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.     

Adaptive k-space sampling design for edge-enhanced DCE-MRI using compressed sensing

The critical challenge in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is the trade-off between spatial and temporal resolution due to the limited availability of acquisition time. To address this, it is imperative to under-sample k-space and to develop specific reconstruction techniques. Our proposed method reconstructs high-quality images from under-sampled dynamic k-space data by proposing two main improvements; i) design of an adaptive k-space sampling lattice and ii) edge-enhanced reconstruction technique. A high-resolution data set obtained before the start of the dynamic phase is utilized. The sampling pattern is designed to adapt to the nature of k-space energy distribution obtained from the static high-resolution data. For image reconstruction, the well-known compressed sensing-based total variation (TV) minimization constrained reconstruction scheme is utilized by incorporating the gradient information obtained from the static high-resolution data. The proposed method is tested on seven real dynamic time series consisting of 2 breast data sets and 5 abdomen data sets spanning 1196 images in all. For data availability of only 10%, performance improvement is seen across various quality metrics. Average improvements in Universal Image Quality Index and Structural Similarity Index Metric of up to 28% and 24% on breast data and about 17% and 9% on abdomen data, respectively, are obtained for the proposed method as against the baseline TV reconstruction with variable density random sampling pattern.     

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.     

K-space trajectory mapping and its application for ultrashort Echo time imaging

MR images are affected by system delays and gradient field imperfections which induce discrepancies between prescribed and actual k-space trajectories. This could be even more critical for non-Cartesian data acquisitions where even a small deviation from the assumed k-space trajectory results in severe image degradation and artifacts. Knowledge of the actual k-space trajectories is therefore crucial and can be incorporated in the reconstruction of high quality non-Cartesian images. A novel MR method for the calibration of actual gradient waveforms was developed using a combination of phase encoding increments and subsequent detection of the exact time point at which the corresponding trajectory is crossing the k-space origin. The measured sets of points were fitted to a parametrical model to calculate the complete actual acquisition trajectory. Measurements performed on phantoms and volunteers, positioned both in- and off-isocenter of the magnet, clearly demonstrate the improvement in reconstructed ultrashort echo time (UTE) images, when information from calibration of k-space sampling trajectories is employed in the MR image reconstruction procedure. The unique feature of the proposed method is its robustness and simple experimental setup, making it suitable for quick acquisition trajectory calibration procedures e.g. for non-Cartesian radial fast imaging.     

Sparse MRI reconstruction using multi-contrast image guided graph representation

Accelerating the imaging speed without sacrificing image structures plays an important role in magnetic resonance imaging. Under-sampling the k-space data and reconstructing the image with sparsity constraint is one efficient way to reduce the data acquisition time. However, achieving high acceleration factor is challenging since image structures may be lost or blurred when the acquired information is not sufficient. Therefore, incorporating extra knowledge to improve image reconstruction is expected for highly accelerated imaging. Fortunately, multi-contrast images in the same region of interest are usually acquired in magnetic resonance imaging protocols. In this work, we propose a new approach to reconstruct magnetic resonance images by learning the prior knowledge from these multi-contrast images with graph-based wavelet representations. We further formulate the reconstruction as a bi-level optimization problem to allow misalignment between these images. Experiments on realistic imaging datasets demonstrate that the proposed approach improves the image reconstruction significantly and is practical for real world application since patients are unnecessarily to stay still during successive reference image scans.     

