Performance of new signal‐to‐noise ratio estimation for SEM images based on single image noise cross‐correlation

A new technique for estimation of signal‐to‐noise ratio in scanning electron microscope images is reported. The method is based on the image noise cross‐correlation estimation model recently developed. We derive the basic performance limits on a single image signal‐to‐noise ratio estimation using the Cramer–Rao inequality. The results are compared with those from existing estimation methods including the nearest neighbourhood (the simple method), the first order linear interpolator, and the autoregressive based estimator. The comparisons were made using several tests involving different images within the performance bounds. From the results obtained, the efficiency and accuracy of image noise cross‐correlation estimation technique is considerably better than the other three methods.     

Image signal-to-noise ratio and noise variance estimation using autoregressive model

During the last three decades, several techniques have been proposed for signal-to-noise ratio (SNR) and noise variance estimation in images, with different degrees of success. Recently, a novel technique based on the statistical autoregressive model (AR) was developed and proposed as a solution to SNR estimation in scanning electron microscope (SEM) image. In this paper, the efficiency of the developed technique with different imaging systems is proven and presented as an optimum solution to image noise variance and SNR estimation problems. Simulation results are carried out with images like Lena, remote sensing, and SEM. The two image parameters, SNR and noise variance, are estimated using different techniques and are compared with the AR-based estimator.     

Image noise cross-correlation for signal-to-noise ratio estimation in scanning electron microscope images

A new and robust parameter estimation technique, named image noise cross-correlation, is proposed to predict the signal-to-noise ratio (SNR) of scanning electron microscope images. The results of SNR and variance estimation values are tested and compared with nearest neighborhood and first-order interpolation. Overall, the proposed method is best as its estimations for the noise-free peak and SNR are most consistent and accurate to within a certain acceptable degree, compared with the others.     

Image signal‐to‐noise ratio estimation using adaptive slope nearest‐neighbourhood model

A new technique based on nearest neighbourhood method is proposed. In this paper, considering the noise as Gaussian additive white noise, new technique single‐image‐based estimator is proposed. The performance of this new technique such as adaptive slope nearest neighbourhood is compared with three of the existing method which are original nearest neighbourhood (simple method), first‐order interpolation method and shape‐preserving piecewise cubic hermite autoregressive moving average. In a few cases involving images with different brightness and edges, this adaptive slope nearest neighbourhood is found to deliver an optimum solution for signal‐to‐noise ratio estimation problems. For different values of noise variance, the adaptive slope nearest neighbourhood has highest accuracy and less percentage estimation error. Being more robust with white noise, the new proposed technique estimator has efficiency that is significantly greater than those of the three methods.     

Nonlinear least squares regression for single image scanning electron microscope signal‐to‐noise ratio estimation

A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal‐to‐noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first‐order interpolation and the combination of both nearest neighbourhood and first‐order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods.     

Effect of shot noise and secondary emission noise in scanning electron microscope images

The effect of shot noise and emission noise due to materials that have different emission properties was simulated. Local variations in emission properties affect the overall signal‐to‐noise ratio (SNR) value of the scanning electron microscope image. In the case in which emission noise is assumed to be absent, the image SNRs for silicon and gold on a black background are identical. This is because only shot noise in the primary beam affects the SNRs, irrespective of the assumed noiseless secondary electron emission or backscattered electron emission processes. The addition of secondary emission noise degrades the SNR. Materials with higher secondary electron yield and backscattering electron yield give rise to higher SNR. For images formed from two types of material, the contrast of the image is lower. The reduction in image signal reduces the overall image SNR. As expected, large differences in δ or η give rise to higher SNR images.     

Adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in wavelet domain for scanning electron microscope images

Image processing is introduced to remove or reduce the noise and unwanted signal that deteriorate the quality of an image. Here, a single level two‐dimensional wavelet transform is applied to the image in order to obtain the wavelet transform sub‐band signal of an image. An estimation technique to predict the noise variance in an image is proposed, which is then fed into a Wiener filter to filter away the noise from the sub‐band of the image. The proposed filter is called adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in the wavelet domain. The performance of this filter is compared with four existing filters: median filter, Gaussian smoothing filter, two level wavelet transform with Wiener filter and adaptive noise Wiener filter. Based on the results, the adaptive tuning piecewise cubic Hermite interpolation with Wiener filter in wavelet domain has better performance than the other four methods.     

