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Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging
 MAGNETIC RESONANCE IN MEDICINE 58:1182–1195
, 2007
"... The sparsity which is implicit in MR images is exploited to significantly undersample kspace. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finit ..."
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Cited by 538 (11 self)
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The sparsity which is implicit in MR images is exploited to significantly undersample kspace. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finitedifferences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled kspace data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noiselike interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudorandom variabledensity undersampling of phaseencodes. The reconstruction is performed by minimizing the ℓ1 norm of a transformed image, subject to data fidelity constraints. Examples demonstrate improved spatial resolution and accelerated acquisition for multislice fast spinecho brain imaging and 3D contrast enhanced angiography.
Adaptive sensitivity encoding incorporating temporal filtering (TSENSE). Magn Reson Med 2001
"... A number of different methods have been demonstrated which increase the speed of MR acquisition by decreasing the number of sequential phase encodes. The UNFOLD technique is based on time interleaving of kspace lines in sequential images and exploits the property that the outer portion of the field ..."
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Cited by 67 (13 self)
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A number of different methods have been demonstrated which increase the speed of MR acquisition by decreasing the number of sequential phase encodes. The UNFOLD technique is based on time interleaving of kspace lines in sequential images and exploits the property that the outer portion of the fieldofview is relatively static. The differences in spatial sensitivity of multiple receiver coils may be exploited using SENSE or SMASH techniques to eliminate the aliased component that results from undersampling kspace. In this article, an adaptive method of sensitivity encoding is presented which incorporates both spatial and temporal filtering. Temporal filtering and spatial encoding may be combined by acquiring phase encodes in an interleaved manner. In this way the aliased components are alternating phase. The SENSE formulation is not altered by the phase of the alias artifact; however, for imperfect estimates of coil sensitivities the residual artifact will have alternating phase using this approach. This is the essence of combining temporal filtering (UNFOLD) with spatial sensitivity encoding (SENSE). Any residual artifact will be temporally frequencyshifted to the band edge and thus may be further suppressed by temporal lowpass filtering. By combining both temporal and spatial filtering a high degree of alias artifact rejection may be achieved with less stringent requirements on accuracy of coil sensitivity estimates and temporal lowpass filter selectivity than would be required using each method individually. Experimental results that demonstrate the adaptive spatiotemporal filtering method (adaptive TSENSE) with acceleration factor R 5 2, for realtime nonbreathheld cardiac MR imaging during exercise induced stress are presented. Magn Reson Med 45:846–852, 2001.
kt BLAST and kt SENSE: Dynamic MRI with High Frame Rate Exploiting Spatiotemporal Correlations
, 2003
"... series of images at a high frame rate. Conceptually, the straightforward approach would be to acquire the full data for reconstructing each time frame separately. This requires the acquisition of each time frame to be short relative to the object motion in order to effectively obtain an instantaneou ..."
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Cited by 53 (0 self)
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series of images at a high frame rate. Conceptually, the straightforward approach would be to acquire the full data for reconstructing each time frame separately. This requires the acquisition of each time frame to be short relative to the object motion in order to effectively obtain an instantaneous snapshot. However, this approach is limited by physical (e.g., gradient strength and slew rate) and physiological (e.g., nerve stimulation) constraints on the speed of data acquisition. Over the years a number of strategies have been proposed to further increase the acquisition rate by reducing the amount of acquired data by a given factor, referred to as the acceleration factor hereafter. These strategies are able to reduce data acquisition without compromising image quality significantly because typical image series exhibit a high degree of spatiotemporal correlations, either by nature or by design. Therefore, there is a certain amount of redundancy within the data. In general, such stra
On the optimality of the gridding reconstruction algorithm
 IEEE Trans.Med.Imag.,vol.19,no.4,pp.306–317,2000
"... Abstract—Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction e ..."
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Cited by 36 (0 self)
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Abstract—Gridding reconstruction is a method to reconstruct data onto a Cartesian grid from a set of nonuniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction (LSR), on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise. Hence, it is rarely used in practice. Despite their seemingly different approaches, the gridding and LSR methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as the ones which yield the minimum approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This problem is studied and solved in the general form of approximation using linearly structured matrices. This method not only supports more general forms of the gridding algorithm, it can also be used to accelerate the reconstruction techniques from incomplete data. The application of this method to a case of twodimensional (2D) spiral magnetic resonance imaging shows a reduction of more than 4 dB in the average reconstruction error. Index Terms—Gridding reconstruction, image reconstruction, matrix approximation, nonuniform sampling. I.
Dynamic autocalibrated parallel imaging using temporal GRAPPA (TGRAPPA). Magn Reson Med 2005;53:981–985
"... Current parallel imaging techniques for accelerated imaging require a fully encoded reference data set to estimate the spatial coil sensitivity information needed for reconstruction. In dynamic parallel imaging a timeinterleaved acquisition scheme can be used, which eliminates the need for separat ..."
