软门限去噪法在X射线能谱分析中的应用

从函数空间的剖分和理想滤波器组的角度分析了多分辨率信号的分解与重构，提出了一种X射线能谱去噪的方法，即应用Mallat算法对谱信号进行小波分解，然后应用一个非线性软门限函数在小波域内将噪声抑制和消除，最后重构得到去噪后的能谱。该方法明显改善了能谱定量分析的结果。     

Automated correction of unwanted phase jumps in reference signals which corrupt MRSI spectra after eddy current correction

A commonly applied step in the postprocessing of gradient localized proton MR spectroscopy, is correction for eddy current effects using the water signal as a reference. However, this method can degrade some of the metabolite signals, in particular if applied on proton MR spectroscopic imaging data. This artifact arises from the water reference signal in the presence of a second signal which resonates close to the main water resonance. The interference of both resonances will introduce jumps in the phase of the reference time domain signal. Using this phase for eddy current correction will result in a ringing artifact in the frequency domain of the metabolite signal over the whole frequency range. We propose a moving window correction algorithm, which screens the phase of reference signals and removes phase jumps in time domain caused by interference of signals from multiple spin systems. The phase jumps may be abrupt or gradually distributed over several time data points. Because the correction algorithm only corrects time data points which contain phase jumps, the phase is minimally disrupted. Furthermore, the algorithm is automated for large datasets, correcting only those water reference signals which are corrupted. After correction of the corrupted reference signals, normal eddy current correction may be performed. The algorithm is compared with a method which uses a low-pass filter and tested on simulated data as well as on in vivo proton spectroscopic imaging data from a healthy volunteer and from patients with a brain tumor.     

Reference deconvolution. Elimination of distortions arising from reference line truncation

Reference deconvolution (G. A. Morris; J. Magn. Reson. 80, 547 (1988)) or reference lineshape adjustment (J. M. Wouters and G. A. Petersson, J. Magn. Reson. 28,81 (1977); J. M. Wouters, G. A. Petersson, W. C. Agosta, F. H. Field, W. A. Gibbons, H. Wyssbrod, and D. Cowburn, J. Magn. Reson. 28, 93 (1977)) relies on extracting the signal of a known reference material from an experimental spectrum and using a comparison between the experimental reference signal and that predicted by theory to correct instrumental contributions to the full experimental spectrum. Truncation of the reference line can produce unwanted artifacts and distortions in the final spectrum. The source of these anomalies usually lies in the dispersion-mode rather than in the absorption-mode data, as discontinuities are formed when the dispersion “wings” are truncated. These discontinuities can be reduced by a numerical extrapolation covering the lost region; this is sufficient to provide adequate results in most cases, but fails where spectra have baseline errors. A method of recreating the full dispersion signal directly from the corresponding adsorption data, based on the Hilbert transform relationship between the real and imaginary parts of a Fourier transform, is demonstrated here. This method results in the removal of truncation distortions from the deconvoluted spectrum, thus extending the range of application of the reference deconvolution technique.     

Sensitivity to point-spread function parameters in medical ultrasound image deconvolution

Clinical ultrasound images are often perceived as difficult to interpret due to image blurring and speckle inherent in the ultrasound imaging. But the image quality can be improved by deconvolution using an estimate of the point-spread function. However, it is difficult to obtain a sufficiently accurate estimate of the point-spread function in vivo because of the unknown properties of the soft tissue in clinical applications. Local variations in the speed of sound and attenuation change the pulse and beam shape. These in turn affect the point-spread function. The purpose and novelty of this paper is therefore to explore the sensitivity of a state-of-the-art deconvolution algorithm to uncertainty in the point-spread function. The point-spread function in our restoration algorithm is made shift invariant in the lateral dimension but shift dependent in the axial direction, and is modelled to match a 128-element 1D linear array often found in clinical use. We present simulated and in vitro sensitivity analyses of two-dimensional deconvolution while varying six parameters on which the point-spread function depends. Uncertainty in the ultrasound machine is analysed by varying the axial depths of lateral and elevational foci alongside height and width of transducer elements. Sensitivity to tissue influence is investigated by varying the speed of sound and frequency-dependent attenuation of the electro-mechanical impulse response. The results are analysed both quantitatively and in terms of the perceived image quality. First, the assessment of deconvolution using the logarithmic image amplitude is found to be a better indicator of the perceived improvement in the restoration. Secondly, the two most critical parameters for two-dimensional deconvolution are discovered to be the lateral focus and the speed of sound, because the success of deconvolution is perceived primarily in terms of deblurring. We also observed similar patterns for the simulation and in vitro experiment. Finally, we show that it is possible to restore in vivo ultrasound images using an assumed point-spread function and hence conclude that an exact point-spread function is not necessary for enhancing ultrasound image quality by deconvolution.     