Motion correction based reconstruction method for compressively sampled cardiac MR imaging

Respiratory motion during Magnetic Resonance (MR) acquisition causes strong blurring artifacts in the reconstructed images. These artifacts become more pronounced when used with the fast imaging reconstruction techniques like compressed sensing (CS). Recently, an MR reconstruction technique has been done with the help of compressed sensing (CS), to provide good quality sparse images from the highly under-sampled k-space data. In order to maximize the benefits of CS, it is obvious to use CS with the motion corrected samples. In this paper, we propose a novel CS based motion corrected image reconstruction technique. First, k-space data have been assigned to different respiratory state with the help of frequency domain phase correlation method. Then, multiple sparsity constraints has been used to provide good quality reconstructed cardiac cine images with the highly under-sampled k-space data. The proposed method exploits the multiple sparsity constraints, in combination with demon based registration technique and a novel reconstruction technique to provide the final motion free images. The proposed method is very simple to implement in clinical settings as compared to existing motion corrected methods. The performance of the proposed method is examined using simulated data and clinical data. Results show that this method performs better than the reconstruction of CS based method of cardiac cine images. Different acceleration rates have been used to show the performance of the proposed method.     

Compressed Sensing MRI Using Sparsity Averaging and FISTA

Magnetic resonance imaging (MRI) is widely adopted for clinical diagnosis due to its non-invasively detection. However, acquisition of full k-space data limits its imaging speed. Compressed sensing (CS) provides a new technique to significantly reduce the measurements with high-quality MR image reconstruction. The sparsity of the MR images is one of the crucial bases of CS-MRI. In this paper, we present to use sparsity averaging prior for CS-MRI reconstruction in the basis of that MR images have average sparsity over multiple wavelet frames. The problem is solved using a Fast Iterative Shrinkage Thresholding Algorithm (FISTA), each iteration of which includes a shrinkage step. The performance of the proposed method is evaluated for several types of MR images. The experiment results illustrate that our approach exhibits a better performance than those methods that using redundant frame or a single orthonormal basis to promote sparsity.     

Phase-constrained parallel MR image reconstruction

A generalized method for phase-constrained parallel MR image reconstruction is presented that combines and extends the concepts of partial-Fourier reconstruction and parallel imaging. It provides a framework for reconstructing images employing either or both techniques and for comparing image quality achieved by varying k-space sampling schemes. The method can be used as a parallel image reconstruction with a partial-Fourier reconstruction built in. It can also be used with trajectories not readily handled by straightforward combinations of partial-Fourier and SENSE-like parallel reconstructions, including variable-density, and non-Cartesian trajectories. The phase constraint specifies a better-conditioned inverse problem compared to unconstrained parallel MR reconstruction alone. This phase-constrained parallel MRI reconstruction offers a one-step alternative to the standard combination of homodyne and SENSE reconstructions with the added benefit of flexibility of sampling trajectory. The theory of the phase-constrained approach is outlined, and its calibration requirements and limitations are discussed. Simulations, phantom experiments, and in vivo experiments are presented.     

Methods for quantitative image quality evaluation of MRI parallel reconstructions: detection and perceptual difference model

Many reconstruction algorithms are being proposed for parallel magnetic resonance imaging (MRI), which uses multiple coils and subsampled k-space data, and a quantitative method for comparison of algorithms is sorely needed. On such images, we compared three methods for quantitative image quality evaluation: human detection, computer detection model and a computer perceptual difference model (PDM). One-quarter sampling and three different reconstruction methods were investigated: a regularization method developed by Ying et al., a simplified regularization method and an iterative method proposed by Pruessmann et al. Images obtained from a full complement of k-space data were also included as reference images. Detection studies were performed using a simulated dark tumor added on MR images of fresh bovine liver. Human detection depended strongly on reconstruction methods used, with the two regularization methods achieving better performance than the iterative method. Images were also evaluated using detection by a channelized Hotelling observer model and by PDM scores. Both predicted the same trends as observed from human detection. We are encouraged that PDM gives trends similar to that for human detection studies. Its ease of use and applicability to a variety of MRI situations make it attractive for evaluating image quality in a variety of MR studies.     

