Noise estimation in parallel MRI: GRAPPA and SENSE

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods – based on a single noise level for the whole image – fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.     

Singular Value Decomposition Using Jacobi Algorithm in pMRI and CS

Parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) have been recently used to accelerate data acquisition process in MRI. Matrix inversion (for rectangular matrices) is required to reconstruct images from the acquired under-sampled data in various pMRI algorithms (e.g., SENSE, GRAPPA) and CS. Singular value decomposition (SVD) provides a mechanism to accurately estimate pseudo-inverse of a rectangular matrix. This work proposes the use of Jacobi SVD algorithm to reconstruct MR images from the acquired under-sampled data both in pMRI and in CS. The use of Jacobi SVD algorithm is proposed in advance MRI reconstruction algorithms, including SENSE, GRAPPA, and low-rank matrix estimation in L + S model for matrix inversion and estimation of singular values. Experiments are performed on 1.5T human head MRI data and 3T cardiac perfusion MRI data for different acceleration factors. The reconstructed images are analyzed using artifact power and central line profiles. The results show that the Jacobi SVD algorithm successfully reconstructs the images in SENSE, GRAPPA, and L + S algorithms. The benefit of using Jacobi SVD algorithm for MRI image reconstruction is its suitability for parallel computation on GPUs, which may be a great help in reducing the image reconstruction time.     

FPGA implementation of real-time SENSE reconstruction using pre-scan and Emaps sensitivities

Sensitivity Encoding (SENSE) is a widely used technique in Parallel Magnetic Resonance Imaging (MRI) to reduce scan time. Reconfigurable hardware based architecture for SENSE can potentially provide image reconstruction with much less computation time. Application specific hardware platform for SENSE may dramatically increase the power efficiency of the system and can decrease the execution time to obtain MR images. A new implementation of SENSE on Field Programmable Gate Array (FPGA) is presented in this study, which provides real-time SENSE reconstruction right on the receiver coil data acquisition system with no need to transfer the raw data to the MRI server, thereby minimizing the transmission noise and memory usage. The proposed SENSE architecture can reconstruct MR images using receiver coil sensitivity maps obtained using pre-scan and eigenvector (E-maps) methods. The results show that the proposed system consumes remarkably less computation time for SENSE reconstruction, i.e., 0.164 ms @ 200 MHz, while maintaining the quality of the reconstructed images with good mean SNR (29 + dB), less RMSE (< 5 × 10^− 2) and comparable artefact power (< 9 × 10^− 4) to conventional SENSE reconstruction. A comparison of the center line profiles of the reconstructed and reference images also indicates a good quality of the reconstructed images. Furthermore, the results indicate that the proposed architectural design can prove to be a significant tool for SENSE reconstruction in modern MRI scanners and its low power consumption feature can be remarkable for portable MRI scanners.     

Optimization of sensitivity encoding with arbitrary k-space trajectories

Sensitivity encoding (SENSE) is a magnetic resonance technique that unifies gradient and receive coil encoding. SENSE reconstructs the image by solving a large, ill-conditioned inverse problem, which generally requires regularization and preconditioning. The present study suggests a simple heuristic for determining the regularization parameter. Also discussed are the use of density weighting and intensity correction as preconditioners and the role that coil sensitivity estimation has in regularization. A modification to the intensity correction is proposed for use with a phase constraint.     

k-space inherited parallel acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.     

APIR4EMC: Autocalibrated parallel imaging reconstruction for extended multi-contrast imaging

