Estimating contrast transfer function and associated parameters by constrained non-linear optimization

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.     

A fast algorithm for computing and correcting the CTF for tilted, thick specimens in TEM

Today, the resolution in phase-contrast cryo-electron tomography is for a significant part limited by the contrast transfer function (CTF) of the microscope. The CTF is a function of defocus and thus varies spatially as a result of the tilting of the specimen and the finite specimen thickness. Models that include spatial dependencies have not been adopted in daily practice because of their high computational complexity. Here we present an algorithm which reduces the processing time for computing the ‘tilted’ CTF by more than a factor 100. Our implementation of the full 3D CTF has a processing time on the order of a Radon transform of a full tilt-series. We derive and validate an expression for the damping envelope function describing the loss of resolution due to specimen thickness. Using simulations we quantify the effects of specimen thickness on the accuracy of various forward models. We study the influence of spatially varying CTF correction and subsequent tomographic reconstruction by simulation and present a new approach for space-variant phase-flipping. We show that our CTF correction strategies are successful in increasing the resolution after tomographic reconstruction.     

CTF determination and correction in electron cryotomography

Electron cryotomography (cryoET) has the potential to elucidate the structure of complex biological specimens at molecular resolution but technical and computational improvements are still needed. This work addresses the determination and correction of the contrast transfer function (CTF) of the electron microscope in cryoET. Our approach to CTF detection and defocus determination depends on strip-based periodogram averaging, extended throughout the tilt series to overcome the low contrast conditions found in cryoET. A method for CTF correction that deals with the defocus gradient in images of tilted specimens is also proposed. These approaches to CTF determination and correction have been applied here to several examples of cryoET of pleomorphic specimens and of single particles. CTF correction is essential for improving the resolution, particularly in those studies that combine cryoET with single particle averaging techniques.     

基于图像反卷积的平板探测器信号串扰校正

平板探测器是锥束CT的关键组成部件，像元间的信号串扰是造成平板探测器投影图像空间分辨率低于极限值的主要因素，校正平板探测器信号串扰对提高锥束CT检测精度具有重要意义。本文基于点扩散函数矩阵反卷积投影图像去串扰校正思路，研究了点扩散函数矩阵的准确性对投影图像串扰校正的影响、点扩散函数和线扩散函数的关系及其与X射线成像的相似性，提出一种结合刀口法测量线扩散函数与平行束CT扫描重建的平板探测器点扩散函数矩阵测算方法。DR/CT扫描成像实验中，应用本文方法校正信号串扰后，DR成像空间分辨率由约10 lp/mm提升至优于25 lp/mm,高能CT成像空间分辨率由不到4 lp/mm提升至优于5 lp/mm,实验证明，应用本文方法能有效校正平板探测器信号串扰，提升锥束CT图像的空间分辨率和对比度。     

Restoration of weak phase-contrast images recorded with a high degree of defocus: the "twin image" problem associated with CTF correction

Relatively large values of objective-lens defocus must normally be used to produce detectable levels of image contrast for unstained biological specimens, which are generally weak phase objects. As a result, a subsequent restoration operation must be used to correct for oscillations in the contrast transfer function (CTF) at higher resolution. Currently used methods of CTF correction assume the ideal case in which Friedel mates in the scattered wave have contributed pairs of Fourier components that overlap with one another in the image plane. This "ideal" situation may be only poorly satisfied, or not satisfied at all, as the particle size gets smaller, the defocus value gets larger, and the resolution gets higher. We have therefore investigated whether currently used methods of CTF correction are also effective in restoring the single-sideband image information that becomes displaced (delocalized) by half (or more) the diameter of a particle of finite size. Computer simulations are used to show that restoration either by "phase flipping" or by multiplying by the CTF recovers only about half of the delocalized information. The other half of the delocalized information goes into a doubly defocused "twin" image of the type produced during optical reconstruction of an in-line hologram. Restoration with a Wiener filter is effective in recovering the delocalized information only when the signal-to-noise ratio (S/N) is orders of magnitude higher than that which exists in low-dose images of biological specimens, in which case the Wiener filter approaches division by the CTF (i.e. the formal inverse). For realistic values of the S/N, however, the "twin image" problem seen with a Wiener filter is very similar to that seen when either phase flipping or multiplying by the CTF is used for restoration. The results of these simulations suggest that CTF correction is a poor alternative to using a Zernike-type phase plate when imaging biological specimens, in which case the images can be recorded in a close-to-focus condition, and delocalization of high-resolution information is thus minimized.     