Alternate update of shifted extended keyholes (AUSEK): A new accelerating strategy for interventional MRI

Real-time or near-real-time acquisition plays a key role in providing immediate image guidance for interventional magnetic resonance imaging (iMRI). However, the requirement of accurate needle tip localization has made several accelerating techniques, like Keyhole imaging or sliding window reconstruction, difficult to be applied to iMRI. The purpose of this work was to further explore the possible ways of applying view sharing techniques to iMRI. Inspired by Keyhole imaging, we present an easy-to-implement accelerating strategy called “Alternate update of shifted extended keyholes (AUSEK)”. In this method, the keyhole views are not only extended but also shifted towards either high-frequency edge to form two divisions in k-space. The divisions which are mirrored to each other along the center are alternately updated following a reference scan. By using simulations and experiments, we demonstrate that AUSEK could effectively preserve the spatial resolution of the image, especially of the needle, at a temporal acceleration rate of about 2.5. AUSEK was implemented online in an open-configuration low-field MR imaging system.     

Referenceless PRFS MR Thermometry Using Partial Separability Model

Many areas of magnetic resonance (MR)-guided thermal therapy research would benefit from temperature maps with high spatial and temporal resolution. Conventional thermometry relies on the subtraction of baseline images, which makes it sensitive to tissue motion and frequency drift during the course of treatment. For another case is the limit of magnetic resonance imaging sampling speed, it is hard to accurately achieve MR thermometry with high spatiotemporal resolution especially for dynamic organs. To address these issues, a novel method for MR thermometry is presented by exploiting the data redundancy based on partial separability (PS) model and the referenceless thermometry. The PS model highly sparse sample two datasets in the (k–t) space for image reconstruction, which respectively determine the spatial and temporal resolutions. After the phase information is extracted from the images reconstructed by the PS model, the background phase outside the heated region from each acquired phase image through a polynomial fitting is estimated. Extrapolation of the polynomial to the heated region serves as the background phase estimate, which is then subtracted from the actual phase. The thermometry results showed that this method could accurately capture the dynamic change of MR thermometric images with 1.5 mm × 1.5 mm spatial resolution and 250 ms temporal resolution, respectively. The in vivo experiment of MR-guided high intensity focused ultrasound research and the cardiac dynamic MR thermometry are shown to demonstrate the benefits of the proposed method in high spatiotemporal resolution MR thermometry.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

Rapid passive MR catheter visualization for endovascular therapy using nonsymmetric truncated k-space sampling strategies

Passive catheter tracking guidance by MRI is a promising approach for endovascular therapy that may have several clinical advantages over the more frequently employed active MR approaches. However, real-time MR passive tracking is problematic because it is difficult to have an image update rate >1 Hz and preserve adequate spatial and image contrast resolution. One solution for improving real-time temporal performance is the use of nonsymmetric truncated k-space sampling strategies, which acquire only a fraction of the data in both the readout and phase-encoding directions. This article investigated these acquisition strategies in combination with using (a) multicycle projection dephaser (mcPD) gradients for background suppression and (b) the projection-onto-convex sets (POCS) algorithm to reconstruct the images. The use of mcPD gradients allowed the data sampling strategies to exploit the k-space energy structure of the catheter, and POCS allowed reconstruction of high-quality MR images that were suitable for real-time passive catheter tracking and demonstrated improved geometric representations of catheter width and tip position compared to zero filling. The use of nonsymmetric truncated k-space reduced the total acquisition time.     

Exploiting the wavelet structure in compressed sensing MRI

Sparsity has been widely utilized in magnetic resonance imaging (MRI) to reduce k-space sampling. According to structured sparsity theories, fewer measurements are required for tree sparse data than the data only with standard sparsity. Intuitively, more accurate image reconstruction can be achieved with the same number of measurements by exploiting the wavelet tree structure in MRI. A novel algorithm is proposed in this article to reconstruct MR images from undersampled k-space data. In contrast to conventional compressed sensing MRI (CS-MRI) that only relies on the sparsity of MR images in wavelet or gradient domain, we exploit the wavelet tree structure to improve CS-MRI. This tree-based CS-MRI problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved by an iterative scheme. Simulations and in vivo experiments demonstrate the significant improvement of the proposed method compared to conventional CS-MRI algorithms, and the feasibleness on MR data compared to existing tree-based imaging algorithms.     

