Acceleration of Perfusion MRI Using Locally Low-Rank Plus Sparse Model

Daňková, Marie; Rajmic, Pavel; Jiřík, Radovan

doi:10.1007/978-3-319-22482-4_60

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…Now, return back to Equation (10). Suppose that z ∈ Γ; then, (Lz) ∈ [b 1 , b 2 ]; from Equation 11, we have proj [b 1 ,b 2 ] (Lz) = Lz; and, from Equation 10, we get proj Γ (z) = z, which is correct.…”

Section: Definitionmentioning

confidence: 90%

“…Proximal algorithms are a modern branch of mathematical optimization, whose principal building blocks are the so-called proximal operators [1][2][3][4]. In applications, the model of the problem often involves the composition of a non-linear function with a linear operator [5][6][7][8][9][10]. When proximal optimization is utilized to find approximate solution iteratively, the proximal operator of such a composition is needed, making the resulting algorithms computationally expensive in general [11].…”

Section: Introductionmentioning

confidence: 99%

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A New Generalized Projection and Its Application to Acceleration of Audio Declipping

Rajmic

Záviška

Veselý

et al. 2019

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In convex optimization, it is often inevitable to work with projectors onto convex sets composed with a linear operator. Such a need arises from both the theory and applications, with signal processing being a prominent and broad field where convex optimization has been used recently. In this article, a novel projector is presented, which generalizes previous results in that it admits to work with a broader family of linear transforms when compared with the state of the art but, on the other hand, it is limited to box-type convex sets in the transformed domain. The new projector is described by an explicit formula, which makes it simple to implement and requires a low computational cost. The projector is interpreted within the framework of the so-called proximal splitting theory. The convenience of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

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Section: Definitionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

A New Generalized Projection and Its Application to Acceleration of Audio Declipping

Rajmic

Záviška

Veselý

et al. 2019

Axioms

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“…Recently, Hankel or block‐Hankel matrix completion has been used for recovering undersampled spectral data and calibrationless parallel imaging reconstruction . The low‐rank property of dynamic MRI data has also been demonstrated and utilized in accelerated reconstructions .…”

Section: Introductionmentioning

confidence: 99%

Accelerated high-bandwidth MR spectroscopic imaging using compressed sensing

et al. 2016

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Purpose To develop a compressed sensing (CS) acceleration method with a high spectral bandwidth exploiting the spatial-spectral sparsity of MR spectroscopic imaging (MRSI). Methods Accelerations were achieved using blip gradients during the readout to perform non-overlapped and stochastically delayed random walks in kx-ky-t space, combined with block-Hankel matrix completion for efficient reconstruction. Both retrospective and prospective CS accelerations were applied to 13C MRSI experiments, including in vivo rodent brain and liver studies with administrations of hyperpolarized [1-13C] pyruvate at 7T and [2-13C] dihydroxyacetone at 3T, respectively. Results In retrospective undersampling experiments using in vivo 7T data, the proposed method preserved spectral, spatial and dynamic fidelities with R2 ≥ 0.96 and ≥ 0.87 for pyruvate and lactate signals, respectively, 750-Hz spectral separation and up to 6.6-fold accelerations. In prospective in vivo experiments, with 3.8-fold acceleration, the proposed method exhibited excellent spatial localization of metabolites and peak recovery for pyruvate and lactate at 7T as well as for dihydroxyacetone and its metabolic products with a 4.5-kHz spectral span (140 ppm at 3T). Conclusion This study demonstrated the feasibility of a new CS approach to accelerate high spectral bandwidth MRSI experiments.

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