PurposeTo improve image quality of multi-contrast imaging with the proposed Autocalibrated Parallel Imaging Reconstruction for Extended Multi-Contrast Imaging (APIR4EMC).MethodsAPIR4EMC reconstructs multi-contrast images in an autocalibrated parallel imaging reconstruction framework by adding contrasts as virtual coils. Compensation of signal evolution along the echo train of different contrasts is performed to improve signal prediction for missing samples. As a proof of concept, we performed prospectively accelerated phantom and in-vivo brain acquisitions with T1, T1-fat saturated (Fatsat), T2, PD, and FLAIR contrasts. The k-space sampling patterns of these acquisitions were jointly optimized. Images were jointly reconstructed with the proposed APIR4EMC method as well as individually with GRAPPA. Root mean square error (RMSE) to fully sampled reference images and g-factor maps were computed for both methods in the phantom experiment. Visual evaluation was performed in the in-vivo experiment.ResultsCompared to GRAPPA, APIR4EMC reduced artifacts and improved SNR of the reconstructed images in the phantom acquisitions. Quantitatively, APIR4EMC substantially reduced noise amplification (g-factor) as well as RMSE compared to GRAPPA. Signal evolution compensation reduced artifacts. In the in-vivo experiments, 1 mm³ isotropic 3D images with contrasts of T1, T1-Fatsat, T2, PD, and FLAIR were acquired in as little as 7.5 min with the acceleration factor of 9. Reconstruction quality was consistent with the phantom results.ConclusionCompared to single contrast reconstruction with GRAPPA, APIR4EMC reduces artifacts and noise amplification in accelerated multi-contrast imaging.     

Joint Reconstruction of Multi-contrast Images and Multi-channel Coil Sensitivities

Magnetic resonance imaging (MRI) has an important feature that it provides multiple images with different contrasts for complementary diagnostic information. However, a large amount of data is needed for multi-contrast images depiction, and thus, the scan is time-consuming. Many methods based on parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) are applied to accelerate multi-contrast MR imaging. Nevertheless, the image reconstructed by sophisticated pMRI methods contains residual aliasing artifact that degrades the quality of the image when the acceleration factor is high. Other methods based on CS always suffer the regularization parameter-selecting problem. To address these issues, a new method is presented for joint multi-contrast image reconstruction and coil sensitivity estimation. The coil sensitivities can be shared during the reconstruction due to the identity of coil sensitivity profiles of different contrast images for imaging stationary tissues. The proposed method uses the coil sensitivities as sharable information during the reconstruction to improve the reconstruction quality. As a result, the residual aliasing artifact can be effectively removed in the reconstructed multi-contrast images even if the acceleration factor is high. Besides, as there is no regularization term in the proposed method, the troublesome regularization parameter selection in the CS can also be avoided. Results from multi-contrast in vivo experiments demonstrated that multi-contrast images can be jointly reconstructed by the proposed method with effective removal of the residual aliasing artifact at a high acceleration factor.     

Calibration-less multi-coil MR image reconstruction

In parallel magnetic resonance imaging (MRI), the problem is to reconstruct an image given the partial K-space scans from all the receiver coils. Depending on its position within the scanner, each coil has a different sensitivity profile. All existing parallel MRI techniques require estimation of certain parameters pertaining to the sensitivity profile, e.g., the sensitivity map needs to be estimated for the SENSE and SMASH and the interpolation weights need to be calibrated for GRAPPA and SPIRiT. The assumption is that the estimated parameters are applicable at the operational stage. This assumption does not always hold, consequently the reconstruction accuracies of existing parallel MRI methods may suffer. We propose a reconstruction method called Calibration-Less Multi-coil (CaLM) MRI. As the name suggests, our method does not require estimation of any parameters related to the sensitivity maps and hence does not require a calibration stage. CaLM MRI is an image domain method that produces a sensitivity encoded image for each coil. These images are finally combined by the sum-of-squares method to yield the final image. It is based on the theory of Compressed Sensing (CS). During reconstruction, the constraint that "all the coil images should appear similar" is introduced within the CS framework. This leads to a CS optimization problem that promotes group-sparsity. The results from our proposed method are comparable (at least for the data used in this work) with the best results that can be obtained from state-of-the-art methods.     