基于半盲解卷积复原的高分辨率视网膜成像系统

为获得高分辨率视网膜图像,建立了基于自适应光学的视网膜成像系统,并以成像时获得的残余像差作为图像复原的估计参数,通过半盲解卷积进行图像复原以获得高质量图像.通过Hartmann-Shark波前传感器和微机械薄膜变形镜组成的自适应光学系统对活体人眼像差进行测量与校正,并在成像时记录系统残余像差,据此重建光学传递函数作为图像复原模型初始参数估计,对获得的视网膜图像进行条件约束迭代半盲解卷积复原,消除像差对成像质量的影响,从而得到高分辨率视网膜图像.实验表明,系统获得的图像经该方法处理后可获得较满意视网膜图像,图像质量提高近一倍,成像成功率由38％提高至78％,成像时间缩短为原来的1/7.该方法在满足使用要求的前提下有效缩短了校正时间,提高了成像的成功率,提升了系统的适用范围.     

Improvement in the resolution of three-dimensional data sets collected using optical serial sectioning

In this paper an approach for improving the quality of 3-D microscopic images obtained through optical serial sectioning is described and implemented. A serially sectioned image is composed of a sequence of 2-D images obtained by incrementing the focusing plane of the microscope through the specimen of interest; ideally, the image obtained at each focusing plane should be in focus, and should contain information lying only within that plane. In practice, however, the images obtained contain redundant information from neighbouring focusing planes and are blurred by a three-dimensional low-pass distortion. These degradations are a consequence of the limited aperture of any optical system; using principles of geometric optics and allowing for the passage of light through the specimen, we are able to demonstrate that the microscope distortion can be described as a linear system, if the absorption of the specimen is assumed to be linear and non-diffractive. The transfer function of the microscope is found to zero a biconic region of 3-D spatial frequencies orientated along the optical axis; a closed-form expression is derived for the low-pass transfer function of the microscope outside the region of missing frequencies. The planar resolution of the serial sections can be greatly improved by convolving the image obtained with the inverse of the low-pass distortion function, although the missing cone of frequencies is not recoverable. The reconstruction technique is demonstrated using both simulated images, to demonstrate more clearly the effects of the distortion and the accuracy of the subsequent reconstruction, and actual experiments with a pollen grain and a stained preparation of human cerebellum tissue.     

Ewald sphere correction for single-particle electron microscopy

Most algorithms for three-dimensional (3D) reconstruction from electron micrographs assume that images correspond to projections of the 3D structure. This approximation limits the attainable resolution of the reconstruction when the dimensions of the structure exceed the depth of field of the microscope. We have developed two methods to calculate a reconstruction that corrects for the depth of field. Either method applied to synthetic data representing a large virus yields a higher resolution reconstruction than a method lacking this correction.     

High resolution at low beam energy in the SEM: resolution measurement of a monochromated SEM

The resolution of secondary electron low beam energy imaging of a scanning electron microscope equipped with a monochromator is quantitatively measured using the contrast transfer function (CTF) method. High-resolution images, with sub-nm resolutions, were produced using low beam energies. The use of a monochromator is shown to quantitatively improve the resolution of the SEM at low beam energies by limiting the chromatic aberration contribution to the electron probe size as demonstrated with calculations and images of suitable samples. Secondary electron image resolution at low beam energies is ultimately limited by noise in the images as shown by the CTFs.     

Three-dimensional reconstruction of single particles negatively stained or in vitreous ice.

