Effective noise estimation and filtering from correlated multiple-coil MR data

Modern magnetic resonance (MR) imaging protocols based on multiple-coil acquisitions have carried on a new attention to noise and signal statistical modeling, as long as most of the existing techniques for data processing are model based. In particular, nonaccelerated multiple-coil and GeneRalized Autocalibrated Partially Parallel Acquisitions (GRAPPA) have brought noncentral-χ (nc-χ) statistics into stake as a suitable substitute for traditional Rician distributions. However, this model is only valid when the signals received by each coil are roughly uncorrelated. The recent literature on this topic suggests that this is often not the case, so nc-χ statistics are in principle not adequate. Fortunately, such model can be adapted through the definition of a set of effective parameters, namely, an effective noise power (greater than the actual power of thermal noise in the Radio Frequency receiver) and an effective number of coils (smaller than the actual number of RF receiving coils in the system). The implications of these artifacts in practical algorithms have not been discussed elsewhere. In the present paper, we aim to study their actual impact and suggest practical rules to cope with them. We define the main noise parameters in this context, introducing a new expression for the effective variance of noise which is of capital importance for the two image processing problems studied: first, we propose a new method to estimate the effective variance of noise from the composite magnitude signal of MR data when correlations are assumed. Second, we adapt several model-based image denoising techniques to the correlated case using the noise estimation techniques proposed. We show, through a number of experiments with synthetic, phantom, and in vivo data, that neglecting the correlated nature of noise in multiple-coil systems implies important errors even in the simplest cases. At the same time, the proper statistical characterization of noise through effective parameters drives to improved accuracy (both qualitatively and quantitatively) for both of the problems studied.     

Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images

Effective denoising is vital for proper analysis and accurate quantitative measurements from magnetic resonance (MR) images. Even though many methods were proposed to denoise MR images, only few deal with the estimation of true signal from MR images acquired with phased-array coils. If the magnitude data from phased array coils are reconstructed as the root sum of squares, in the absence of noise correlations and subsampling, the data is assumed to follow a non central-χ distribution. However, when the k-space is subsampled to increase the acquisition speed (as in GRAPPA like methods), noise becomes spatially varying. In this note, we propose a method to denoise multiple-coil acquired MR images. Both the non central-χ distribution and the spatially varying nature of the noise is taken into account in the proposed method. Experiments were conducted on both simulated and real data sets to validate and to demonstrate the effectiveness of the proposed method.     

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.     

面向语音增强的约束序贯高斯混合模型噪声功率谱估计

提出了一种基于极大似然的噪声对数功率谱估计方法,采用高斯混合模型对每一个频带上的功率谱包络构建统计模型,将时序包络划分为语音和非语音类,它们分别对应于高斯混合模型的两个高斯分量,描述语音和非语音的统计分布,其中非语音高斯分量的均值即为噪声功率谱的最优估计.采用序贯学习的方法,在极大似然准则下逐帧更新模型参数,并逐帧给出噪声功率谱的最优估计值。此外,由于序贯更新过程中语音信号长时缺失,容易导致模型失稳,提出了一种在线的最小描述长度准则(MDL)来判断语音信号是否长时缺失,从而保证了模型的稳定性.实验表明,算法性能整体优于经典的MS和IMCRA算法。     

Optimal estimation of the diffusion coefficient from non-averaged and averaged noisy magnitude data

The magnitude operation changes the signal distribution in MRI images from Gaussian to Rician. This introduces a bias that must be taken into account when estimating the apparent diffusion coefficient. Several estimators are known in the literature. In the present paper, two novel schemes are proposed. Both are based on simple least squares fitting of the measured signal, either to the median (MD) or to the maximum probability (MP) value of the Probability Density Function (PDF). Fitting to the mean (MN) or a high signal-to-noise ratio approximation to the mean (HS) is also possible. Special attention is paid to the case of averaged magnitude images. The PDF, which cannot be expressed in closed form, is analyzed numerically. A scheme for performing maximum likelihood (ML) estimation from averaged magnitude images is proposed. The performance of several estimators is evaluated by Monte Carlo (MC) simulations. We focus on typical clinical situations, where the number of acquisitions is limited. For non-averaged data the optimal choice is found to be MP or HS, whereas uncorrected schemes and the power image (PI) method should be avoided. For averaged data MD and ML perform equally well, whereas uncorrected schemes and HS are inadequate. MD provides easier implementation and higher computational efficiency than ML. Unbiased estimation of the diffusion coefficient allows high resolution diffusion tensor imaging (DTI) and may therefore help solving the problem of crossing fibers encountered in white matter tractography.     