模糊条码图像的正则化复原算法

由条码扫描仪获得条码图像的过程可以用理想条码信号与扫描仪光学系统点扩散函数的卷积模型来描述。反卷积是消除由光学系统点扩散带来的模糊现象的最好办法。为克服反卷积的病态问题,研究了反卷积的正则化方法;针对条码信号的特点,构建了适合于条码信号复原的惩罚项,提出了条码信号的正则化复原算法及其适合于计算机运算的迭代算法。通过实验研究了算法在不同情况下的抗干扰能力。实验结果表明,正则化条码信号复原算法在消除系统点扩散函数的影响的同时能够很好地抑制噪声。     

Spectral restoration from low signal-to-noise,distorted NMR signals: application to hyphenated capillary electrophoresis-NMR

In capillary electrophoresis separations coupled to NMR signal detection using small solenoidal coils, electrophoretic currents cause substantial distortion in the NMR spectral linewidths and peak heights, distortions which cannot be fully counteracted through shimming. The NMR spectra also have a low signal-to-noise ratio due to the small amounts of material, typically <1nmol, associated with such microseparations. This study proposes a two-step, signal processing method to restore spectral lines from the distorted NMR spectrum. First, a reference signal is acquired to estimate the broadening function, as a combination of several Lorentzian functions, using a gradient descent method. Then multi-resolution wavelet analysis is applied to the distorted spectrum to determine an initial estimate of the frequencies of the spectral lines. Convergence to the final spectrum, a second set of Lorentzians, involves deconvolution with the estimated broadening function using a gradient descent method. Experimental CE-NMR data show that considerable improvements in spectral quality are possible using this approach, although fine splittings can not be resolved if the broadening function is large.     

盲目反卷积光谱图超分辨复原算法

反卷积是实现光谱图超分辨复原的重要手段,与常规反卷积相比,盲目反卷积具有不需要预先准确获取卷积核函数的优势。着眼于充分利用光谱信号的特点和已有的光谱图反卷积成果,详细讨论了空域迭代盲目反卷积方法用于光谱图反卷积时的算法实现问题,并在分析光谱图卷积退化过程的基础上,针对光谱图反卷积算法特点,提出了光谱图卷积退化简化计算模型和最小二乘高斯拟合模型,以解决算法中相应的计算问题。基于Matlab平台的仿真表明,对于所用的高斯型谱线和点扩散函数,空域迭代盲目反卷积算法效果良好,在信噪比为50 dB时,分辨率提高约30％。     

空间外差光谱仪干涉图非均匀性校正研究

空间外差光谱仪在研制加工过程中,由于加工误差及胶合误差会使CCD接收到的干涉图存在光强分布不均匀现象,降低了变换光谱的准确性。基于对空间外差光谱仪干涉图光强非均匀性的产生机制与特点分析基础上,提出了一种干涉图非均匀性校正方法,该方法通过对实际干涉图进行单调分解、分段归一化及重新组合过程求解出光强分布函数,然后将变换光谱与光强分布函数倒数的傅里叶变换结果进行卷积来获得非均匀性校正后的光谱,最后将校正光谱进行逆傅里叶变换从而实现干涉图的非均匀性校正。将此方法应用于空间外差试验仪的近红外实测单色光干涉图的非均匀性校正,结果显示,该方法可以有效改善干涉图光强分布的非均匀性,抑制变换光谱的边频信号,通过与仿真的理想光谱对比,1 571和1 572 nm光谱校正前后噪声的减小率分别达到40.7%和24%,提高了光谱信噪比和准确性。     

Fast Removal of Residual Water in Proton Spectra

Quantification of metabolites in¹H spectra is difficult because of the presence of an unwanted water signal. Preprocessing, or removing the water contribution of a¹H spectrum, in the time domain is usually done using the state-space approach HSVD. HSVD removes the residual water and its side lobes, thereby reducing the baseline for the metabolites of interest and allowing subsequent data analysis using more sophisticated nonlinear least squares algorithms. However, the HSVD algorithm is computationally expensive because it estimates the signal subspace using the singular value decomposition (SVD). We show here that replacing the SVD by a low-rank revealing decomposition speeds up the computations without affecting the accuracy of the wanted parameter estimates.     

