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Accelerating SENSE using compressed sensing
"... Both parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are emerging techniques to accelerate conventional MRI by reducing the number of acquired data. The combination of pMRI and CS for further acceleration is of great interests. In this paper, we propose two methods to combine ..."
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Cited by 21 (3 self)
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Both parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are emerging techniques to accelerate conventional MRI by reducing the number of acquired data. The combination of pMRI and CS for further acceleration is of great interests. In this paper, we propose two methods to combine SENSE, one of the standard methods for pMRI, and SparseMRI, a recently proposed method for CSMRI with Cartesian trajectories. The first method, named SparseSENSE, directly formulates the reconstruction from multichannel reduced kspace data as the same nonlinear convex optimization problem as SparseMRI, except that the encoding matrix is the Fourier transform of the channelspecific sensitivity modulation. The second method, named CSSENSE, first employs SparseMRI to reconstruct a set of aliased reducedfieldofview images in each channel, and then applies Cartesian SENSE to reconstruct the final image. The results from simulations, phantom and in vivo experiments demonstrate that both SparseSENSE and CSSENSE can achieve a reduction factor higher than those achieved by SparseMRI and SENSE individually, and CSSENSE outperforms SparseSENSE in most cases. MR imaging speed is usually limited by the large number of samples needed along the phase encoding direction. In conventional MRI using Fourier encoding, the required number of samples is determined by
Sparse methods for biomedical data
 SIGKDD Explor. Newsl
, 2012
"... Following recent technological revolutions, the investigation of massive biomedical data with growing scale, diversity, and complexity has taken a center stage in modern data analysis. Although complex, the underlying representations of many biomedical data are often sparse. For example, for a certa ..."
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Cited by 12 (2 self)
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Following recent technological revolutions, the investigation of massive biomedical data with growing scale, diversity, and complexity has taken a center stage in modern data analysis. Although complex, the underlying representations of many biomedical data are often sparse. For example, for a certain disease such as leukemia, even though humans have tens of thousands of genes, only a few genes are relevant to the disease; a gene network is sparse since a regulatory pathway involves only a small number of genes; many biomedical signals are sparse or compressible in the sense that they have concise representations when expressed in a proper basis. Therefore, finding sparse representations is fundamentally important for scientific discovery. Sparse methods based on the ℓ1 norm have attracted a great amount of research efforts in the past decade due to its sparsityinducing property, convenient convexity, and strong theoretical guarantees. They have achieved great success in various applications such as biomarker selection, biological network construction, and magnetic resonance imaging. In this paper, we review stateoftheart sparse methods and their applications to biomedical data.
Nonlinear GRAPPA: A kernel approach to parallel MRI reconstruction,” Magn
 2012. et al.: SPARSITYPROMOTING CALIBRATION FOR GRAPPA ACCELERATED PARALLEL MRI RECONSTRUCTION 1335
"... GRAPPA linearly combines the undersampled kspace signals to estimate the missing kspace signals where the coefficients are obtained by fitting to some autocalibration signals (ACS) sampled with Nyquist rate based on the shiftinvariant property. At high acceleration factors, GRAPPA reconstructio ..."
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Cited by 4 (0 self)
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GRAPPA linearly combines the undersampled kspace signals to estimate the missing kspace signals where the coefficients are obtained by fitting to some autocalibration signals (ACS) sampled with Nyquist rate based on the shiftinvariant property. At high acceleration factors, GRAPPA reconstruction can suffer from a high level of noise even with a large number of autocalibration signals. In this work, we propose a nonlinear method to improve GRAPPA. The method is based on the socalled kernel method which is widely used in machine learning. Specifically, the undersampled kspace signals are mapped through a nonlinear transform to a highdimensional feature space, and then linearly combined to reconstruct the missing kspace data. The linear combination coefficients are also obtained through fitting to the ACS data but in the new feature space. The procedure is equivalent to adding many virtual channels in reconstruction. A polynomial kernel with explicit mapping functions is investigated in this work. Experimental results using phantom and in vivo data demonstrate that the proposed nonlinear GRAPPA method can significantly improve the reconstruction quality over GRAPPA and its
Article Calibrationless Parallel Magnetic Resonance Imaging: A Joint Sparsity Model
, 2013
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Magnetic Resonance in Medicine 60:674–682 (2008) Image Reconstruction by Regularized Nonlinear Inversion—Joint Estimation of Coil Sensitivities and Image Content
"... The use of parallel imaging for scan time reduction in MRI faces problems with image degradation when using GRAPPA or SENSE for high acceleration factors. Although an inherent loss of SNR in parallel MRI is inevitable due to the reduced measurement time, the sensitivity to image artifacts that resul ..."
