantage of both image magnitude and phase to achieve better reconstruction performance. Finally, some applications are presented of parallel imaging being used to accelerate MR Spectroscopic Imaging.

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Section: Phase-constrained Parallel Imagingmentioning

confidence: 99%

Recent advances in parallel imaging for MRI

Hamilton

Franson

Seiberlich

2017

Progress in Nuclear Magnetic Resonance Spectroscopy

181

125

View full text Add to dashboard Cite

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“…The linear dependencies between the Fourier coefficients exploited the in structured low-rank matrix priors result from a variety of assumptions, including continuous domain analogs of sparsity [3], [6], [8], [9], correlations in the locations of the sparse coefficients in space [8], [9], multi-channel sampling [2], [10], [11], or smoothly varying complex phase [4]. For example, the LORAKS framework [4] capitalized on the sparsity and smooth phase of the continuous domain image using structured low-rank priors, which offers improved reconstructions over conventional ℓ 1 recovery.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the LORAKS framework [4] capitalized on the sparsity and smooth phase of the continuous domain image using structured low-rank priors, which offers improved reconstructions over conventional ℓ 1 recovery. Similarly, we have shown that the Fourier coefficients of continuous domain piecewise constant images whose discontinuities are localized to zero level-set of a bandlimited function satisfy an annihilation relationship [9]; their recovery from undersampled Fourier measurements translates to a convolutional structured low-rank matrix completion problem [8].…”

Section: Introductionmentioning

confidence: 99%

“…Despite improvements in empirical and statistical recovery performance over traditional methods as seen from [2]–[4], [6], [8], [16], these structured low-rank matrix recovery schemes are associated with a dramatic increase in computational complexity and memory demand; this restricts their direct extension to multi-dimensional imaging applications, such as dynamic MRI reconstruction. In particular, these algorithms involve the recovery of a large-scale Toeplitz-like matrix whose combined dimensions are several orders of magnitude larger than those of the image.…”

Section: Introductionmentioning

confidence: 99%

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A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Ongie

Jacob

2017

IEEE Trans. Comput. Imaging

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Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multi-level generalizations, built from Fourier data of the image should be low-rank. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from a lifting the image data to a large scale matrix. We introduce a fast and memory efficient approach called the Generic Iterative Reweighted Annihilation Filter (GIRAF) algorithm that exploits the convolutional structure of the lifted matrix to work in the original un-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm is considerably faster than previously proposed algorithms, and can accommodate much larger problem sizes than previously studied.

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“…Since a series of images with the same anatomy but different image contrast is acquired in contrast enhanced MR angiography, methods that exploit the spatiotemporal correlation of the dynamic image series, such as keyhole, various k-t (K-space domain and time doman) methods, and low-rank methods, can also be applied [11–19]. Promising results in contrast enhanced MR angiography have been achieved using parallel imaging, compressed sensing and low-rank methods or the combination of these methods [20–29]. …”

Section: Introductionmentioning

confidence: 99%

Clinical performance of a free-breathing spatiotemporally accelerated 3-D time-resolved contrast-enhanced pediatric abdominal MR angiography

et al. 2015

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Background Pediatric contrast-enhanced MR angiography is often limited by respiration, other patient motion and compromised spatiotemporal resolution. Objective To determine the reliability of a free-breathing spatiotemporally accelerated 3-D time-resolved contrast enhanced MR angiography method for depicting abdominal arterial anatomy in young children. Materials and methods With IRB approval and informed consent, we retrospectively identified 27 consecutive children (16 males and 11 females; mean age: 3.8 years, range: 14 days to 8.4 years) referred for contrast enhanced MR angiography at our institution, who had undergone free-breathing spatiotemporally accelerated time-resolved contrast enhanced MR angiography studies. An radio-frequency-spoiled gradient echo sequence with Cartesian variable density k-space sampling and radial view ordering, intrinsic motion navigation and intermittent fat suppression was developed. Images were reconstructed with soft-gated parallel imaging locally low-rank method to achieve both motion correction and high spatiotemporal resolution. Quality of delineation of 13 abdominal arteries in the reconstructed images was assessed independently by two radiologists on a five-point scale. Ninety-five percent confidence intervals of the proportion of diagnostically adequate cases were calculated. Interobserver agreements were also analyzed. Results Eleven out of 13 arteries achieved acceptable image quality (mean score range: 3.9–5.0) for both readers. Fair to substantial interobserver agreement was reached on nine arteries. Conclusion Free-breathing spatiotemporally accelerated 3-D time-resolved contrast enhanced MR angiography frequently yields diagnostic image quality for most abdominal arteries for pediatric contrast enhanced MR angiography.

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Low-Rank Modeling of Local <formula formulatype="inline"> <tex Notation="TeX">$k$</tex></formula>-Space Neighborhoods (LORAKS) for Constrained MRI

Cited by 256 publications

References 50 publications

Recent advances in parallel imaging for MRI

Recent advances in parallel imaging for MRI

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Clinical performance of a free-breathing spatiotemporally accelerated 3-D time-resolved contrast-enhanced pediatric abdominal MR angiography

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