基于双带宽高斯滤波器的磁共振弹性图局域频率估算算法研究与实现

本文对生物体软组织的生物力学模型进行了分析推导和简化,得到了磁共振相位图与生物组织弹性之间的力学关系,根据该关系研究了局域频率估算算法,应用Matlab对算法进行了编程实现,体模弹性图的实现验证了算法有效性,为后续开展临床肝纤维化分级研究奠定基础. 关键词： 磁共振弹性成像 弹性生物力学模型 局域频率估算     

An MRI denoising method using image data redundancy and local SNR estimation

This paper presents an LMMSE-based method for the three-dimensional (3D) denoising of MR images assuming a Rician noise model. Conventionally, the LMMSE method estimates the noise-less signal values using the observed MR data samples within local neighborhoods. This is not an efficient procedure to deal with this issue while the 3D MR data intrinsically includes many similar samples that can be used to improve the estimation results. To overcome this problem, we model MR data as random fields and establish a principled way which is capable of choosing the samples not only from a local neighborhood but also from a large portion of the given data. To follow the similar samples within the MR data, an effective similarity measure based on the local statistical moments of images is presented. The parameters of the proposed filter are automatically chosen from the estimated local signal-to-noise ratio. To further enhance the denoising performance, a recursive version of the introduced approach is also addressed. The proposed filter is compared with related state-of-the-art filters using both synthetic and real MR datasets. The experimental results demonstrate the superior performance of our proposal in removing the noise and preserving the anatomical structures of MR images.     

Noise and nonlinear estimation with optimal schemes in DTI

In general, the estimation of the diffusion properties for diffusion tensor experiments (DTI) is accomplished via least squares estimation (LSE). The technique requires applying the logarithm to the measurements, which causes bad propagation of errors. Moreover, the way noise is injected to the equations invalidates the least squares estimate as the best linear unbiased estimate. Nonlinear estimation (NE), despite its longer computation time, does not possess any of these problems. However, all of the conditions and optimization methods developed in the past are based on the coefficient matrix obtained in a LSE setup. In this article, NE for DTI is analyzed to demonstrate that any result obtained relatively easily in a linear algebra setup about the coefficient matrix can be applied to the more complicated NE framework. The data, obtained using non-optimal and optimized diffusion gradient schemes, are processed with NE. In comparison with LSE, the results show significant improvements, especially for the optimization criterion. However, NE does not resolve the existing conflicts and ambiguities displayed with LSE methods.     

Characterization of water distribution in bread during storage using magnetic resonance imaging

A soy bread of fully acceptable quality and containing 49% soy ingredients (with or without 5% almond powder) has been recently developed in our laboratory.

An investigation on water distribution and mobility, as probed by proton signal intensity and T₂ magnetic resonance images, during storage was designed to examine possible relations between water states and hindered staling rate upon soy or soy–almond addition.

Water proton distribution throughout soy-containing loaves was found to be very homogeneous in fresh breads with and without almond, with minimal water migration occurring during prolonged storage. In contrast, traditional wheat bread displayed an inhomogeneous water proton population that tended to change (with higher moisture migration towards the outer perimeter of the slice) during storage. Similar results were found for water mobility throughout the loaves, as depicted in T₂ images. On intensity images of all considered bread varieties, the outer perimeter corresponding to the crust exhibited lower signal intensity due to decreased water content. Higher T₂ values were found in the crust of soy breads with and without almond, which were attributed to lipids.