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The use of parallel imaging for scan time reduction in MRI faces problems with image degradation when using GRAPPA or SENSE for high acceleration factors. Although an inherent loss of SNR in parallel MRI is inevitable due to the reduced measurement time, the sensitivity to image artifacts that result from severe undersampling can be ameliorated by alternative reconstruction methods. While the introduction of GRAPPA and SENSE extended MRI reconstructions from a simple unitary transformation (Fourier transform) to the inversion of an illconditioned linear system, the next logical step is the use of a nonlinear inversion. Here, a respective algorithm based on a Newtontype method with appropriate regularization terms is demonstrated to improve the performance of autocalibrating parallel MRI—mainly due to a better estimation of the coil sensitivity profiles. The approach yields images with considerably
Magnetic Resonance in Medicine 63:1456–1462 (2010) Nonlinear Inverse Reconstruction for RealTime MRI of the Human Heart Using Undersampled Radial FLASH
"... Apreviously proposednonlinear inverse reconstruction for autocalibrated parallel imaging simultaneously estimates coil sensitivities and image content. This work exploits this property for realtime MRI, where coil sensitivities need to be dynamically adapted to the conditions generated by moving ..."
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Apreviously proposednonlinear inverse reconstruction for autocalibrated parallel imaging simultaneously estimates coil sensitivities and image content. This work exploits this property for realtime MRI, where coil sensitivities need to be dynamically adapted to the conditions generated by moving objects. The development comprises (i) an extension of the nonlinear inverse algorithm to nonCartesian kspace encodings, (ii) its implementation on a graphical processing unit to reduce reconstruction times, and (iii) the use of a convolutionbased iteration, which considerably simplifies the graphical processing unit implementation compared to a gridding technique. The method is validated for realtime MRI of the human heart at 3 T using radio frequencyspoiled radial FLASH (pulse repetition time/echo time = 2.0/1.3 ms, flip angle 8◦). The results demonstrate artifactfree reconstructions from only 65–85 spokes,
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 kspace) 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 kspace) 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 sample enough points of kspace for the desired field of view (FOV), resolution, and signaltonoise ratio (SNR). GRAPPA, an accelerated parallel imaging method, and compressed sensing (CS) have been successfully employed to accelerate the acquisition process by reducing the number of kspace samples required. GRAPPA leverages the different spatial weightings of each receiver coil to undo the aliasing from the reduction in FOV induced by undersampling kspace. 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 Statistical Approach to SENSE Regularization With Arbitrary kSpace Trajectories
"... SENSE reconstruction suffers from an illconditioning problem, which increasingly lowers the signaltonoise ratio (SNR) as the reduction factor increases. Illconditioning also degrades the convergence behavior of iterative conjugate gradient reconstructions for arbitrary trajectories. Regularizat ..."
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SENSE reconstruction suffers from an illconditioning problem, which increasingly lowers the signaltonoise ratio (SNR) as the reduction factor increases. Illconditioning also degrades the convergence behavior of iterative conjugate gradient reconstructions for arbitrary trajectories. Regularization techniques are often used to alleviate the illconditioning problem. Based on maximum a posteriori statistical estimation with a Huber Markov random field prior, this study presents a new method for adaptive regularization using the image and noise statistics. The adaptive Huber regularization addresses the blurry edges in Tikhonov regularization and the blocky effects in total variation (TV) regularization. Phantom and in vivo experiments demonstrate improved image quality and convergence speed over both the unregularized conjugate gradient method and Tikhonov regularization method, at no increase in total compu
A Convex Optimization Approach to pMRI Reconstruction
, 2013
"... In parallel magnetic resonance imaging (pMRI) reconstruction without using preestimation 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 preestimation 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 sensitivity functions by regularized optimization which is a nonconvex 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 twostep convex optimization problem, which produces a globally optimal solution. An algorithm based on splitbregman and nuclear norm regularized optimizations is proposed to implement the twostep convex optimization and its applications to phantom and invivo MRI data sets result in superior reconstruction performance compared with existing algorithms.