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**1 - 4**of**4**### Accelerating Magnetic Resonance Imaging by Unifying Sparse Models and Multiple Receivers

, 2012

"... Magnetic resonance imaging (MRI) is an increasingly versatile diagnostic tool for a variety of medical purposes. During a conventional MRI scan, samples are acquired along a trajectory in the spatial Fourier transform domain (called k-space) and the image is reconstructed using an inverse discrete F ..."

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Magnetic resonance imaging (MRI) is an increasingly versatile diagnostic tool for a variety of medical purposes. During a conventional MRI scan, samples are acquired along a trajectory in the spatial Fourier transform domain (called k-space) and the image is reconstructed using an inverse discrete Fourier transform. The affordability, availability, and applications of MRI remain limited by the time required to sam-ple enough points of k-space for the desired field of view (FOV), resolution, and signal-to-noise ratio (SNR). GRAPPA, an accelerated parallel imaging method, and compressed sensing (CS) have been successfully employed to accelerate the acquisi-tion process by reducing the number of k-space samples required. GRAPPA leverages the different spatial weightings of each receiver coil to undo the aliasing from the re-duction in FOV induced by undersampling k-space. However, accelerated parallel imaging reconstruction methods like GRAPPA amplify the noise present in the data, reducing the SNR by a factor greater than that due to only the level of undersampling. Completely separate from accelerated parallel imaging, which capitalizes on observ-

### A Convex Optimization Approach to pMRI Reconstruction

, 2013

"... In parallel magnetic resonance imaging (pMRI) reconstruction without using pre-estimation of coil sensitivity functions, one group of algorithms reconstructs sensitivity encoded images of the coils first followed by the magnitude image reconstruction, e.g. GRAPPA. Another group of algorithms jointly ..."

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In parallel magnetic resonance imaging (pMRI) reconstruction without using pre-estimation of coil sensitivity functions, one group of algorithms reconstructs sensitivity encoded images of the coils first followed by the magnitude image reconstruction, e.g. GRAPPA. Another group of algorithms jointly computes the image and sensi-tivity functions by regularized optimization which is a non-convex problem with local only solution. For the magnitude image reconstruction, this paper derives a reconstruction formulation, which is linear in the magnitude image, and an associated convex hull in the solution space of the formulated equation containing the magnitude image. As a result, the magnitude image reconstruction for pMRI is formulated into a two-step convex optimization problem, which produces a globally optimal solution. An algorithm based on split-bregman and nuclear norm regularized optimizations is proposed to implement the two-step convex optimization and its applications to phantom and in-vivo MRI data sets result in superior reconstruction perfor-mance compared with existing algorithms.

### LAPLACIAN TRANSFORM BASED SPARSITY REGULARIZATION

"... The SENSE model with sparsity regularization acts as an unconstrained minimization problem to reconstruct the MRI, which obtain better reconstruction results than the traditional SENSE. To implement the sparsity constraints, discrete wavelet transform (DWT) and total variation (TV) are common exploi ..."

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The SENSE model with sparsity regularization acts as an unconstrained minimization problem to reconstruct the MRI, which obtain better reconstruction results than the traditional SENSE. To implement the sparsity constraints, discrete wavelet transform (DWT) and total variation (TV) are common exploited together to sparsify the MR image. In this paper, a novel sparsifying transform based on the combination of singular value decomposition (SVD) and Laplacian (LP) transform is proposed for parallel MR image reconstruction. The proposed algorithm adopts the SVD of the MR image as sparsifying transform instead of exploiting the wavelet domain sparsity of the image, and uses the LP-norm as an alternative to TV-norm in the sparsity regularization term. The performances of the proposed method are evaluated on two typical types of MR image (complex brain MR image and sparse angiogram MR image). Compared with the DWT-TV sparsifying transform, the proposed SVD-LP method can significantly achieve better reconstruction quality and considerably improve the computation efficiency.

### Sparse Models and Multiple Receivers

, 2012

"... Magnetic resonance imaging (MRI) is an increasingly versatile diagnostic tool for a variety of medical purposes. During a conventional MRI scan, samples are acquired along a trajectory in the spatial Fourier transform domain (called k-space) and the image is reconstructed using an inverse discrete F ..."

Abstract
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(Show Context)
Magnetic resonance imaging (MRI) is an increasingly versatile diagnostic tool for a variety of medical purposes. During a conventional MRI scan, samples are acquired along a trajectory in the spatial Fourier transform domain (called k-space) and the image is reconstructed using an inverse discrete Fourier transform. The affordability, availability, and applications of MRI remain limited by the time required to sam-ple enough points of k-space for the desired field of view (FOV), resolution, and signal-to-noise ratio (SNR). GRAPPA, an accelerated parallel imaging method, and compressed sensing (CS) have been successfully employed to accelerate the acquisi-tion process by reducing the number of k-space samples required. GRAPPA leverages the different spatial weightings of each receiver coil to undo the aliasing from the re-duction in FOV induced by undersampling k-space. However, accelerated parallel imaging reconstruction methods like GRAPPA amplify the noise present in the data,