Data consistency criterion for selecting parameters for k-space-based reconstruction in parallel imaging

k-space-based reconstruction in parallel imaging depends on the reconstruction kernel setting, including its support. An optimal choice of the kernel depends on the calibration data, coil geometry and signal-to-noise ratio, as well as the criterion used. In this work, data consistency, imposed by the shift invariance requirement of the kernel, is introduced as a goodness measure of k-space-based reconstruction in parallel imaging and demonstrated. Data consistency error (DCE) is calculated as the sum of squared difference between the acquired signals and their estimates obtained based on the interpolation of the estimated missing data. A resemblance between DCE and the mean square error in the reconstructed image was found, demonstrating DCE's potential as a metric for comparing or choosing reconstructions. When used for selecting the kernel support for generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction and the set of frames for calibration as well as the kernel support in temporal GRAPPA reconstruction, DCE led to improved images over existing methods. Data consistency error is efficient to evaluate, robust for selecting reconstruction parameters and suitable for characterizing and optimizing k-space-based reconstruction in parallel imaging.     

Line Profile Measure as a Stopping Criterion in CG-SENSE Algorithm

Conjugate gradient SENSE (CG-SENSE) is a parallel magnetic resonance imaging reconstruction algorithm which solves the inversion problem of SENSE iteratively. One major limitation of CG-SENSE is the appropriate choice of the number of iterations required for good reconstruction results. Fewer iterations result in aliasing artifacts and too many iterations result in an increased noise level. This paper proposes a novel method to define the stopping criterion of CG-SENSE algorithm which is based on the use of correlation measure between the line profiles of the reconstructed images in the current and the previous iterations. The results are compared with Bregman distance-stopping criterion. Artifact power and peak signal-to-noise ratio are used to quantify the quality of the reconstructed images. The results demonstrate that the line profile correlation measure acts as an effective stopping criterion in CG-SENSE.     

Rapid MR imaging by sensitivity profile indexing and deconvolution reconstruction (SPID)

A new parallel MR imaging technique, which uses localized information from the elements of a multi-coil array to accelerate imaging, is described. The technique offers an alternative reconstruction approach to currently available techniques (e.g., SMASH and SENSE). Following a partial k-space data acquisition, image reconstruction in this approach proceeds in two steps: first, fitting the measured coil sensitivities to a set of partially localized target functions, a blurred intermediate image of the studied object is produced. Blurring is obtained in a systematic manner, forming images of the studied object convolved with a known convolution kernel. Full spatial resolution is then recovered by deconvolution of the blurred images with the known kernel function. The technique offers flexibility in the arrangement of the acquired signal data k-lines, and a mechanism for controlling reconstruction quality through the convolution the deconvolution procedure. The technique was validated in phantom and in vivo imaging experiments demonstrating high time reduction factors.     

Optimization of hyperparameters for SMS reconstruction

PurposeSimultaneous multi-slice (SMS) imaging accelerates MRI data acquisition by exciting multiple image slices with a single radiofrequency pulse. Overlapping slices encoded in acquired signal are separated using a mathematical model, which requires estimation of image reconstruction kernels using calibration data. Several parameters used in SMS reconstruction impact the quality and fidelity of final images. Therefore, finding an optimal set of reconstruction parameters is critical to ensure that accelerated acquisition does not significantly degrade resulting image quality.MethodsGradient-echo echo planar imaging data were acquired with a range of SMS acceleration factors from a cohort of five volunteers with no known neurological pathology. Images were collected using two available phased-array head coils (a 48-channel array and a reduced diameter 32-channel array) that support SMS. Data from these coils were identically reconstructed offline using a range of coil compression factors and reconstruction kernel parameters. A hybrid space (k-x), externally-calibrated coil-by-coil slice unaliasing approach was used for image reconstruction. The image quality of the resulting reconstructed SMS images was assessed by evaluating correlations with identical echo-planar reference data acquired without SMS. A finger tapping functional MRI (fMRI) experiment was also performed and group analysis results were compared between data sets reconstructed with different coil compression levels.ResultsBetween the two RF coils tested in this study, the 32-channel coil with smaller dimensions clearly outperformed the larger 48-channel coil in our experiments. Generally, a large calibration region (144–192 samples) and small kernel sizes (2–4 samples) in k_y direction improved image quality. Use of regularization in the kernel fitting procedure had a notable impact on the fidelity of reconstructed images and a regularization value 0.0001 provided good image quality. With optimal selection of other hyperparameters in the hybrid space SMS unaliasing algorithm, coil compression caused small reduction in correlation between single-band and SMS unaliased images. Similarly, group analysis of fMRI results did not show a significant influence of coil compression on resulting image quality.ConclusionsThis study demonstrated that the hyperparameters used in SMS reconstruction need to be fine-tuned once the experimental factors such as the RF receive coil and SMS factor have been determined. A cursory evaluation of SMS reconstruction hyperparameter values is therefore recommended before conducting a full-scale quantitative study using SMS technologies.     