The results indicated that the addition of soy to bread improved the homogeneous distribution of water molecules, which may hinder the staling rate of soy-containing breads. However, incorporation of almond had little effect on the water proton distribution or mobility of soy breads.     

线阵CCD相机MTF的系统模型估计法与图像复原

线阵推扫CCD图像在获取与传输过程中产生退化。针对其复原问题,从图像降质机理的角度,提出用系统模型法估计MTF,并使用维纳滤波、Lucy-Richardson迭代法等方法对大气状况较好时的实验图像进行复原,采用复原图像的MTF曲线和MTFA(MTF area)等指标评价复原图像质量,并与从图像上提取PSF的图像估计法进行比较。实验结果表明,系统模型法能够更简便、准确地估计出MTF,进而取得良好的复原效果。     

Depth of focus estimation based on exposure dose distribution

A defocusing exposure dose distribution model is established with the integral effect of light intensity on time taken into account for laser direct writing on a thin photoresist with total reflection substrate. Exposure dose distribution curves are established using the established model for different photoresist depths. A side slope angle is established for each defocusing amount in accordance with the exposure dose distribution curves, and so depth of focus can be estimated by simply checking to see if the maximum side slope angle with the horizontal is in the range of 80-100°. Simulation results indicate that when laser direct writing is done on a thin photoresist with total reflection substrate using a laser with wavelength equal to 442 nm and a lens with numerical aperture equal to 0.5, the depth of focus estimated using the proposed method is 1 μm, which is just 1/3 of the depth of focus estimated using the method based on intensity distribution. It is therefore concluded that it is the integral effect of light intensity on time that causes the depth of focus estimation error, and the proposed method can be used to achieve a more accurate depth of focus estimation compared to the intensity distribution based method.     

A subpixel motion estimation algorithm based on digital correlation for illumination variant and noise image sequences

One of the challenges in practical subpixel motion estimation is how to obtain high accuracy with sufficient robustness to both illumination variations and additive noise. Motivated by the fact that the normalized spatial cross-correlation is invariant to illumination, we introduce a gradient-based subpixel registration method by maximizing the digital correlation (DC) function between the reference and target frames. Such DC function is remodeled with the presence of image noise, yielding that the correlation coefficient is only sensitive to noise standard variance. To fairly suppress the noise corruption, not only the target frame but also the reference one is reformulated into Taylor gradient expression with half but opposite motion vector. The final solution to motion estimates can be approximated into a closed form by reserving first-order coefficient terms of unregistered motion variables. The error trend of approximated solution is discussed. Computer simulations and actual experiments’ results demonstrate the superiority of the proposed method to the LMSE-based method and ordinary DC method when illumination variations and noise exist. Among the experiments, the influences of real subpixel translation value and noise variance degree on accuracy are studied; correspondingly, an optimized iterative idea for big translations and the recommended noise level adaptive to our method are introduced.     

Quantitative estimation of brain white matter abnormalities in elderly subjects using magnetic resonance imaging

Twenty-five elderly subjects were examined with brain magnetic resonance imaging (MRI). The subjects were divided into two groups: those with Mini-Mental State Examination (MMSE) scores above 25, and those subjects with MMSE scores between 18 and 24. The degree of white matter abnormalities (WMA) (expressed as relative volumes) as well as the presence of cerebrovascular risk factors were evaluated in the two groups. We found that a) subjects with low MMSE scores had significantly larger relative volumes of WMA than the subjects with higher scores, b) a significant correlation (r_s = 0.53, p < 0.009) between MMSE scores and the relative volume of WMA was also established, and c) a weak significant correlation (r_s = −0.51, p < 0.05) between arterial blood pressure and WMA was found in the subjects with high MMSE scores. Besides these findings no other correlations between the presence of cerebrovascular risk factors and WMA were found in any of the groups.     

