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Highly Undersampled 3D Golden Ratio Radial Imaging with Iterative Reconstruction
... Real-time 4D acquisitions are being accelerated using under-sampled non-Cartesian k-space trajectories and compressed sensing or iterative image reconstruction methods [3] [4]. Unfortunately, these techniques require computationally intensive and time-consuming image reconstruction algorithms [3]. ...
... As shown in Fig. 1, ACNS is described as the three steps: feature extraction, nonlinear mapping, and reconstruction. In feature extraction, local features of Y are extracted depending on receptive fields as follows: (4) where an operator '*' denotes a convolution, max(0,·) + α min(·, 0) is an activation function, i.e., Parametric Rectified Linear Unit (PReLU) function [70], and W1 and B1 represent filters and biases of feature extraction operation, respectively. The size of W1 is w1, which restricts a unit range to extract the local features on Y. ...
... We denote the ACNS according to the network parameters, such as ACNS(Nfeature, Nmap, w1, wn+3, p, n). For ACNS (16,8,5,9,5,4), it took approximately 6 hours and 30 mins for training 183 images (91 non-medical images, 50 XCAT images, and [79]. The maximum number of recursions of the inference network was 16. ...
Objective:
To introduce an MRI in-plane resolution enhancement method that estimates High-Resolution (HR) MRIs from Low-Resolution (LR) MRIs.
Method & materials:
Previous CNN-based MRI super-resolution methods cause loss of input image information due to the pooling layer. An Autoencoder-inspired Convolutional Network-based Super-resolution (ACNS) method was developed with the deconvolution layer that extrapolates the missing spatial information by the convolutional neural network-based nonlinear mapping between LR and HR features of MRI. Simulation experiments were conducted with virtual phantom images and thoracic MRIs from four volunteers. The Peak Signal-to-Noise Ratio (PSNR), Structure SIMilarity index (SSIM), Information Fidelity Criterion (IFC), and computational time were compared among: ACNS; Super-Resolution Convolutional Neural Network (SRCNN); Fast Super-Resolution Convolutional Neural Network (FSRCNN); Deeply-Recursive Convolutional Network (DRCN).
Results:
ACNS achieved comparable PSNR, SSIM, and IFC results to SRCNN, FSRCNN, and DRCN. However, the average computation speed of ACNS was 6, 4, and 35 times faster than SRCNN, FSRCNN, and DRCN, respectively under the computer setup used with the actual average computation time of 0.15 s per [Formula: see text].
... In radial sampling, radial spokes passing through the k-space origin are acquired with uniform angular spacing. However, homogenous coverage and higher incoherence values were achieved by sampling with non-uniform golden-angle angular spacing [23][24][25]. This reduces the symmetry of the point spread function (PSF) of radial sampling, allowing for better compressed sensing reconstruction. ...
... This allows for better performance in capturing dynamic information. Besides, radial undersampling results in relatively mild streaking artifacts, which can be effectively removed by novel compressed sensing reconstruction methods making the technique suitable for high acceleration factors [23,24]. The short TE that can be achieved in UTE sequences traditionally finds applications in bone, fibro-cartilage and lung imaging [30,31]. ...
... Ultimately, volumetric imaging with 3D radial readout would be even more favorable. In 3D, the undersampling artifacts display more incoherence, which allows for a higher degree of acquisition undersampling [17,23]. Moreover, in our sequence TE could be further reduced from 290 ls for 2D to about 20-50 ls for 3D due to the absence of a slice selection refocusing gradient. ...
We introduce a fast protocol for ultra-short echo time (UTE) Cine magnetic resonance imaging (MRI) of the beating murine heart. The sequence involves a self-gated UTE with golden-angle radial acquisition and compressed sensing reconstruction. The self-gated acquisition is performed asynchronously with the heartbeat, resulting in a randomly undersampled kt-space that facilitates compressed sensing reconstruction. The sequence was tested in 4 healthy rats and 4 rats with chronic myocardial infarction, approximately 2 months after surgery. As a control, a non-accelerated self-gated multi-slice FLASH sequence with an echo time (TE) of 2.76 ms, 4.5 signal averages, a matrix of 192 × 192, and an acquisition time of 2 min 34 s per slice was used to obtain Cine MRI with 15 frames per heartbeat. Non-accelerated UTE MRI was performed with TE = 0.29 ms, a reconstruction matrix of 192 × 192, and an acquisition time of 3 min 47 s per slice for 3.5 averages. Accelerated imaging with 2×, 4× and 5× undersampled kt-space data was performed with 1 min, 30 and 15 s acquisitions, respectively. UTE Cine images up to 5× undersampled kt-space data could be successfully reconstructed using a compressed sensing algorithm. In contrast to the FLASH Cine images, flow artifacts in the UTE images were nearly absent due to the short echo time, simplifying segmentation of the left ventricular (LV) lumen. LV functional parameters derived from the control and the accelerated Cine movies were statistically identical.
