MRF-ZOOM for the unbalanced steady-state free precession (ubSSFP) magnetic resonance fingerprinting

In magnetic resonance fingerprinting (MRF), tissue parameters are determined by finding the best-match to the acquired MR signal from a predefined signal dictionary. This dictionary searching (DS) process is generally performed in an exhaustive manner, which requires a large predefined dictionary and long searching time. A fast MRF DS algorithm, MRF-ZOOM, was recently proposed based on DS objective function optimization. As a proof-of-concept study, MRF-ZOOM was only tested with one of the earliest MRF sequences but not with the recently more popular unbalanced steady state free precession MRF sequence (MRF-ubSSFP, or MRF-FISP). Meanwhile noise effects on MRF and MRF-ZOOM have not been examined. The purpose of this study was to address these open questions and to verify whether MRF-ZOOM can be combined with a dictionary-compression based method to gain further speed. Numerical simulations were performed to evaluate the DS objective function properties, noise effects on MRF, and to compare MRF-ZOOM with other methods in terms of speed and accuracy. In-vivo experiments were performed as well. Evaluation results showed that premises of MRF-ZOOM held for MRF-FISP; noise did not affect MRF-ZOOM more than the conventional MRF method; when SNR ≥ 1, MRF quantification yielded accurate results. Dictionary compression introduced quantification errors more to T2 quantification. MRF-ZOOM was thousands of times faster than the conventional MRF method. Combining MRF-ZOOM with dictionary compression showed no benefit in terms of fitting speed. In conclusion, MRF-ZOOM is valid for MRF- FISP, and can remarkably save MRF dictionary generation and searching time without sacrificing matching accuracy.     

snapMRF: GPU-accelerated magnetic resonance fingerprinting dictionary generation and matching using extended phase graphs

Purpose:Magnetic resonance fingerprinting (MRF) is a state-of-the-art quantitative MRI technique with a computationally demanding reconstruction process, the accuracy of which depends on the accuracy of the signal model employed. Having a fast, validated, open-source MRF reconstruction would improve the dependability and accuracy of clinical applications of MRF.Methods:We parallelized both dictionary generation and signal matching on the GPU by splitting the simulation and matching of dictionary atoms across threads. Signal generation was modeled using both Bloch equation simulation and the extended phase graph (EPG) formalism. Unit tests were implemented to ensure correctness. The new package, snapMRF, was tested with a calibration phantom and an in vivo brain.Results:Compared with other online open-source packages, dictionary generation was accelerated by 10–1000× and signal matching by 10–100×. On a calibration phantom, T₁ and T₂ values were measured with relative errors that were nearly identical to those from existing packages when using the same sequence and dictionary configuration, but errors were much lower when using variable sequences that snapMRF supports but that competitors do not.Conclusion:Our open-source package snapMRF was significantly faster and retrieved accurate parameters, possibly enabling real-time parameter map generation for small dictionaries. Further refinements to the acquisition scheme and dictionary setup could improve quantitative accuracy.     

Matrix completion-based reconstruction for undersampled magnetic resonance fingerprinting data

An iterative reconstruction method for undersampled magnetic resonance fingerprinting data is presented. The method performs the reconstruction entirely in k-space and is related to low rank matrix completion methods. A low dimensional data subspace is estimated from a small number of k-space locations fully sampled in the temporal direction and used to reconstruct the missing k-space samples before MRF dictionary matching. Performing the iterations in k-space eliminates the need for applying a forward and an inverse Fourier transform in each iteration required in previously proposed iterative reconstruction methods for undersampled MRF data. A projection onto the low dimensional data subspace is performed as a matrix multiplication instead of a singular value thresholding typically used in low rank matrix completion, further reducing the computational complexity of the reconstruction. The method is theoretically described and validated in phantom and in-vivo experiments. The quality of the parameter maps can be significantly improved compared to direct matching on undersampled data.     

