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.     

Parallel magnetic resonance imaging using coils with localized sensitivities

The purpose of this study was to present clinical examples and illustrate the inefficiencies of a conventional reconstruction using a commercially available phased array coil with localized sensitivities. Five patients were imaged at 1.5 T using a cardiac-synchronized gadolinium-enhanced acquisition and a commercially available four-element phased array coil. Four unique sets of images were reconstructed from the acquired k-space data: (a) sum-of-squares image using four elements of the coil; localized sum-of-squares images from the (b) anterior coils and (c) posterior coils and a (c) local reconstruction. Images were analyzed for artifacts and usable field-of-view. Conventional image reconstruction produced images with fold-over artifacts in all cases spanning a portion of the image (mean 90 mm; range 36-126 mm). The local reconstruction removed fold-over artifacts and resulted in an effective increase in the field-of-view (mean 50%; range 20-70%). Commercially available phased array coils do not always have overlapping sensitivities. Fold-over artifacts can be removed using an alternate reconstruction method. When assessing the advantages of parallel imaging techniques, gains achieved using techniques such as SENSE and SMASH should be gauged against the acquisition time of the localized method rather than the conventional sum-of-squares method.     

Accelerated magnetic resonance imaging using the sparsity of multi-channel coil images

Joint estimation of coil sensitivities and output image (JSENSE) is a promising approach that improves the reconstruction of parallel magnetic resonance imaging (pMRI). However, when acceleration factor increases, the signal to noise ratio (SNR) of JSENSE reconstruction decreases as quickly as that of the conventional pMRI. Although sparse constraints have been used to improve the JSENSE reconstruction in recent years, these constraints only use the sparsity of the output image, which cannot fully exploit the prior information of pMRI. In this paper, we use the sparsity of coil images, instead of the output image, to exploit more prior information for JSENSE. Numerical simulation, phantom and in vivo experiments demonstrate that the proposed method has better performance than the SparseSENSE method and the constrained JSENSE method using the sparsity of the output image only.     

Nuclear norm-regularized SENSE reconstruction

SENSitivity Encoding (SENSE) is a mathematically optimal parallel magnetic resonance (MRI) imaging technique when the coil sensitivities are known. In recent times, compressed sensing (CS)-based techniques are incorporated within the SENSE reconstruction framework to recover the underlying MR image. CS-based techniques exploit the fact that the MR images are sparse in a transform domain (e.g., wavelets). Mathematically, this leads to an l(1)-norm-regularized SENSE reconstruction. In this work, we show that instead of reconstructing the image by exploiting its transform domain sparsity, we can exploit its rank deficiency to reconstruct it. This leads to a nuclear norm-regularized SENSE problem. The reconstruction accuracy from our proposed method is the same as the l(1)-norm-regularized SENSE, but the advantage of our method is that it is about an order of magnitude faster.     

Comparison of different methods for combining phase-contrast images obtained with multiple coils

The ability to determine coil sensitivities implies that a method optimized in terms of maximized signal-to-noise ratio (SNR) can be applied to the combination of multiple coil images. An optimization of SNR subsequently results in a minimized variance in quantitative velocity measurements using phase-contrast imaging. When coil sensitivities are unknown, the weighted mean method, utilizing the square of the signal magnitude as weights, is suitable for combination of multiple phase images. In this study, the optimized method using estimated coil sensitivities was compared to the weighted mean method both theoretically and experimentally. It is shown that absence of noise correlation between the different coil images implies no difference between the methods regarding the variance of the phase. In the practical situation, noise correlation does exist, implying an opportunity for further reduction of phase variance using the optimized method. In vitro and in vivo studies showed, however, no significant difference between the two methods studied.     

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.     

电子信息装备体系对抗试验方法论

基于复杂系统的基本理论,研究了体系的概念、内涵及典型实例。根据体系对抗及体系对抗试验作为复杂系统的表现和特点,从非线性、涌现性这两个主要方面分析了体系对抗试验的复杂性。剖析了传统性能试验方法的特点,根据这些特点总结得出性能试验方法不能适应体系对抗条件的试验,其根本原因在于性能试验方法所遵循的还原论思想不适用于体系对抗试验的复杂性;接着,着重从方法论方面分析了性能试验方法在体系对抗条件下的不足之处,进而针对这些不足之处得到了应该从复杂系统角度研究适用于体系对抗试验的方法论等结论。     

基于OPM的电子信息装备体系复杂性建模

对于电子信息装备体系的复杂系统,以往以还原论为指导的建模方法无法充分体现电子信息装备体系的涌现性等复杂性,探索采用应对复杂性的对象过程方法论(OPM)来解决此难题。根据传统系统级或体系级建模在方法论上的根本困难,分析电子信息装备体系复杂性建模需求。基于对象过程方法论研究电子信息装备体系建模方法,在统一视图框架下同时对电子信息装备体系组成中不同领域、不同专业的结构、功能和行为建模,通过OPM分别对电子信息装备体系结构和对抗过程进行建模,再把这两个静动态模型结合起来进行整体概念建模。以防空反导体系对抗为例,演示了OPM进行体系概念模型开发的方法,说明了方法的有效性。     