Performance of signal‐to‐noise ratio estimation for scanning electron microscope using autocorrelation Levinson–Durbin recursion model

A new technique to quantify signal‐to‐noise ratio (SNR) value of the scanning electron microscope (SEM) images is proposed. This technique is known as autocorrelation Levinson–Durbin recursion (ACLDR) model. To test the performance of this technique, the SEM image is corrupted with noise. The autocorrelation function of the original image and the noisy image are formed. The signal spectrum based on the autocorrelation function of image is formed. ACLDR is then used as an SNR estimator to quantify the signal spectrum of noisy image. The SNR values of the original image and the quantified image are calculated. The ACLDR is then compared with the three existing techniques, which are nearest neighbourhood, first‐order linear interpolation and nearest neighbourhood combined with first‐order linear interpolation. It is shown that ACLDR model is able to achieve higher accuracy in SNR estimation.     

Robust image signal-to-noise ratio estimation using mixed Lagrange time delay estimation autoregressive model

A new technique based on the statistical autoregressive (AR) model has recently been developed as a solution to signal-to-noise (SNR) estimation in scanning electron microscope (SEM) images. In the present study, we propose to cascade the Lagrange time delay (LTD) estimator with the AR model. We call this technique the mixed Lagrange time delay estimation autoregressive (MLTDEAR) model. In a few test cases involving different images, this model is found to present an optimum solution for SNR estimation problems under different noise environments. In addition, it requires only a small filter order and has no noticeable estimation bias. The performance of the proposed estimator is compared with three existing methods: simple method, first-order linear interpolator, and AR-based estimator over several images. The efficiency of the MLTDEAR estimator, being more robust with noise, is significantly greater than that of the other three methods.     

Image signal-to-noise ratio estimation using the autoregressive model

In the last two decades, a variety of techniques for signal-to-noise ratio (SNR) estimation in scanning electron microscope (SEM) images have been proposed. However, these techniques can be divided into two groups: first, SNR estimators of good accuracy, but based on impractical assumptions; second, estimators based on realistic assumptions but of poor accuracy. In this paper we propose the implementation of autoregressive (AR)-model interpolation as a solution to the problem. Unlike others, the proposed technique is based on a single SEM image and offers the required accuracy and robustness in estimating SNR values.     

基于几何纹理与Anscombe变换的蜂窝材料太赫兹图像降噪模型

为解决太赫兹（Terahertz,THz）图像内泊松高斯混合噪声导致芳纶纤维蜂窝材料脱粘缺陷轮廓检测精度低的问题,基于Anscombe变换与小波阈值法构建了THz图像降噪模型。高斯噪声方差为降噪模型的必要参数,但实际THz图像噪声分布未知,且噪声与纹理在高频混叠,给方差准确估计提出了挑战。为此,首先以样件纹理几何形状为先验信息,构造Benzene-ring算子去除THz图像纹理,使其小波域高频分量中仅含有噪声;然后提出改进的Logistic混沌映射提高样本集的多样性,以训练Elman神经网络准确建立高频分量与高斯噪声方差间映射关系;最后依据噪声方差估计值,基于Anscombe变换将泊松高斯混合噪声转化为高斯噪声,并利用小波阈值法与Anscombe逆变换得到了最终THz降噪图像。仿真与试验结果表明,所提出的方法降噪效果最佳并有效提高缺陷轮廓检测精度,相比于高斯滤波、小波阈值以及非局部均值法,平均梯度指标分别提升12%、33%、9%,缺陷面积绝对误差分别降低234 mm²、304 mm²、263 mm²。     

Adaptive Gaussian Noise Image Removal Algorithm Using Filtering-Based Noise Estimation

This paper proposes a spatially denoising algorithm using filtering-based noise estimation for an image corrupted by Gaussian noise.The proposed algorithm consists of two stages:estimation and elimination of noise density.To adaptively deal with variety of the noise amount,a noisy input image is firstly filtered by a lowpass filter.Standard deviation of the noise is computed from different images between the noisy input and its filtered image.In addition,a modified Gaussian noise removal filter based on the local statistics such as local weighted mean,local weighted activity and local maximum is used to control the degree of noise suppression.Experiments show the effectiveness of the proposed algorithm.     