AIR-MRF: Accelerated iterative reconstruction for magnetic resonance fingerprinting

Existing approaches for reconstruction of multiparametric maps with magnetic resonance fingerprinting (MRF) are currently limited by their estimation accuracy and reconstruction time. We aimed to address these issues with a novel combination of iterative reconstruction, fingerprint compression, additional regularization, and accelerated dictionary search methods. The pipeline described here, accelerated iterative reconstruction for magnetic resonance fingerprinting (AIR-MRF), was evaluated with simulations as well as phantom and in vivo scans. We found that the AIR-MRF pipeline provided reduced parameter estimation errors compared to non-iterative and other iterative methods, particularly at shorter sequence lengths. Accelerated dictionary search methods incorporated into the iterative pipeline reduced the reconstruction time at little cost of quality.     

一种无线传感器网络中的混沌信号重构算法

将无线传感器网络节点观测区域中的一个混沌信号发送到融合中心,进行信号重构.由于节点的通信带宽受限,信号传输之前需要进行量化,给信号带来量化噪声,使得信号重构工作变得更为棘手.本文提出用平方根容积卡尔曼滤波器对融合中心收集的信号进行重构.首先估计观测信号的概率密度函数,使用最优量化器量化观测信号,在有限的量化比特数下,取得最优的信号量化性能.平方根容积卡尔曼滤波器相对无先导卡尔曼算法具有较少的求容积分点,因此具有计算量小的优点,同时迭代过程采用传递误差矩阵的平方根矩阵,保证迭代过程的稳定性和提高数据估计精度.仿真结果表明,该算法能够有效和快速地重构观测信号,并且比基于无先导卡尔曼滤波的算法更快.     

一种强噪声背景下微弱超声信号提取方法研究

为解决在强噪声背景下获取超声信号的难题,基于粒子群优化算法和稀疏分解理论提出一种强噪声背景下微弱超声信号提取方法.该方法将降噪问题转换为在无穷大参数集上对函数进行优化的问题,首先以稀疏分解理论和超声信号的结构特点为依据构建了粒子群优化算法运行所需要的目标函数及去噪后信号的重构函数,从而将粒子群优化算法和超声信号降噪联系在一起;然后根据粒子群优化算法可以在连续参数空间寻优的特点建立了用于匹配超声信号的连续超完备字典,并采用改进的自适应粒子群优化算法在该字典中对目标函数进行优化;最后根据对目标函数在字典上的优化结果确定最优原子,并利用最优原子按照重构函数重构出降噪后的超声信号.通过对仿真超声信号和实测超声信号的处理,结果表明本文提出的方法可以有效提取信噪比低至-4 dB的强噪声背景下的微弱超声信号,且和基于自适应阈值的小波方法相比本文方法表现出更好的降噪性能.     

Signal reconstruction in wireless sensor networks based on a cubature Kalman particle filter

For solving the issues of the signal reconstruction of nonlinear non-Gaussian signals in wireless sensor networks(WSNs), a new signal reconstruction algorithm based on a cubature Kalman particle filter(CKPF) is proposed in this paper.We model the reconstruction signal first and then use the CKPF to estimate the signal. The CKPF uses a cubature Kalman filter(CKF) to generate the importance proposal distribution of the particle filter and integrates the latest observation, which can approximate the true posterior distribution better. It can improve the estimation accuracy. CKPF uses fewer cubature points than the unscented Kalman particle filter(UKPF) and has less computational overheads. Meanwhile, CKPF uses the square root of the error covariance for iterating and is more stable and accurate than the UKPF counterpart. Simulation results show that the algorithm can reconstruct the observed signals quickly and effectively, at the same time consuming less computational time and with more accuracy than the method based on UKPF.     

Adaptive data acquisition in MRI

We propose an adaptive data acquisition technique that depends on the object to be imaged in magnetic resonance (MR) imaging. In this paper, we employed a matching pursuit (MP) algorithm to achieve the adaptive data acquisition. Since the matching pursuit is a greedy algorithm to find RF and gradient waveforms which are the best match for an object-signal, the signal can be decomposed with a few iterations and thereby lead reduction of imaging time in MR. To adopt the matching pursuit algorithm to the adaptive data acquisition in MRI, we have designed a dictionary which contains a windowed Fourier basis set. Because the basis set is localized spatially, the image signal could be divided into segmented signals so that matching pursuit with the segmented signals could lead to effective and object-dependent data acquisition. To verify the proposed technique, computer simulations and experiments are performed with a 1.0 T whole body MRI system.     