自适应的EEMD残余相关基线校正算法

基线校正是光谱分析的重要环节,现有算法通常需要设定关键参数,不具备自适应性。根据总体平均经验模态分解(ensemble empirical mode decomposition,EEMD)残余量特点,提出用残余量拟合光谱基线。通过残余量与信号相关性、残余量自相关和互相关性(称为残余相关准则)判断残余量是否是基线组成部分,以此为基础提出一种自适应的EEMD残余相关基线校正算法。对叠加曲线背景和线性背景的模拟光谱数据进行实验,结果显示在已知基线数学假设情况下,EEMD残余相关法逊于多项式拟合,同非线性拟合相差不多,优于小波分解。在没有光谱背景知识情况下,对真实拉曼光谱数据进行试验。经过上述方法预处理过的玉米叶片光谱采用3层BP神经网络建立与叶绿素之间预测模型,经过残余相关基线校正的模型具有最大校正相关系数和预测相关系数,最小交叉验证标准差和相对分析误差。各种基线校正方法中,残余相关基线校正对特征峰峰位、峰强和峰宽影响最小。实验表明,该算法可用于拉曼谱图基线校正,无需分析样品成分的先验知识,无需选择合适的拟合函数、拟合数据点、拟合阶次以及基函数和分解层数,也无需基线信号分布的数学假设,自适应性很强。     

激光诱导植物荧光寿命校正技术及其特性分析

激光诱导植物荧光寿命测量法是在植物荧光光谱分析法基础上开发的一种评估植物生长状况及环境监测的新技术。根据植物叶绿素荧光信号的物理特性,利用信息仿真技术开发了一种叶绿素荧光寿命校正方法,可提高植物叶绿素荧光寿命的测量精度。利用激光诱导叶绿素荧光寿命测量系统分别测得叶绿素荧光及其背景信号,先用解卷积法叶绿素荧光信号中分离出荧光衰减函数,可获取荧光寿命估计值。再结合叶绿素荧光寿命校正技术就能反演得到高精度的植物荧光寿命。仿真与实验结果表明：该方法可实现高精度的植物荧光寿命实时监测;并对不同含量的叶绿素提取液进行了测试,构建了植物荧光寿命与叶绿素含量的对应关系模型。未来该技术可用于遥感监测海洋、湖泊、河流中藻类植物的生物含量。     

改进的傅里叶域小波域联合去模糊算法

傅里叶域与小波域的联合去模糊算法在低噪声时具有优越的恢复效果,但是这种联合去模糊算法并不适用于含噪声的模糊图像.为了解决这一问题,本文将先验约束分别引入傅里叶域的去模糊步骤和小波域的去噪步骤.在傅里叶域,用矩阵形式表示目标函数.对目标函数添加平滑约束并且通过噪声水平和模糊图像高频信息计算得到平滑约束项的滤波系数.同样方式,在小波域对小波域目标函数添加能量约束,实现小波域目标函数的正则化过程.分析傅里叶域的噪声放大程度,通过傅里叶域的滤波系数计算得到小波域能量约束的滤波系数.傅里叶域的平滑约束可以抑制滤波过程中噪声的产生,小波域的能量约束可以提高小波域滤波的鲁棒性.仿真实验表明,改进的算法相比于原始算法具有更好的鲁棒性,可以有效提高图像的恢复质量.对于噪声标准差为0.010.1的模糊图像,改进算法恢复图像峰值信噪比比原始算法恢复图像的峰值信噪比高1左右.并且改进算法对于高斯型点扩散函数误差具有鲁棒性,当点扩散函数估计方差与实际方差相差0.4时,改进算法的恢复效果仍优于原始算法.     

基于BLCD分解与ACO-DBN网络的光纤振动信号识别

针对光纤振动信号受噪声干扰严重、特征提取单一和识别时间长的问题,提出了改进的局部特征尺度分解和蚁群算法优化深度置信网络的识别方法.首先,采用三次B样条函数插值拟合均值曲线改进局部特征尺度分解算法,并对原始信号进行分解得到一系列内禀尺度分量之和.其次,利用峭度因子和能谱系数构成融合指标筛选有效分量.然后,分别提取有效分量...     