Graphical Abstract
... An empirical value, 0.01, is proposed for scaling. Using [9] and [10], the weight of sparsity constraint term is automatically defined by the g-factor. If mean (g) is very close to 1, the initial SENSE reconstruction can be used as the final result to avoid prolonged reconstruction time due to further steps. ...
... If mean (g) is very close to 1, the initial SENSE reconstruction can be used as the final result to avoid prolonged reconstruction time due to further steps. More clarification on the values of a and the scalar in [10] will be provided in Restults and Discussion sections. Beside the regularization parameters, there is one extra parameter for the number of iterations of sub-problems [5] and [9]. ...
... To demonstrate the rationale of the choice of parameters, two set of experiments using the proposed method were processed with a wide range of parameters. In one set of experiment, the l was defined by Eq. [10] , and a was changed from 0 to 4 gradually . In the other experimental set, a was fixed to be 0.5 and the scalar in Eq. [10] was changed from 0 to 0.1 gradually. ...
The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve even higher acceleration factors. However, there are two major problems in the existing sparsity-constrained PPI techniques: speed and robustness. By introducing an auxiliary variable and decomposing the original minimization problem into two subproblems that are much easier to solve, a fast and robust numerical algorithm for sparsity-constrained PPI technique is developed in this work. The specific implementation for a conventional Cartesian trajectory data set is named self-feeding Sparse Sensitivity Encoding (SENSE). The computational cost for the proposed method is two conventional SENSE reconstructions plus one spatially adaptive image denoising procedure. With reconstruction time approximately doubled, images with a much lower root mean square error (RMSE) can be achieved at high acceleration factors. Using a standard eight-channel head coil, a net acceleration factor of 5 along one dimension can be achieved with low RMSE. Furthermore, the algorithm is insensitive to the choice of parameters. This work improves the clinical applicability of SENSE at high acceleration factors.
... However, the problem of radial sampling or projection acquisition, such that projections are relatively uniform throughout acquisition becomes far more complicated in 3D. The golden ratio has been expanded to higher dimensions (49) and applied to 3D MRI k-space sampling (50,51). The golden ratio sampling method is particularly suited for the case where there are an unknown arbitrary number of projections to be acquired. ...
Purpose: Electron paramagnetic resonance imaging (EPRI) is a projection based imaging modality that noninvasively provides 3D images of absolute oxygen concentration (pO2) in vivo with excellent spatial and pO2 resolution. When studying physiologic parameters, such as tissue pO2, in living animals, the situation is inherently dynamic. This may be due to physical movement during imaging leading to artifacts or physiologically relevant temporal changes in pO2 (i.e. acute hypoxia). In order to properly study such a dynamic system, improvements in temporal resolution and experimental versatility are necessary. Methods: For projection based imaging, uniformly distributed projections Result in efficient use of data for image reconstruction. This has led to the current equal‐solid‐angle (ESA) spacing of projections for EPRI. However, acquisition sequencing must still be optimized in order to achieve uniformity throughout imaging. An object‐independent method for uniform acquisition of projections, using the ESA distribution for the final set of projections, is presented. Each successive projection is selected in such a way as to minimize the electrostatic potential energy between itself and prior projections, when projection direction points are considered to be point charges on the unit sphere. Results: This maximally spaced projection sequencing (MSPS) method significantly improves image quality for intermediate images reconstructed from incomplete projection sets. This enables useful real‐time reconstruction. Additionally, the MSPS method provides improved experimental versatility, reduced artifacts, and the ability to adjust temporal resolution post factum to best fit the data and its application. Conclusion: The MSPS method in EPRI provides necessary improvements in order to more appropriately image and study physiologic changes in a dynamic system. This work was supported by grants from the NIH (P41 EB002034 and R01 CA98575).