Signal‐to‐noise ratio enhancement on SEM images using a cubic spline interpolation with Savitzky–Golay filters and weighted least squares error

A new technique based on cubic spline interpolation with Savitzky–Golay smoothing using weighted least squares error filter is enhanced for scanning electron microscope (SEM) images. A diversity of sample images is captured and the performance is found to be better when compared with the moving average and the standard median filters, with respect to eliminating noise. This technique can be implemented efficiently on real‐time SEM images, with all mandatory data for processing obtained from a single image. Noise in images, and particularly in SEM images, are undesirable. A new noise reduction technique, based on cubic spline interpolation with Savitzky–Golay and weighted least squares error method, is developed. We apply the combined technique to single image signal‐to‐noise ratio estimation and noise reduction for SEM imaging system. This autocorrelation‐based technique requires image details to be correlated over a few pixels, whereas the noise is assumed to be uncorrelated from pixel to pixel. The noise component is derived from the difference between the image autocorrelation at zero offset, and the estimation of the corresponding original autocorrelation. In the few test cases involving different images, the efficiency of the developed noise reduction filter is proved to be significantly better than those obtained from the other methods. Noise can be reduced efficiently with appropriate choice of scan rate from real‐time SEM images, without generating corruption or increasing scanning time.     

Reduction in acquisition time of scanning electron microscopy image using complex hysteresis smoothing

Complex hysteresis smoothing (CHS), which was developed for noise removal of scanning electron microscopy (SEM) images some years ago, is utilized in acquisition of an SEM image. When using CHS together, recording time can be reduced without problems by about one-third under the condition of SEM signal with a comparatively high signal-to-noise ratio (SNR). We do not recognize artificiality in a CHS-filtered image, because it has some advantages, that is, no degradation of resolution, only one easily chosen processing parameter (this parameter can be fixed and used in this study), and no processing artifacts. This originates in the fact that its criterion for distinguishing noise depends simply on the amplitude of the SEM signal. The automation of reduction in acquisition time is not difficult, because CHS successfully works for almost all varieties of SEM images with a fairly high SNR.     

Image signal-to-noise ratio estimation using Shape-Preserving Piecewise Cubic Hermite Autoregressive Moving Average model

We propose to cascade the Shape-Preserving Piecewise Cubic Hermite model with the Autoregressive Moving Average (ARMA) interpolator; we call this technique the Shape-Preserving Piecewise Cubic Hermite Autoregressive Moving Average (SP2CHARMA) model. In a few test cases involving different images, this model is found to deliver an optimum solution for signal to noise ratio (SNR) estimation problems under different noise environments. The performance of the proposed estimator is compared with two existing methods: the autoregressive-based and autoregressive moving average estimators. Being more robust with noise, the SP2CHARMA estimator has efficiency that is significantly greater than those of the two methods.     