Application of perceptual difference model on regularization techniques of parallel MR imaging

Parallel magnetic resonance imaging through sensitivity encoding using multiple receiver coils has emerged as an effective tool to reduce imaging time or to improve image SNR. The quality of reconstructed images is limited by the inaccurate estimation of the sensitivity map, noise in the acquired k-space data and the ill-conditioned nature of the coefficient matrix. Tikhonov regularization is a popular method to reduce or eliminate the ill-conditioned nature of the problem. In this approach, selection of the regularization map and the regularization parameter is very important. Perceptual difference model (PDM) is a quantitative image quality evaluation tool that has been successfully applied to varieties of MR applications. High correlation between the human rating and PDM score shows that PDM should be suitable to evaluate image quality in parallel MR imaging. By applying PDM, we compared four methods of selecting the regularization map and four methods of selecting the regularization parameter. We found that a regularization map obtained using generalized series (GS) together with a spatially adaptive regularization parameter gave the best reconstructions. PDM was also used as an objective function for optimizing two important parameters in the spatially adaptive method. We conclude that PDM enables one to do comprehensive experiments and that it is an effective tool for designing and optimizing reconstruction methods in parallel MR imaging.     

Visually weighted reconstruction of compressive sensing MRI

Compressive sensing (CS) enables the reconstruction of a magnetic resonance (MR) image from undersampled data in k-space with relatively low-quality distortion when compared to the original image. In addition, CS allows the scan time to be significantly reduced. Along with a reduction in the computational overhead, we investigate an effective way to improve visual quality through the use of a weighted optimization algorithm for reconstruction after variable density random undersampling in the phase encoding direction over k-space. In contrast to conventional magnetic resonance imaging (MRI) reconstruction methods, the visual weight, in particular, the region of interest (ROI), is investigated here for quality improvement. In addition, we employ a wavelet transform to analyze the reconstructed image in the space domain and fully utilize data sparsity over the spatial and frequency domains. The visual weight is constructed by reflecting the perceptual characteristics of the human visual system (HVS), and then applied to ?₁ norm minimization, which gives priority to each coefficient during the reconstruction process. Using objective quality assessment metrics, it was found that an image reconstructed using the visual weight has higher local and global quality than those processed by conventional methods.     

MR image reconstruction of sparsely sampled 3D k-space data by projection-onto-convex sets

In many rapid three-dimensional (3D) magnetic resonance (MR) imaging applications, such as when following a contrast bolus in the vasculature using a moving table technique, the desired k-space data cannot be fully acquired due to scan time limitations. One solution to this problem is to sparsely sample the data space. Typically, the central zone of k-space is fully sampled, but the peripheral zone is partially sampled. We have experimentally evaluated the application of the projection-onto-convex sets (POCS) and zero-filling (ZF) algorithms for the reconstruction of sparsely sampled 3D k-space data. Both a subjective assessment (by direct image visualization) and an objective analysis [using standard image quality parameters such as global and local performance error and signal-to-noise ratio (SNR)] were employed. Compared to ZF, the POCS algorithm was found to be a powerful and robust method for reconstructing images from sparsely sampled 3D k-space data, a practical strategy for greatly reducing scan time. The POCS algorithm reconstructed a faithful representation of the true image and improved image quality with regard to global and local performance error, with respect to the ZF images. SNR, however, was superior to ZF only when more than 20% of the data were sparsely sampled. POCS-based methods show potential for reconstructing fast 3D MR images obtained by sparse sampling.     

