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.     

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.     

Feature evaluation of complex hysteresis smoothing and its practical applications to noisy SEM images

Quality of a scanning electron microscopy (SEM) image is strongly influenced by noise. This is a fundamental drawback of the SEM instrument. Complex hysteresis smoothing (CHS) has been previously developed for noise removal of SEM images. This noise removal is performed by monitoring and processing properly the amplitude of the SEM signal. As it stands now, CHS may not be so utilized, though it has several advantages for SEM. For example, the resolution of image processed by CHS is basically equal to that of the original image. In order to find wide application of the CHS method in microscopy, the feature of CHS, which has not been so clarified until now is evaluated correctly. As the application of the result obtained by the feature evaluation, cursor width (CW), which is the sole processing parameter of CHS, is determined more properly using standard deviation of noise Nσ. In addition, disadvantage that CHS cannot remove the noise with excessively large amplitude is improved by a certain postprocessing. CHS is successfully applicable to SEM images with various noise amplitudes. SCANNING 35:292‐301, 2013. © 2012 Wiley Periodicals, Inc     

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 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.     

Mixed lagrange time delay estimation autoregressive Wiener filter application for real-time SEM image enhancement

A new filter is developed for the enhancement of scanning electron microscope (SEM) images. A mixed Lagrange time delay estimation auto-regression (MLTDEAR)-based interpolator is used to provide an estimate of noise variance to a standard Wiener filter. A variety of images are captured and the performance of the filter is shown to surpass the conventional noise filters. As all the information required for processing is extracted from a single image, this method is not constrained by image registration requirements and thus can be applied in real-time in cases where specimen drift is presented in the SEM image.     

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.     

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.     

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/ .     

Metrics for focusing in extremely noisy scanning electron microscopy condition

Finding a best focused image in very noisy condition is an extremely difficult task for the SEM user. If a performance, which is much higher than that of an expert in focusing, can be achieved in a computer-controlled scanning electron microscope (SEM), it will be very helpful for our field due to the many possible applications. To accomplish this work, we employ a powerful metric-the covariance obtained by a special scanning method. It can select the best focused image from a series of SEM images acquired by altering the focus of the objective lens under an extremely noisy SEM image condition. The noise immunity of the present method is quantitatively evaluated, and it is further improved based on the obtained evaluation result.     

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.     

Simulated SEM images for resolution measurement

Resolution is a key performance metric, which often defines the quality of a scanning electron microscope (SEM). Traditionally, there is the subjective measurement of the distance between two points on special "resolution" samples and there are several computer-based resolution-calculation methods. These computer-based resolution-calculation methods are much more precise than direct measurement, but none of them can currently be considered an objective way of measuring the resolution. The methods are still under development; therefore, objective testing is necessary. One approach to algorithm testing is to use simulated images. Simulated images are very useful for this purpose because they can be well-defined in all parameters unlike the real SEM images. Simulated images can be generated that closely mimic the gold-on-carbon SEM test sample images that usually consist of bright grains on a dark background. Simulation can account for edge effect, roughness of the substrate, different focusing, drift and vibration, and noise. Shapes, positions, and sizes of the grain structures are random. The simulated images can be then used for testing the resolution-calculation methods, especially for finding how the particular properties of SEM images affect the resultant instrument performance and image resolution. To support this testing, NIST has developed and made available a reference set of simulated SEM images generated using the methods described in this article.     

基于L-曲率流滤波器的图像降噪算法

提出了L-曲率流滤波器的图像降噪(滤波)算法,该方法按图像信噪比大小分高、中、低3类,分别由L滤波器降噪、多级L滤波器降噪以及多次迭代的组合滤波器降噪,并进行了实验研究。结果表明:该算法与均值和中值滤波器相比,输入图像信噪比越低,滤波效果越明显。当输入图像为低信噪比时,对于受高斯噪声污染的图像,该算法滤波比均值滤波平均提高2.98 dB;对于受脉冲噪声污染的图像,该算法滤波比中值滤波平均提高11.09 dB,说明该算法对降低不同种类和不同信噪比的图像噪声有较强的适应性。     

Single-image signal-to-noise ratio estimation

A method for estimating the signal-to-noise ratio from a single image is presented in this paper. The autocorrelation-based technique requires that image details be correlated over distances of a few pixels, while the noise is assumed to be uncorrelated from pixel to pixel. The latter is shown to be a good approximation in the case of scanning electron microscope (SEM) images provided that the video signal is not band limited. The noise component is derived from the difference between the image autocorrelation at zero offset and an estimate of the corresponding noise-free autocorrelation. Nonlinear effects introduced by intensity saturation and their implications on the image signal-to-noise ratio are also discussed.     