分段匹配追踪式Karhunen-Loeve非相干字典语音压缩感知

压缩感知(Compressed Sensing,CS)理论突破了经典采样定理的理论边界,为信号压缩提供了另一种途径。基于CS理论框架,做了两方面工作:为提高语音字典对信号的匹配性,设计了一种基于K-L展开的非相干语音字典;针对现有匹配追踪(MP,OMP)算法的不足,提出分段匹配追踪(Segment MP,SegMP)算法。首先对语音自相关函数进行建模并估计模型参数,构造语音自适应非相干字典,然后采用SegMP对语音稀疏向量分段观测,获得多个低维矢量,最后结合模型参数重建字典并重构信号,实现了语音压缩感知。语音测试结果表明:相比现有方案,本文方案对信号的稀疏表示更为精准,具有更好的重构质量,且降低了计算复杂度。      

Development of fast deep learning quantification for magnetic resonance fingerprinting in vivo

PurposeA deep neural network was developed for magnetic resonance fingerprinting (MRF) quantification. This study aimed at extending previous studies of deep learning MRF to in vivo applications, allowing sub-second computation time for large-scale data.MethodsWe applied the deep learning methodology based on our previously published multi-layer perceptron. The number of layers was four, which was optimized to balance the model capacity and noise robustness. The training sets were obtained from MRF dictionaries with 9000 to 28,000 atoms, depending on the desired T1 and T2 ranges. The simulated MRF undersampling artifact based on the k-space acquisition scheme and noise were both added to the training data to reduce the error in estimates.ResultsThe neural network achieved high fidelity (R2 _ 0.98) as compared to the T1 and T2 values of the ISMRM standardized phantom. In brain MRF experiment, the model trained with simulated artifacts and noise showed less error compared to that without. The in vivo application of our neural network for liver and prostate were also demonstrated. For an MRF slice with 256 _ 256 image resolution, the computation time of our neural network was 0.12 s, compared with the _ 28 s-pre-slice for the conventional dictionary matching method.ConclusionOur neural network achieved fast computation speed for MRF quantification. The model trained with simulated artifacts and noise showed less error and achieved optimal performance for phantom experiment and in vivo normal brain and liver, and prostate cancer patient.     

Matching pursuit of an adaptive impulse dictionary for bearing fault diagnosis

The sparse decomposition based on matching pursuit is an adaptive sparse expression of the signals. An adaptive matching pursuit algorithm that uses an impulse dictionary is introduced in this article for rolling bearing vibration signal processing and fault diagnosis. First, a new dictionary model is established according to the characteristics and mechanism of rolling bearing faults. The new model incorporates the rotational speed of the bearing, the dimensions of the bearing and the bearing fault status, among other parameters. The model can simulate the impulse experienced by the bearing at different bearing fault levels. A simulation experiment suggests that a new impulse dictionary used in a matching pursuit algorithm combined with a genetic algorithm has a more accurate effect on bearing fault diagnosis than using a traditional impulse dictionary. However, those two methods have some weak points, namely, poor stability, rapidity and controllability. Each key parameter in the dictionary model and its influence on the analysis results are systematically studied, and the impulse location is determined as the primary model parameter. The adaptive impulse dictionary is established by changing characteristic parameters progressively. The dictionary built by this method has a lower redundancy and a higher relevance between each dictionary atom and the analyzed vibration signal. The matching pursuit algorithm of an adaptive impulse dictionary is adopted to analyze the simulated signals. The results indicate that the characteristic fault components could be accurately extracted from the noisy simulation fault signals by this algorithm, and the result exhibited a higher efficiency in addition to an improved stability, rapidity and controllability when compared with a matching pursuit approach that was based on a genetic algorithm. We experimentally analyze the early-stage fault signals and composite fault signals of the bearing. The results further demonstrate the effectiveness and superiority of the matching pursuit algorithm that uses the adaptive impulse dictionary. Finally, this algorithm is applied to the analysis of engineering data, and good results are achieved.     