基于虚拟线圈和卷积神经网络的多层同时激发图像重建

本文提出一种基于虚拟共轭线圈（Virtual Coil Concept,VCC）技术和k空间插值鲁棒人工神经网络（Robust Artificial-neural-networks for k-space Interpolation,RAKI）的图像重建方法,用于磁共振多层同时激发成像（Simultaneous Multi-Slice imaging,SMS）,该方法能够有效提升重建图像的质量,被命名为VIRGINIA（VIRtual conjuGate coIls Neural-networks InterpolAtion）.为了得到更高质量的SMS图像,本文提出的VIRGINIA方法利用磁共振线圈数据的复数共轭对称性质扩展了SMS所获取的多通道数据,并将扩展后的数据用于RAKI网络的训练,利用训练后的网络实现高质量的SMS图像重建.本文将VIRGINIA方法和其他SMS图像重建方法（RAKI和Slice-GRAPPA方法）进行了对比,并采用结构相似指数（Structural Similarity Index,SSIM）、峰值信噪比（Peak Signal-to-Noise Ratio,PSNR）和均方根误差（Root Mean Square Error,RMSE）对不同方法的重建图像进行了量化对比分析.结果显示,在相同的SMS加速倍数下,使用VIRGINIA方法进行重建的图像质量均好于RAKI方法,且远好于传统Slice-GRAPPA方法.     

DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution

This paper proposes a multi-channel image reconstruction method, named DeepcomplexMRI, to accelerate parallel MR imaging with residual complex convolutional neural network. Different from most existing works which rely on the utilization of the coil sensitivities or prior information of predefined transforms, DeepcomplexMRI takes advantage of the availability of a large number of existing multi-channel groudtruth images and uses them as target data to train the deep residual convolutional neural network offline. In particular, a complex convolutional network is proposed to take into account the correlation between the real and imaginary parts of MR images. In addition, the k-space data consistency is further enforced repeatedly in between layers of the network. The evaluations on in vivo datasets show that the proposed method has the capability to recover the desired multi-channel images. Its comparison with state-of-the-art methods also demonstrates that the proposed method can reconstruct the desired MR images more accurately.     

Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics

The statistical properties of background noise such as its standard deviation and mean value are frequently used to estimate the original noise level of the acquired data. This requires the knowledge of the statistical intensity distribution of the background signal, that is, the probability density of the occurrence of a certain signal intensity. The influence of many new MRI techniques and, in particular, of various parallel-imaging methods on the noise statistics has neither been rigorously investigated nor experimentally demonstrated yet. In this study, the statistical distribution of background noise was analyzed for MR acquisitions with a single-channel and a 32-channel coil, with sum-of-squares (SoS) and spatial-matched-filter (SMF) data combination, with and without parallel imaging using k-space and image-domain algorithms, with real-part and conventional magnitude reconstruction and with several reconstruction filters. Depending on the imaging technique, the background noise could be described by a Rayleigh distribution, a noncentral chi-distribution or the positive half of a Gaussian distribution. In particular, the noise characteristics of SoS-reconstructed multichannel acquisitions (with k-space-based parallel imaging or without parallel imaging) differ substantially from those with image-domain parallel imaging or SMF combination. These effects must be taken into account if mean values or standard deviations of background noise are employed for data analysis such as determination of local noise levels. Assuming a Rayleigh distribution as in conventional MR images or a noncentral chi-distribution for all multichannel acquisitions is invalid in general and may lead to erroneous estimates of the signal-to-noise ratio or the contrast-to-noise ratio.     

An iterative method for coil sensitivity estimation in multi-coil MRI systems

This paper presents an iterative coil sensitivity estimation method for multi-coil MRI systems. The proposed method works with coil images in the magnitude image domain. It determines a region of support (RoS), a region being composed of the same type of tissues, by a region growing algorithm, which makes use of both intensities and intensity gradients of pixels. By repeating this procedure, it can determine multiple regions of support, which together cover most of the concerned image area. The union of these regions of support provides a rough estimate of the sensitivity of each coil through dividing the intensities of pixels by the average intensity inside every region of support. The obtained rough coil sensitivity estimate is further approached with the product of multiple low-order polynomials, rather than a single one. The product of these polynomials provides a smooth estimate of the sensitivity of each coil. With the obtained sensitivities of coils, it can produce a better reconstructed image, which determines more correct regions of support and yields preciser estimates of the sensitivities of coils. In other words, the method can be iteratively implemented to improve the estimation performance. The proposed method was verified through both simulated data and clinical data from different body parts. The experimental results confirm the superiority of our method to some conventional methods.     