近红外“3R”法双谱自适应去噪

针对近红外透射和吸收双光谱提出一种自适应的去噪方法。同步采集样品的近红外透射谱和吸收谱,在相同分解原则下总体经验模态法分解两组光谱,得到单组分特征模态分量。计算特征模态分量与原透射谱、吸收谱之间相关性,以及两组特征模态分量之间相关性,相关性最小模态分量初判为噪声分量。分析该分量在光谱中点处自相关性,若中点处很大,其他点几乎为零或很小,可以判断该分量为噪声。这种基于模态分量相关性的噪声判别方法称为“3R”法则。剔除噪声分量,重构光谱信号,循环上述分解过程,直到不满足“3R”法则,降噪过程结束。构造理想光谱,叠加噪声,“3R”法降噪效果优于EMD和EEMD低通滤波器,略逊于小波分解。真实光谱实验中,经过上述方法降噪处理过的玉米叶片光谱采用3层BP神经网络建立与叶绿素之间预测模型,“3R”法处理模型具有最大校正相关系数和预测相关系数,最小校正标准差和预测标准差。在四种降噪方法中,“3R”法对光谱谱峰位置和峰高的影响最小。实验表明,“3R”双谱去噪方法无需预设迭代次数,不用考虑分解层数,没有基函数,是自适应的,该方法适合近红外光谱去噪。     

Cerebral blood flow estimation from perfusion-weighted MRI using FT-based MMSE filtering method

INTRODUCTION: Perfusion-weighted MRI can be used for estimating blood flow parameters using bolus tracking technique based on dynamic susceptibility contrast MRI. In order to extract flow parameters, several deconvolution techniques have been proposed, of which the singular value decomposition (SVD) and Fourier transform (FT)-based techniques are more popular and widely used. In this work, an FT-based method has been proposed that involves derivation of an optimal shaped filter (defined as a filter function) estimated using minimum mean-squared error (MMSE) technique in the frequency domain. The proposed technique has been compared with the well-established SVD technique using simulation experiments. SIMULATION METHODS: Simulation was performed in multiple steps. An arterial input function (AIF) was first defined based on a certain blood flow value. The T2* signal change was then derived from this AIF, and noise was added to the signal. Then, a unique and optimal shaped filter function Phi(f) was derived in order to obtain the best estimate of scaled residue function. One way is by minimizing the mean-squared error between the noiseless and noisy scaled residue function, i.e., using an MMSE method. The effect of low and moderate noise and distorted AIF on cerebral blood flow (CBF) estimates was obtained by using FT-based MMSE method. Results were compared with the SVD technique. In this work, SVD technique was assumed to be the standard reference deconvolution technique. RESULTS AND DISCUSSION: For low-noise condition, the FT-based technique was more stable than the SVD technique, while for moderate noise, both techniques consistently underestimated CBF. SVD technique was found to be more stable in presence of AIF distortions. However, SVD technique was found to be unstable due to AIF delay compared to the FT-based MMSE method. The shaped filter function was found to be sensitive to effect of AIF distortions.     

The velocity of acoustic phonons in crystals with edge dislocations and point impurities

The velocity of longitudinal long-wave phonons in crystals with a small number of randomly distributed static edge dislocations was shown to be the same as in ideal crystals. The correction to the velocity of phonons is determined by their interaction with the field of lattice deformations caused by the presence of dislocations. The field of deformations of dislocation displacements is long-range. In addition, these deformations experience sign reversal when the sign of the coordinate perpendicular to the dislocation line and Burgers vector changes. It follows that a crystal contracts or expands in this direction because of the interaction of phonons with dislocations as the defect deformation sign alters. Such an anisotropic volume (and density) change over the whole crystal should however be balanced somehow. For this reason, the density of samples with edge dislocations should remain constant, and the correction δc to the velocity of phonons should be zero. The procedure for averaging that gives δc = 0 is based on the independence of this macro value from the orientation of phonon momemtum incident on randomly distributed dislocations, the unaveraged correction being a diverging value because of the long-range character of the field of defect deformations. For comparison, the correction to the velocity of phonons in crystals with point impurities was calculated. Lattice deformation caused by such defects is isotropic. For this reason, the mean density of crystals with point impurities and the velocity of phonons in them are different from those in ideal crystals. All calculations were performed using the Dyson equation derived on the basis of the Keldysh diagram technique.     

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.     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势. 关键词： 谱域光学相干层析 Lucy-Richardson解卷积 有效点扩散函数     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势.     

An alternative approach for measuring the scattered acoustic pressure field of immersed single and multiple cylinders

The form function of an elastic target can be obtained from the scattered signal through a deconvolution process. The deconvolution process uses the signal measured from an acoustically hard target (reference signal) to compensate for the impulse response of the measurement system. In this paper, it is shown that this approach limits the usable frequency range of the signal and leads to inaccuracies in the final results. An alternative approach is proposed in which the reference signal is replaced by the specular echo. A procedure is described for extracting the specular echo from the measured signal even in cases where it is not completely isolated from the resonant components. Modifications are made to the existing deconvolution formulation and it is further extended to be applicable to multiple scattering measurements. Experimental results show that the new approach provides improved accuracy and wider usable frequency range in both single and multiple scattering experiments.