基于高阶统计特征的FY-2气象卫星全视场杂散光估计

在分析FY 2VISSR杂散光成因的基础上,对其中的主要部分,即折镜直接反射形成杂散光的物理过程进行了建模。提取了特定区域目标的高阶统计特征,通过对地球圆盘外区域杂散光特征的学习,得出了系统杂散光作用矩阵A的总体最小二乘解,并将其推广到地球圆盘区域内,得到了在该模型下对全视场杂散光的有效估计。分析结果表明:对于红外和水汽通道而言,地球圆盘区域外的杂散光反演误差均值小于1bit,可见光通道反演出的杂散光日变化相对稳定,且各通道去除杂散光后图像的目视效果有了很大的改观。该估计方法有望在近期进入FY 2B及其后续卫星的业务运行中。     

基于独立成分分析的全波核磁共振信号噪声滤除方法研究

核磁共振测深(MRS)探水仪探测到的纳伏级微弱信号极易受到各种环境噪声的干扰, 严重影响信号特征参数的准确提取, 导致后续反演解释错误率增高. 针对这一难题, 提出了基于独立成分分析的快速固定点算法进行信噪分离. 首先分析了该算法用于全波MRS信号消噪的适用性; 其次, 采用数字正交法解决欠定盲源分离问题, 提出了频谱校正法实现分离信号幅值的有效恢复. 仿真结果表明, 该算法能够有效地实现全波MRS信号的信噪分离, 且数据拟合后初始振幅和弛豫时间的相对误差小于± 5.00%; 通过与其他经典算法的对比分析, 进一步证明了该算法消噪性能的优越性. 将该算法应用到野外实测信号处理, 结果证明其能有效滤除环境噪声.     

Correlation between liver iron content and magnetic resonance imaging in rats

Currently, serum ferritin concentration is the best noninvasive estimator of liver iron content. This study investigated the ability of magnetic resonance imaging to determine hepatic iron concentration. Fisher rats were treated with either parenteral iron to increase levels or phlebotomy to lower them and achieved a wide range of liver iron concentrations. Rats were imaged using a clinical whole body scanner at 1.5 Tesla with a 15-cm Helmholtz surface coil and a 23-cm field of view. The ratio of signal intensity of liver to skeletal muscle from images of the live intact rats correlated well with chemically measured iron concentration of the liver (r = −.89, p < .0001, linear regression analysis). Transverse relaxation rates (1/calculated T₂ relaxation times) also correlated with liver iron content (r = .66, p < .0001). The observation of a significant correlation between liver iron content and both signal intensities and T₂ relaxation rates, obtained by magnetic resonance imaging, may have considerable clinical relevance. If adapted to humans, this technique would have obvious applications in the diagnosis and management of diseases associated with iron overload as well as in the investigation of the overall role of iron in various human liver diseases.     

基于信道估计的自适应连续变量量子密钥分发方法

为使连续变量量子密钥分发协议获得稳定的密钥生成率,需要根据信道变化动态调整发送光脉冲的强度.将光纤量子信道看作加性玻色量子高斯信道,给出高斯态通过玻色量子高斯信道仍得到高斯态的证明过程.通过平衡零差检测后,采用最大似然估计法得到了信道参数,进而根据估计的噪声大小自适应调整Alice发送的光脉冲的强度,从而获得稳定的密钥生成率. 关键词： 量子密钥分发 连续变量 玻色量子高斯信道 信道估计     

Information processing in nuclear magnetic resonance imaging

An extended image analysis and classification system is presented to discuss the principal composition of the components as well as the methods of its realization in the field of reference based NMR diagnostics and tissue characterization.     

基于暗通道先验和区间估计的视频去雾方法

为了提高雾天视频的可用性,提出了一种基于暗通道先验和区间估计的视频去雾方法。利用暗通道先验知识,采用区间估计的方式,运用图像融合的思想,通过背景图像求取大气光值和介质传输率,并应用于视频的所有帧以去除雾气。与几种典型的视频去雾方法相比,具有较快的运算速度,能有效地避免去雾视频中出现颜色跳变的问题。以暗通道先验理论为基础,采用区间估计的方式对大气光值和介质传输率进行估计,从而能有效地提高去雾视频的整体亮度、清晰度和对比度,同时获得较好的图像颜色。