... During the last years the golden angle ordering scheme has found widespread use in various applications from real-time imaging, over self-gated acquisition, to single scan T1-and T2-mapping [4]- [10]. In particular, radial trajectories with a golden angle ordering scheme have been used in combination with parallel imaging and compressed sensing [11]- [13] due to the intrinsic properties of this trajectory. First, the variable density sampling in k-space that oversamples the k-space center, second the flexibility in the degree of retrospective undersampling, and last the incoherent aliasing artifacts that are essential for compressed sensing [14], [15]. ...
In golden angle radial MRI a constant azimuthal radial profile spacing of 111.246...° guarantees a nearly uniform azimuthal profile distribution in k-space for an arbitrary number of radial profiles. Even though this profile order is advantageous for various real-time imaging methods, in combination with balanced SSFP sequences the large azimuthal angle increment may lead to strong image artifacts, due to the varying eddy currents introduced by the rapidly switching gradient scheme. Based on a generalized Fibonacci sequence, a new sequence of smaller irrational angles is introduced (49.750...°, 32.039...°, 27.198...°, 23.628...°, ... ). The subsequent profile orders guarantee the same sampling efficiency as the golden angle if at least a minimum number of radial profiles is used for reconstruction. The suggested angular increments are applied for dynamic imaging of the heart and the temporomandibular joint. It is shown that for balanced SSFP sequences, trajectories using the smaller golden angle surrogates strongly reduce the image artifacts, while the free retrospective choice of the reconstruction window width is maintained.
... This offers a remarkable scan-time reduction and renders radial sampling highly attractive for time critical applications. Meanwhile, several related studies have been published in the context of compressed sensing [138,139,140,141], which support the results presented in this thesis and confirm the gain of image quality arising from the advanced reconstruction strategy. ...
To describe how a robust implementation of a radial 3D gradient-echo sequence with stack-of-stars sampling can be achieved, to review the imaging properties of radial acquisitions, and to share the experience from more than 5000 clinical patient scans.
... By recording multiple data sets in parallel, temporal/spatial resolution is increased, and motion-related artifacts are suppressed [17,18,25]. The missing Fourier components lead to aliasing artifacts in images, which are removed through the image reconstruction process [4,10,17,18,25]. One way to reconstruct the image employs sensitivity encoding which uses knowledge of the coil sensitivities to separate aliased pixels; this approach can be modeled as the minimization (1.1). ...
An alternating direction approximate Newton method (ADAN) is developed for solving inverse problems of the form min{φ(Bu) + (1/2) − f 2 2 }, where φ is convex and possibly nonsmooth, and A and B are matrices. Problems of this form arise in image reconstruction where A is the matrix describing the imaging device, f is the measured data, φ is a regularization term, and B is a derivative operator. The proposed algorithm is designed to handle applications where A is a large dense, ill condition matrix. The algorithm is based on the alternating direction method of multipliers (ADMM) and an approximation to Newton's method in which Newton's Hessian is replaced by a Barzilai-Borwein approximation. It is shown that ADAN converges to a solution of the inverse problem; neither a line search nor an estimate of problem parameters, such as a Lipschitz constant, are required. Numerical results are provided using test problems from parallel magnetic resonance imaging (PMRI). ADAN performed better than the other schemes that were tested.
... CS enables the acquisition of all of this information in a single exam. Although several authors (e.g., [5][6][7][8]) have successfully demonstrated the application of CS methods to CE-MRA, the computationally intensive nature of these applications has so far precluded their clinical viability (e.g., published CS reconstruction times for a single 3D volume (CE-MRA or not) are often on the order of hours [4,7,[9][10][11]). As the results of a CE-MRA exam are often needed as soon as the acquisition completes (either for immediate clinical intervention or to guide additional scans), it is not practical to wait for the result of any currently implemented CS reconstructions. ...