Optimizing Image Reconstruction in SENSE Using GPU

Parallel magnetic resonance imaging (MRI) (pMRI) uses multiple receiver coils to reduce the MRI scan time. To accelerate the data acquisition process in MRI, less amount of data is acquired from the scanner which leads to artifacts in the reconstructed images. SENSitivity Encoding (SENSE) is a reconstruction algorithm in pMRI to remove aliasing artifacts from the undersampled multi coil data and recovers fully sampled images. The main limitation of SENSE is computing inverse of the encoding matrix. This work proposes the inversion of encoding matrix using Jacobi singular value decomposition (SVD) algorithm for image reconstruction on GPUs to accelerate the reconstruction process. The performance of Jacobi SVD is compared with Gauss–Jordan algorithm. The simulations are performed on two datasets (brain and cardiac) with acceleration factors 2, 4, 6 and 8. The results show that the graphics processing unit (GPU) provides a speed up to 21.6 times as compared to CPU reconstruction. Jacobi SVD algorithm performs better in terms of acceleration in reconstructions on GPUs as compared to Gauss–Jordan method. The proposed algorithm is suitable for any number of coils and acceleration factors for SENSE reconstruction on real time processing systems.     

Pattern-adaptive error diffusion algorithm for improved phase-only hologram generation

The bidirectional error diffusion(BERD) algorithm is free from random phase modulation that introduces speckle noise on the reconstructed images, compared with other computer-generated phase-only hologram(POH) approaches. During the POH generation process, the amplitudes of all pixels are traditionally set to one for diffusing the errors to their neighborhood of unprocessed pixels. In this paper, we reveal that the reconstruction quality depends on the uniform amplitude value for different object pattern. The pattern-adaptive BERD(PA-BERD) algorithm is proposed for high-quality holographic reconstruction. The optimized amplitude value can be acquired for each object pattern and each propagation distance.The PA-BERD-based POHs have shown higher reconstruction quality than traditional BERD-based POHs in simulations as well as optical experiments.     

并行MRI图像重建算法比较及软件实现

首先介绍了不加速的并行MRI图像重建方法,然后对加速的并行MRI的4种图像重建算法进行了比较,得出结论：加速因子相同时,重建质量上,GRAPPA和SENSE的重建质量最好,SMASH的重建质量次之, PILS算法对线圈位置要求极高,重建质量最差;重建速度上,SMASH的重建速度最快,其次是SENSE和PILS,GRAPPA的重建速度最慢. 当加速因子变大时,所有算法重建质量都变差. 最后介绍了算法实现软件,该软件可以读入原始数据,显示数据采集轨迹,计算线圈灵敏度,选择图像重建方法,分析和比较重建图像质量. 该软件为我国在MRI成像领域提供了一个学习和进一步研究图像重建算法的有力工具.     