用于压缩感知磁共振成像的分割字典学习算法

字典学习算法可以根据数据本身的特点构建稀疏域中的基,从而使数据的表示更加稀疏.该文在传统的字典学习算法基础上提出了分割字典学习算法,由于部分磁共振图像组织结构简单、可以进行图像分割,因此可根据此特点来优化字典中基函数的构建,使磁共振图像的表达更为稀疏,从而获得更高的重建图像质量.该文利用模拟数据和真实数据进行了重建实验,结果表明与传统的字典学习算法相比,分割字典学习算法能进一步改善重建图像质量.     

字典奇异值分解加权压缩感知多径信号参数估计

为提高水声信道多径参数估计的分辨率,提出了一种基于字典奇异值分解的加权压缩感知算法。对于有源声呐,根据发射信号构造字典,对字典进行奇异值分解,利用大特征值对应的特征向量构造信号子空间,然后使用信号子空间对接收信号进行滤波。对滤波结果进行加权压缩感知参数估计,得出最终时延估计结果。仿真实验表明,所提方法能够对水声多径参数进行超分辨估计,适用于任何脉冲信号。湖试处理结果显示,混响背景下该方法也有较好的多径参数估计性能,能够降低接收数据的噪声成分,提高对水声信道的多径时延、个数和幅度的估计精度。      

Simultaneous quantification of SPIO and gadolinium contrast agents using MR fingerprinting

PurposeDevelop a magnetic resonance fingerprinting (MRF) methodology with R₂¹ quantification, intended for use with simultaneous contrast agent concentration mapping, particularly gadolinium (Gd) and iron labelled CD8+ T cells.MethodsVariable-density spiral SSFP MRF was used, modified to allow variable TE, and with an exp.(−TE·R₂¹) dictionary modulation. In vitro phantoms containing SPIO labelled cells and/or gadolinium were used to validate parameter maps, probe undersampling capacity, and verify dual quantification capabilities. A C57BL/6 mouse was imaged using MRF to demonstrate acceptable in vivo resolution and signal at 8× undersampling necessary for a 25-min scan.ResultsStrong agreement was found between conventional and MRF-derived values for R₁, R₂, and R₂¹. Expanded MRF allowed quantification of iron-loaded CD8+ T cells. Results were robust to 8× undersampling and enabled recreation of relaxation profiles for both a Gd agent and iron labelled cells simultaneously. In vivo data demonstrated sufficient SNR in undersampled data for parameter mapping to visualise key features.ConclusionMRF can be expanded to include R₁, R₂, and R₂¹ mapping required for simultaneous quantification of gadolinium and SPIO in vitro, allowing for potential implementation of a variety of future in vivo studies using dual MR contrast agents, including molecular imaging of labelled cells.     

Towards predicting the encoding capability of MR fingerprinting sequences

Sequence optimization and appropriate sequence selection is still an unmet need in magnetic resonance fingerprinting (MRF). The main challenge in MRF sequence design is the lack of an appropriate measure of the sequence's encoding capability. To find such a measure, three different candidates for judging the encoding capability have been investigated: local and global dot-product-based measures judging dictionary entry similarity as well as a Monte Carlo method that evaluates the noise propagation properties of an MRF sequence. Consistency of these measures for different sequence lengths as well as the capability to predict actual sequence performance in both phantom and in vivo measurements was analyzed. While the dot-product-based measures yielded inconsistent results for different sequence lengths, the Monte Carlo method was in a good agreement with phantom experiments. In particular, the Monte Carlo method could accurately predict the performance of different flip angle patterns in actual measurements. The proposed Monte Carlo method provides an appropriate measure of MRF sequence encoding capability and may be used for sequence optimization.     

RF slice profile effects in magnetic resonance fingerprinting

The radio frequency (RF) slice profile effects on T1 and T2 estimation in magnetic resonance fingerprinting (MRF) are investigated with respect to time-bandwidth product (TBW), flip angle (FA) level and field inhomogeneities. Signal evolutions are generated incorporating the non-ideal slice selective excitation process using Bloch simulation and matched to the original dictionary with and without the non-ideal slice profile taken into account. For validation, phantom and in vivo experiments are performed at 3T. Both simulations and experiments results show that T1 and T2 error from non-ideal slice profile increases with increasing FA level, off-resonance, and low TBW values. Therefore, RF slice profile effects should be compensated for accurate determination of the MR parameters.     