Compressive sensing (CS) describes how sparse
signals can be accurately reconstructed from many fewer samples
than required by the Nyquist criterion. Since MRI scan duration
is proportional to the number of acquired samples, CS has been
gaining significant attention in MRI. However, the computationally
intensive nature of CS reconstructions has precluded their
use in routine clinical practice. In this work, we investigate how
different throughput-oriented architectures can benefit one CS
algorithm and what levels of acceleration are feasible on different
modern platforms. We demonstrate that a CUDA-based code
running on an NVIDIA Tesla C2050 GPU can reconstruct a
256 × 160 × 80 volume from an 8-channel acquisition in 19 seconds,
which is in itself a significant improvement over the state of the art. We then
show that Intel's Knights Ferry can perform the same 3D MRI
reconstruction in only 12 seconds, bringing CS methods even
closer to clinical viability.
A disadvantage of three-dimensional (3D) isotropic acquisition in whole-heart coronary MRI is the prolonged data acquisition time. Isotropic 3D radial trajectories allow undersampling of k-space data in all three spatial dimensions, enabling accelerated acquisition of the volumetric data. Compressed sensing (CS) reconstruction can provide further acceleration in the acquisition by removing the incoherent artifacts due to undersampling and improving the image quality. However, the heavy computational overhead of the CS reconstruction has been a limiting factor for its application. In this article, a parallelized implementation of an iterative CS reconstruction method for 3D radial acquisitions using a commercial graphics processing unit is presented. The execution time of the graphics processing unit-implemented CS reconstruction was compared with that of the C++ implementation, and the efficacy of the undersampled 3D radial acquisition with CS reconstruction was investigated in both phantom and whole-heart coronary data sets. Subsequently, the efficacy of CS in suppressing streaking artifacts in 3D whole-heart coronary MRI with 3D radial imaging and its convergence properties were studied. The CS reconstruction provides improved image quality (in terms of vessel sharpness and suppression of noise-like artifacts) compared with the conventional 3D gridding algorithm, and the graphics processing unit implementation greatly reduces the execution time of CS reconstruction yielding 34-54 times speed-up compared with C++ implementation. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.
Free-breathing three-dimensional whole-heart coronary MRI is a noninvasive alternative to X-ray coronary angiography. However, the existing navigator-gated approaches do not meet the requirements of clinical practice, as they perform with suboptimal accuracy and require prolonged acquisition times. Self-navigated techniques, applied to bright-blood imaging sequences, promise to detect the position of the blood pool directly in the readouts acquired for imaging. Hence, the respiratory displacement of the heart can be calculated and used for motion correction with high accuracy and 100% scan efficiency. However, additional bright signal from the chest wall, spine, arms, and liver can render the isolation of the blood pool impossible. In this work, an innovative method based on a targeted combination of the output signals of an anterior phased-array surface coil is implemented to efficiently suppress such additional bright signal. Furthermore, an algorithm for the automatic segmentation of the blood pool is proposed. Robust self-navigation is achieved by cross-correlation. These improvements were integrated into a three-dimensional radial whole-heart coronary MRI sequence and were compared with navigator-gated imaging in vivo. Self-navigation was successful in all cases and the acquisition time was reduced up to 63%. Equivalent or slightly superior image quality, vessel length, and sharpness were achieved.
While radial 3D acquisition has been discussed in cardiac MRI for its excellent results with radial undersampling, the self-navigating properties of the trajectory need yet to be exploited. Hence, the radial trajectory has to be interleaved such that the first readout of every interleave starts at the top of the sphere, which represents the shell covering all readouts. If this is done sub-optimally, the image quality might be degraded by eddy current effects, and advanced density compensation is needed. In this work, an innovative 3D radial trajectory based on a natural spiral phyllotaxis pattern is introduced, which features optimized interleaving properties: (1) overall uniform readout distribution is preserved, which facilitates simple density compensation, and (2) if the number of interleaves is a Fibonacci number, the interleaves self-arrange such that eddy current effects are significantly reduced. These features were theoretically assessed in comparison with two variants of an interleaved Archimedean spiral pattern. Furthermore, the novel pattern was compared with one of the Archimedean spiral patterns, with identical density compensation, in phantom experiments. Navigator-gated whole-heart coronary imaging was performed in six healthy volunteers. High reduction of eddy current artifacts and overall improvement in image quality were achieved with the novel trajectory.
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