A simple application of compressed sensing to further accelerate partially parallel imaging

Compressed sensing (CS) and partially parallel imaging (PPI) enable fast magnetic resonance (MR) imaging by reducing the amount of k-space data required for reconstruction. Past attempts to combine these two have been limited by the incoherent sampling requirement of CS since PPI routines typically sample on a regular (coherent) grid. Here, we developed a new method, “CS+GRAPPA,” to overcome this limitation. We decomposed sets of equidistant samples into multiple random subsets. Then, we reconstructed each subset using CS and averaged the results to get a final CS k-space reconstruction. We used both a standard CS and an edge- and joint-sparsity-guided CS reconstruction. We tested these intermediate results on both synthetic and real MR phantom data and performed a human observer experiment to determine the effectiveness of decomposition and to optimize the number of subsets. We then used these CS reconstructions to calibrate the generalized autocalibrating partially parallel acquisitions (GRAPPA) complex coil weights. In vivo parallel MR brain and heart data sets were used. An objective image quality evaluation metric, Case-PDM, was used to quantify image quality. Coherent aliasing and noise artifacts were significantly reduced using two decompositions. More decompositions further reduced coherent aliasing and noise artifacts but introduced blurring. However, the blurring was effectively minimized using our new edge- and joint-sparsity-guided CS using two decompositions. Numerical results on parallel data demonstrated that the combined method greatly improved image quality as compared to standard GRAPPA, on average halving Case-PDM scores across a range of sampling rates. The proposed technique allowed the same Case-PDM scores as standard GRAPPA using about half the number of samples. We conclude that the new method augments GRAPPA by combining it with CS, allowing CS to work even when the k-space sampling pattern is equidistant.     

GPU based parallel framework for receiver coil sensitivity estimation in SENSE reconstruction

Magnetic Resonance Imaging (MRI) uses non-ionizing radiations and is safer as compared to CT and X-ray imaging. MRI is broadly used around the globe for medical diagnostics. One main limitation of MRI is its long data acquisition time. Parallel MRI (pMRI) was introduced in late 1990's to reduce the MRI data acquisition time. In pMRI, data is acquired by under-sampling the Phase Encoding (PE) steps which introduces aliasing artefacts in the MR images. SENSitivity Encoding (SENSE) is a pMRI based method that reconstructs fully sampled MR image from the acquired under-sampled data using the sensitivity information of receiver coils. In SENSE, precise estimation of the receiver coil sensitivity maps is vital to obtain good quality images. Eigen-value method (a recently proposed method in literature for the estimation of receiver coil sensitivity information) does not require a pre-scan image unlike other conventional methods of sensitivity estimation. However, Eigen-value method is computationally intensive and takes a significant amount of time to estimate the receiver coil sensitivity maps. This work proposes a parallel framework for Eigen-value method of receiver coil sensitivity estimation that exploits its inherent parallelism using Graphics Processing Units (GPUs). We evaluated the performance of the proposed algorithm on in-vivo and simulated MRI datasets (i.e. human head and simulated phantom datasets) with Peak Signal-to-Noise Ratio (PSNR) and Artefact Power (AP) as evaluation metrics. The results show that the proposed GPU implementation reduces the execution time of Eigen-value method of receiver coil sensitivity estimation (providing up to 30 times speed up in our experiments) without degrading the quality of the reconstructed image.     

Improved matrix inversion in image plane parallel MRI

A new 3D parallel magnetic resonance imaging (MRI) method named Generalized Unaliasing Incorporating Support constraint and sensitivity Encoding (GUISE) is presented. GUISE allows direct image recovery from arbitrary Cartesian k-space trajectories. However, periodic k-space sampling patterns are considered for reconstruction efficiency. Image recovery methods such as 2D SENSE (SENSitivity Encoding) and 2D CAIPIRINHA (Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration) are special instances of GUISE where specific restrictions are placed on the k-space sampling patterns used. It is shown that the sampling pattern has large impacts on the image reconstruction error due to noise. An efficient sampling pattern design method that incorporates prior knowledge of object support and coil sensitivity profile is proposed. It requires no experimental trials and could be used in clinical imaging. Comparison of the proposed sampling pattern design method with 2D SENSE and 2D CAIPIRINHA are made based on both simulation and experiment results. It is seen that this new adaptive sampling pattern design method results in a lower noise level in reconstructions due to better exploitation of the coil sensitivity variation and object support constraint. In addition, elimination of the non-object region from reconstruction potentially allows an acceleration factor higher than the number of receiver coils used.