K-SVD和OMP算法在超声信号去噪中的应用

针对在线采集时超声波检测信号中存在大量噪声,降低了材料内部缺陷诊断准确性的问题,提出了一种基于广义K+奇异值分解算法(K-SVD)和正交匹配追踪算法(OMP)相结合的超声回波信号去噪算法。该算法利用K-SVD算法将Gabor字典训练成能够最有效反映信号结构特征的超完备字典,然后基于训练完成的超完备字典,用OMP算法把一定数量的字典原子进行线性组合来构成原始信号,从而实现信号的去噪。通过仿真实验将本文方法与传统的小波阈值去噪方法进行了对比研究。实验结果表明,该方法对超声回波信号的去噪效果优于小波阈值去噪方法,且噪声越大对比越明显,不仅可更有效地滤除信号中的高斯白噪声,提高信噪比,且尽可能保留了原始信号有用信息。     

稀疏阈值的超分辨率图像重建

为了解决基于字典学习的超分辨重构算法耗时过长的问题,提出了基于稀疏阈值模型的图像超分辨率重建方法。首先,将联合字典理论与图像块稀疏阈值方法相结合,训练得到高、低分辨率过完备图像字典对。接着,通过稀疏阈值OMP算法对图像特征块进行稀疏表示。然后,通过高分辨率字典重构出初始的超分辨图像。最后,通过改进迭代反投影算法对初始的超分辨图像进行全局优化,从而进一步提高图像重构质量。实验结果表明,超分辨图像重构平均峰值信噪比(PSNR)为30.1 d B,平均结构自相似度(SSIM)为0.937 9,平均计算时间为10.2 s。有效提高了超分辨重构的速度,改善了重构高分辨图像的质量。     

一种混沌映射的相空间去噪方法

对于混沌映射来说,它们的频谱比混沌流的频谱更广阔,与噪声频谱的重叠率更高,所以混沌流的去噪方法对它们并不适用. 在半盲分析法的框架下,混沌系统的参数估计问题终将归结为最小二乘估计问题. 本文从最小二乘拟合的角度出发估计混沌映射的演化参数,进而通过相空间重构以及投影操作,实现对观测信号的噪声抑制. 实验结果表明,该算法的去噪效果优于扩展卡尔曼滤波器（extended Kalman filter,EKF）和无先导卡尔曼滤波器（unscneted Kalman filter,UKF）,并且能够较大程度地将信号源的混沌特征量还原. 关键词： 混沌 噪声抑制 相空间重构 投影     

基于匹配追踪的拉曼光谱信号重构算法

拉曼光谱技术是一种高灵敏度、无损伤、振动分子光谱技术,在医药、生物、分析化学等诸多领域有着重要的作用。然而,由于拉曼散射强度低,实际测得的拉曼信号容易被噪声所污染。特别是在较短的曝光时间,收集到的拉曼光谱的信噪比很低。因此,提出了一种基于匹配追踪算法的信号重构方法,用于提取低信噪比的拉曼信号。该方法首先通过阈值循环迭代的方法在平均谱上找出特征峰的位置、估计峰的区间。根据峰的位置区间等信息,用高斯密度函数生成字典。在噪声谱上,根据特征峰位置和区间,将其区分为有信号区间和无信号区间,在有信号区间上利用匹配追踪算法重构被噪声所掩盖的拉曼信号。该算法不仅能够很好的逼近掩盖在噪声中的拉曼信号,且在重构信号的过程中也会对基线进行扣除,无须作基线校正处理。在仿真和实验中对该算法与常规算法进行了比较,结果证明,该算法在低信噪比条件下能够较好的恢复拉曼信号。该算法不同于传统光谱去噪算法,能同时对拉曼光谱进行了基线扣除以及噪声的处理,且能取得较为理想的结果,不需要使用不同的算法对基线和噪声分别处理。其次,在算法上我们创造性地将匹配追踪算法用于拉曼光谱信号的稀疏逼近求解。