Application of an advanced maximum likelihood estimation restoration method for enhanced‐resolution and contrast in second‐harmonic generation microscopy

Second‐harmonic generation (SHG) microscopy has gained popularity because of its ability to perform submicron, label‐free imaging of noncentrosymmetric biological structures, such as fibrillar collagen in the extracellular matrix environment of various organs with high contrast and specificity. Because SHG is a two‐photon coherent scattering process, it is difficult to define a point spread function (PSF) for this modality. Hence, compared to incoherent two‐photon processes like two‐photon fluorescence, it is challenging to apply the various PSF‐engineering methods to improve the spatial resolution to be close to the diffraction limit. Using a synthetic PSF and application of an advanced maximum likelihood estimation (AdvMLE) deconvolution algorithm, we demonstrate restoration of the spatial resolution in SHG images to that closer to the theoretical diffraction limit. The AdvMLE algorithm adaptively and iteratively develops a PSF for the supplied image and succeeds in improving the signal to noise ratio (SNR) for images where the SHG signals are derived from various sources such as collagen in tendon and myosin in heart sarcomere. Approximately 3.5 times improvement in SNR is observed for tissue images at depths of up to ～480 nm, which helps in revealing the underlying helical structures in collagen fibres with an ～26% improvement in the amplitude contrast in a fibre pitch. Our approach could be adapted to noisy and low resolution modalities such as micro‐nano CT and MRI, impacting precision of diagnosis and treatment of human diseases.     

环栅图像的数字莫尔条纹扫描定中方法

提出了数字环栅莫尔条纹扫描方法.该方法不是用实物环光栅与无衍射光的光斑重叠产生环形莫尔条纹.而是先用CCD摄像机将光斑摄入计算机,再与一基本同心的数字环光栅重叠产生环形莫尔条纹.改变该数字光栅的相位,可实现莫尔条纹扫描,用多幅扫描图像可算出光斑图像整体中心.由于利用了整幅图像的数据,该法实现了含噪环栅状光斑图像的亚像素级灵敏度定中心.统计模拟实验证明,它具有良好的抗干扰能力.并介绍了该方法在空间直线度测量方面的应用实验.     

Quality improvement of environmental secondary electron detector signal using helium gas in variable pressure scanning electron microscopy

The quality of the image signal obtained from the environmental secondary electron detector (ESED) employed in a variable pressure (VP) SEM can be dramatically improved by using helium gas. The signal-to-noise ratio (SNR) increases gradually in the range of the pressures that can be used in our modified SEM. This method is especially useful in low-voltage VP SEM as well as in a variety of SEM operating conditions, because helium gas can more or less maintain the amount of unscattered primary electrons. In order to measure the SNR precisely, a digital scan generator system for obtaining two images with identical views is employed as a precondition.     

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.     

Noise Variance Estimation Using Image Noise Cross‐Correlation Model on SEM Images

A number of techniques have been proposed during the last three decades for noise variance and signal‐to‐noise ratio (SNR) estimation in digital images. While some methods have shown reliability and accuracy in SNR and noise variance estimations, other methods are dependent on the nature of the images and perform well on a limited number of image types. In this article, we prove the accuracy and the efficiency of the image noise cross‐correlation estimation model, vs. other existing estimators, when applied to different types of scanning electron microscope images. SCANNING 35: 205‐212, 2013. © 2012 Wiley Periodicals, Inc.     

Replicate-based noise corrected correlation for accurate measurements of colocalization

It is widely recognized that the accuracy of colocalization measurements is dependent upon the quality of the source images. We demonstrate that, as the image quality increases, the measured colocalization, using the Pearson and Spearman rank correlation coefficients, approaches the true colocalization asymptotically. This means that in practice it is difficult to obtain images of sufficient quality for accurate measurements. We introduce the replicate-based noise corrected correlation (RBNCC) which aligns the measured colocalization with the true colocalization: a noise measurement is made for each fluorophore from a pair of replicate images, the two noise measurements are combined to generate a correction factor which is applied to the measured colocalization between the two fluorophores. In consequence, accurate measurements can be obtained even with noisy images, making RBNCC especially attractive for live imaging. Even with images of apparently good quality we found an average discrepancy of about 20% between the measured and corrected colocalization. A case is made for using the Spearman rank coefficient instead of the Pearson coefficient to measure colocalization.