A novel acquisition-reconstruction algorithm for surface magnetic resonance imaging

In U-shaped, hand-size magnetic resonance surface scanners, imaging is performed along only one spatial direction, with the application of just one gradient (one-dimensional imaging). Lateral spatial resolution can be obtained by magnet displacement, but, in this case, resolution is very poor (on the order of some millimeters) and cannot be useful for high-resolution imaging applications. In this article, an innovative technique for acquisition and reconstruction of images produced by U-shaped, hand-size MRI surface scanners is presented. The proposed method is based on the acquisition of overlapping strips and an analytical reconstruction technique; it is capable of arbitrarily improving spatial lateral resolution without either using a second magnetic field gradient or making any assumptions about the imaged sample extension. Numerical simulations on synthetic images are reported demonstrating the method functionalities. The presented method also makes it possible to use U-shaped, hand-size MRI surface scanners for high-resolution biomedical applications, such as the imaging of skin lesions.     

基于同伦l0范数最小化重建的三维动态磁共振成像

高欠采倍数的动态磁共振图像重建具有重要意义,是同时实现高时间分辨率和高空间分辨率动态对比度增强成像的重要环节.本研究提出一种结合黄金角变密度螺旋采样、并行成像和基于同伦l₀范数最小化的压缩感知的图像重建的三维动态磁共振成像方法.黄金角变密度螺旋采样轨迹被用来连续获取k空间数据,具有数据采集效率高、对运动不敏感等优点.在重建算法中,将多线圈稀疏约束应用于时间总变分域,使用基于l₀范数最小化的非线性重建算法代替传统的l₁范数最小化算法,进一步提高了欠采样率.仿真实验和在体实验表明本文所提的方法在保持图像质量的同时,也可以实现较高的空间分辨率和时间分辨率,初步验证了基于同伦l₀范数最小化重建在三维动态磁共振成像上的优势和临床价值.     

Fast single image super-resolution using estimated low-frequency k-space data in MRI

PurposeSingle image super-resolution (SR) is highly desired in many fields but obtaining it is often technically limited in practice. The purpose of this study was to propose a simple, rapid and robust single image SR method in magnetic resonance (MR) imaging (MRI).MethodsThe idea is based on the mathematical formulation of the intrinsic link in k-space between a given (modulus) low-resolution (LR) image and the desired SR image. The method consists of two steps: 1) estimating the low-frequency k-space data of the desired SR image from a single LR image; 2) reconstructing the SR image using the estimated low-frequency and zero-filled high-frequency k-space data. The method was evaluated on digital phantom images, physical phantom MR images and real brain MR images, and compared with existing SR methods.ResultsThe proposed SR method exhibited a good robustness by reaching a clearly higher PSNR (25.77dB) and SSIM (0.991) averaged over different noise levels in comparison with existing edge-guided nonlinear interpolation (EGNI) (PSNR=23.78dB, SSIM=0.983), zero-filling (ZF) (PSNR=24.09dB, SSIM=0.985) and total variation (TV) (PSNR=24.54dB, SSIM=0.987) methods while presenting the same order of computation time as the ZF method but being much faster than the EGNI or TV method. The average PSNR or SSIM over different slice images of the proposed method (PSNR=26.33 dB or SSIM=0.955) was also higher than the EGNI (PSNR=25.07dB or SSIM=0.952), ZF (PSNR=24.97dB or SSIM=0.950) and TV (PSNR=25.70dB or SSIM=0.953) methods, demonstrating its good robustness to variation in anatomical structure of the images. Meanwhile, the proposed method always produced less ringing artifacts than the ZF method, gave a clearer image than the EGNI method, and did not exhibit any blocking effect presented in the TV method. In addition, the proposed method yielded the highest spatial consistency in the inter-slice dimension among the four methods.ConclusionsThis study proposed a fast, robust and efficient single image SR method with high spatial consistency in the inter-slice dimension for clinical MR images by estimating the low-frequency k-space data of the desired SR image from a single spatial modulus LR image.