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Cited by 27 (4 self)
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Current parallel imaging techniques for accelerated imaging require a fully encoded reference data set to estimate the spatial coil sensitivity information needed for reconstruction. In dynamic parallel imaging a timeinterleaved acquisition scheme can be used, which eliminates the need for separately acquiring additional reference data, since the signal from directly adjacent time frames can be merged to build a set of fully encoded fullresolution reference data for coil calibration. In this work, we demonstrate that a timeinterleaved sampling scheme, in combination with autocalibrated GRAPPA (referred to as TGRAPPA), allows one to easily update the coil weights for the GRAPPA algorithm dynamically, thereby improving the acquisition efficiency. This method may update coil sensitivity estimates frame by frame, thereby tracking changes in relative coil sensitivities that may occur during the data acquisition. Magn
Joint image reconstruction and sensitivity estimation
 in SENSE (JSENSE),” Mag. Res. Med
, 2007
"... Parallel magnetic resonance imaging (pMRI) using multichannel receiver coils has emerged as an effective tool to reduce imaging time in various applications. However, the issue of accurate estimation of coil sensitivities has not been fully addressed, which limits the level of speed enhancement achi ..."
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Cited by 25 (4 self)
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Parallel magnetic resonance imaging (pMRI) using multichannel receiver coils has emerged as an effective tool to reduce imaging time in various applications. However, the issue of accurate estimation of coil sensitivities has not been fully addressed, which limits the level of speed enhancement achievable with the technology. The selfcalibrating (SC) technique for sensitivity extraction has been well accepted, especially for dynamic imaging, and complements the common calibration technique that uses a separate scan. However, the existing method to extract the sensitivity information from the SC data is not accurate enough when the number of data is small, and thus erroneous sensitivities affect the reconstruction quality when they are directly applied to the reconstruction equation. This paper considers this problem of error propagation in the sequential procedure of sensitivity estimation followed by image reconstruction in existing methods, such as sensitivity encoding (SENSE) and simultaneous acquisition of spatial harmonics (SMASH), and reformulates the image reconstruction problem as a joint estimation of the coil sensitivities and the desired image, which is solved by an iterative optimization algorithm. The proposed method was tested on various data sets. The results from a set of in vivo data are shown to demonstrate the effectiveness of the proposed method, especially when a rather large net acceleration factor is used. Magn Reson Med 57:
UNFOLDSENSE: a parallel MRI method with selfcalibration and artifact suppression. Magn Reson Med 2004;52:310–320
"... This work aims at improving the performance of parallel imaging by using it with our “unaliasing by Fourierencoding the overlaps in the temporal dimension ” (UNFOLD) temporal strategy. A selfcalibration method called “self, hybrid referencing with UNFOLD and GRAPPA ” (SHRUG) is presented. SHRUG co ..."
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Cited by 22 (2 self)
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This work aims at improving the performance of parallel imaging by using it with our “unaliasing by Fourierencoding the overlaps in the temporal dimension ” (UNFOLD) temporal strategy. A selfcalibration method called “self, hybrid referencing with UNFOLD and GRAPPA ” (SHRUG) is presented. SHRUG combines the UNFOLDbased sensitivity mapping strategy introduced in the TSENSE method by Kellman et al. (5), with the strategy introduced in the GRAPPA method by Griswold et al. (10). SHRUG merges the two approaches to alleviate their respective limitations, and provides fast selfcalibration at any given acceleration factor. UNFOLDSENSE further includes an UNFOLD artifact suppression scheme to significantly suppress artifacts and amplified noise produced by parallel imaging. This suppression scheme, which was published previously (4), is related to another method that was presented independently as part of TSENSE. While the two are equivalent at accelerations ≤ 2.0, the present approach is shown here to be significantly superior at accelerations> 2.0, with up to double the artifact suppression at high accelerations. Furthermore, a slight modification of Cartesian SENSE is introduced, which allows departures from purely Cartesian sampling grids. This technique, termed variabledensity SENSE (vdSENSE), allows the variabledensity data required by SHRUG to be reconstructed with the simplicity and fast processing of Cartesian SENSE. UNFOLDSENSE is given by the combination of SHRUG for sensitivity mapping, vdSENSE for reconstruction, and UNFOLD for artifact/amplified noise suppression. The method was implemented, with online reconstruction, on both an SSFP and a myocardiumperfusion sequence. The results from six patients scanned with UNFOLDSENSE are presented. Magn Reson
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
Motion Estimated and Compensated Compressed Sensing Dynamic Magnetic Resonance Imaging: What We Can Learn From Video Compression Techniques
, 2009
"... ABSTRACT: Compressed sensing has become an extensive research area in MR community because of the opportunity for unprecedented high spatiotemporal resolution reconstruction. Because dynamic magnetic resonance imaging (MRI) usually has huge redundancy along temporal direction, compressed sensing th ..."
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Cited by 17 (0 self)
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ABSTRACT: Compressed sensing has become an extensive research area in MR community because of the opportunity for unprecedented high spatiotemporal resolution reconstruction. Because dynamic magnetic resonance imaging (MRI) usually has huge redundancy along temporal direction, compressed sensing theory can be effectively used for this application. Historically, exploiting the temporal redundancy has been the main research topics in video compression technique. This article compares the similarity and differences of compressed sensing dynamic MRI and video compression and discusses what MR can learn from the history of video compression research. In particular, we demonstrate that the motion estimation and compensation in video compression technique can be also a powerful tool to reduce the sampling requirement in dynamic MRI. Theoretical derivation and experimental results are presented