Background intensity correction for terabyte‐sized time‐lapse images

Several computational challenges associated with large‐scale background image correction of terabyte‐sized fluorescent images are discussed and analysed in this paper. Dark current, flat‐field and background correction models are applied over a mosaic of hundreds of spatially overlapping fields of view (FOVs) taken over the course of several days, during which the background diminishes as cell colonies grow. The motivation of our work comes from the need to quantify the dynamics of OCT‐4 gene expression via a fluorescent reporter in human stem cell colonies. Our approach to background correction is formulated as an optimization problem over two image partitioning schemes and four analytical correction models. The optimization objective function is evaluated in terms of (1) the minimum root mean square (RMS) error remaining after image correction, (2) the maximum signal‐to‐noise ratio (SNR) reached after downsampling and (3) the minimum execution time. Based on the analyses with measured dark current noise and flat‐field images, the most optimal GFP background correction is obtained by using a data partition based on forming a set of submosaic images with a polynomial surface background model. The resulting image after correction is characterized by an RMS of about 8, and an SNR value of a 4 × 4 downsampling above 5 by Rose criterion. The new technique generates an image with half RMS value and double SNR value when compared to an approach that assumes constant background throughout the mosaic. We show that the background noise in terabyte‐sized fluorescent image mosaics can be corrected computationally with the optimized triplet (data partition, model, SNR driven downsampling) such that the total RMS value from background noise does not exceed the magnitude of the measured dark current noise. In this case, the dark current noise serves as a benchmark for the lowest noise level that an imaging system can achieve. In comparison to previous work, the past fluorescent image background correction methods have been designed for single FOV and have not been applied to terabyte‐sized images with large mosaic FOVs, low SNR and diminishing access to background information over time as cell colonies span entirely multiple FOVs. The code is available as open‐source from the following link https://isg.nist.gov/ .     

基于EMMAP的MEMS陀螺噪声估计与滤波方法研究

针对MEMS陀螺仪测量精度低、随机噪声具有不确定性和非线性的问题,提出一种基于最大期望算法(Expectation maximum,EM)和极大后验估计(Maximum a posterion,MAP)的无迹卡尔曼滤波(Unscented Kalman filter,UKF)——EMMAP-UKF的陀螺噪声估计与滤波方法。根据极大后验估计原理,构造出一种次优无偏MAP噪声统计估计模型,并在此基础上引入最大期望算法将噪声估计问题转换为数学期望极大化问题,实现对观测噪声方差的动态调整,最终实现陀螺仪随机漂移误差的估计与滤波处理。最后通过Allan方差对陀螺噪声滤波方法的性能进行评估,通过半实物仿真验证了本方法的有效性。     

基于MAP估计的复小波域局部自适应绝缘子红外热像去噪方法

为了从强白噪声干扰的红外热像中提取真实的绝缘子盘面温度场信息,提出一种基于MAP估计的复小波域局部自适应去噪方法.首次证实了绝缘子红外热像双树复小波变换(DT-CWT)系数服从拉普拉斯分布,并对不同滤波器组采用各自最精细分解层子带系数估计噪声方差,利用待估计点圆形邻域系数估计信号方差,且随分辨率变化调整圆形邻域半径,使得MAP估计的无噪声系数更为准确,提高了去噪图像质量.实验结果表明,该方法比传统的Wiener滤波法、基于离散小波变换和DT-CWT的贝叶斯阈值去噪方法具有更高的信噪比,在有效去除图像噪声的同时,图像细节信息保留更完好.     

基于经验与变分混合分解的超声回波信号噪声消除方法

超声缺陷检测结果易受超声回波信号中复杂噪声的干扰,为了提高超声缺陷检测的准确度,提出一种基于混合分解的 超声回波信号噪声消除方法。 采用经验模态分解算法结合相关系数指标对超声回波信号进行预处理,得到消除低频噪声分量 的超声回波预处理信号。 基于变分模态分解将该预处理信号分解为一系列窄带本征模态函数,引入互信息指标估计变分模态 分解的最优模态数量,并根据窄带本征模态函数与预处理信号的相关系数提取有用的模态分量,实现对超声回波信号去噪结果 的重构。 通过仿真和实测超声回波信号验证了本文方法的去噪性能,并与现有方法进行了对比。 结果表明,本文方法可同时消 除超声回波信号中的高频和低频噪声,在不同信噪比条件下 EMD、VMD 和本文方法去噪结果的 SNR 均值分别为 10. 01、9. 48 和 16. 09 dB,验证了本文方法对于超声回波信号噪声消除的优越性。     

线阵CCD全景图像的噪声分析与去噪方法研究

为便于线阵CCD(charge-coupled device)全景图像的后期运算处理,需要对图像进行去噪处理,以提高图像信噪比.分析了线阵CCD扫描全景成像系统中图像噪声的来源,研究了该系统噪声的特性.对比研究基于小波变换的多种去噪算法的优劣性和使用条件,提出一种基于小波软硬阈值的中值滤波去噪方法.通过实验结果分析,验...