Coil-combined split slice-GRAPPA for simultaneous multi-slice diffusion MRI

Objective: To develop a kernel optimization method called coil-combined split slice-GRAPPA (CC-SSG) to improve the accuracy of the reconstructed coil-combined images for simultaneous multi-slice (SMS) diffusion weighted imaging (DWI) data.Methods: The CC-SSG method optimizes the tuning parameters in the k-space SSG kernels to achieve an optimal trade-off between the intra-slice artifact and inter-slice leakage after the root-sum-of-squares (rSOS) coil combining of the de-aliased SMS DWI data. A detailed analysis is conducted to evaluate the contributions of the intra-slice artifact and inter-slice leakage to the total reconstruction error after coil combining.Results: Comparisons of the proposed CC-SSG method with the slice-GRAPPA (SG) and split slice-GRAPPA (SSG) methods are provided using two in-vivo readout-segmented (RS) EPI datasets collected from stroke patients. The CC-SSG method demonstrates improved accuracy of the reconstructed coil-combined images and the estimated diffusion tensor imaging (DTI) maps.Conclusion: CC-SSG strikes a good balance between the intra-slice artifact and inter-slice leakage for rSOS coil combining, and so can yield better reconstruction performance compared to SG and SSG for rSOS reconstruction. The optimal trade-off between the two artifacts is robust to the contrast of SMS data and the choice of the coil combining method.     

A software channel compression technique for faster reconstruction with many channels

In magnetic resonance imaging, highly parallel imaging using coil arrays with a large number of elements is an area of growing interest. With increasing channel numbers for parallel acquisition, the increased reconstruction time and extensive computer memory requirements have become significant concerns. In this work, principal component analysis (PCA) is used to develop a channel compression technique. This technique efficiently reduces the size of parallel imaging data acquired from a multichannel coil array, thereby significantly reducing the reconstruction time and computer memory requirement without undermining the benefits of multichannel coil arrays. Clinical data collected with a 32-channel cardiac coil are used in all of the experiments. The performance of the proposed method on parallel, partially acquired data, as well as fully acquired data, was evaluated. Experimental results show that the proposed method dramatically reduces the processing time without considerable degradation in the quality of reconstructed images. It is also demonstrated that this PCA technique can be used to perform intensity correction in parallel imaging applications.     

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.     

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.     

Parallel imaging with 3D TPI trajectory: SNR and acceleration benefits

Three-dimensional (3D) twisted projection imaging (TPI) trajectory has a unique advantage in sodium (²³Na) imaging on clinical MRI scanners at 1.5 or 3 T, generating a high signal-to-noise ratio (SNR) with a short acquisition time (∼10 min). Parallel imaging with an array of coil elements transits SNR benefits from small coil elements to acquisition efficiency by sampling partial k-space. This study investigates the feasibility of parallel sodium imaging with emphases on SNR and acceleration benefits provided by the 3D TPI trajectory. Computer simulations were used to find available acceleration factors and noise amplification. Human head studies were performed on clinical 1.5/3-T scanners with four-element coil arrays to verify simulation outcomes. In in vivo studies, proton (¹H) data, however, were acquired for concept–proof purpose. The sensitivity encoding (SENSE) method with the conjugate gradient algorithm was used to reconstruct images from accelerated TPI-SENSE data sets. Self-calibration was employed to estimate coil sensitivities. Noise amplification in TPI-SENSE was evaluated using multiple noise trials. It was found that the acceleration factor was as high as 5.53 (corresponding to acceleration number 2×3, ring-by-rotation), with a small image error of 6.9% when TPI projections were reduced in both polar (ring) and azimuthal (rotation) directions. The average noise amplification was as low as 98.7%, or 27% lower than Cartesian SENSE at that acceleration factor. The 3D nature of both TPI trajectory and coil sensitivities might be responsible for the high acceleration and low noise amplification. Consequently, TPI-SENSE may have potential advantages for parallel sodium imaging.     

基于成熟度评估的武器装备体系集成性能试验方法研究

单装试验到体系试验需要架设集成试验这座桥梁,论文借鉴技术集成成熟度评估方法提出了集成成熟度试验的思路,并建立了基于集成成熟度试验评估的装备体系集成性能试验方法,实现了体系集成性能的试验与评价,并通过示例对所提出的方法进行了演示验证,证明了方法的可行性。     

Compensation of effect of field instability by reference deconvolution with phase reconstruction

A compensation method based on reference deconvolution is developed to obtain high-resolution NMR spectra under an unstable magnetic field. It is shown that the applicability of the original deconvolution method is limited for small fluctuation, and a process what may be called phase reconstruction is proposed to compensate large field fluctuation. We demonstrate the method using a probe with a coil that can generate a fluctuation field artificially. A high-resolution 1H NMR spectrum of ethylbenzene was obtained under the unstable field after compensation with this method.