The random-conical reconstruction method has been highly successful in three-dimensional imaging of macromolecules under low-dose conditions. This article summarizes the different steps of this technique as applied to molecules prepared with negative staining or vitreous ice, and sketches out the current directions of development. We anticipate that by using new instrumental developments, transfer function correction and computational refinement techniques, a resolution in the range of 7-10 A could ultimately be achieved.     

Intensity correction of fluorescent confocal laser scanning microscope images by mean-weight filtering

This paper addresses the problem of intensity correction of fluorescent confocal laser scanning microscope images. Confocal laser scanning microscope images are frequently used in medicine for obtaining 3D information about specimen structures by imaging a set of 2D cross sections and performing 3D volume reconstruction afterwards. However, 2D images acquired from fluorescent confocal laser scanning microscope images demonstrate significant intensity heterogeneity, for example, due to photo‐bleaching and fluorescent attenuation in depth. We developed an intensity heterogeneity correction technique that (a) adjusts the intensity heterogeneity of 2D images, (b) preserves fine structural details and (c) enhances image contrast, by performing spatially adaptive mean‐weight filtering. Our solution is obtained by formulating an optimization problem, followed by filter design and automated selection of filtering parameters. The proposed filtering method is experimentally compared with several existing techniques by using four quality metrics: contrast, intensity heterogeneity (entropy) in a low frequency domain, intensity distortion in a high frequency domain and saturation. Based on our experiments and the four quality metrics, the developed mean‐weight filtering outperforms other intensity correction methods by at least a factor of 1.5 when applied to fluorescent confocal laser scanning microscope images.     

Evaluating image reconstruction methods in improving effective parameters on image quality in IRI-microPET

We intend to improve the image reconstruction for RMS contrast, spatial resolution and signal-to-noise (SNR) parameters for the animal positron emission tomograph IRI—microPET (IRI-Islamic Republic of Iran), designed and built at the Gamma scan laboratory of nuclear science and technology research institute. Acquired images quality from this system depends on different algorithms for image reconstruction in addition to its design and construction. In this paper, system features and tomography method are considered, firstly. Then, image reconstruction algorithms (MLEM, SART, and FBP) were performed on sinogarm. Acquired images quality from these reconstructed algorithms was compared with RMS contrast, spatial resolution and SNR characteristics. Also, reconstructed time and speed of process for three algorithms was considered. According to results, obtained RMS contrast, spatial resolution and signal to noise ratio (SNR) from reconstructed images with MLEM algorithm shows superiority of MLEM algorithm against the SART and FBP algorithms but its computation time is high. Thus, SART algorithm can be suitable replacement for MLEM algorithm.     

Artefacts in restored images due to intensity loss in three-dimensional fluorescence microscopy

Computational algorithms for three-dimensional deconvolution have proven successful in reducing blurring and improving the resolution of fluorescence microscopic images. However, discrepancies between the imaging conditions and the models on which such deconvolution algorithms are based may lead to artefacts and/or distortions in the images restored by application of the algorithms. In this paper, artefacts associated with a decrease of fluorescence intensity with time or slice in three-dimensional wide-field images are demonstrated using simulated images. Loss of intensity, whether due to photobleaching or other factors, leads to artefacts in the form of bands or stripes in the restored images. An empirical method for correcting the intensity losses in wide-field images has been implemented and used to correct biological images. This method is based on fitting a decreasing function to the slice intensity curve computed by summing all pixel values in each slice. The fitted curve is then used for the calculation of correction factors for each slice.     

Correction of image drift and distortion in a scanning electron microscopy

Continuous research on small‐scale mechanical structures and systems has attracted strong demand for ultrafine deformation and strain measurements. Conventional optical microscope cannot meet such requirements owing to its lower spatial resolution. Therefore, high‐resolution scanning electron microscope has become the preferred system for high spatial resolution imaging and measurements. However, scanning electron microscope usually is contaminated by distortion and drift aberrations which cause serious errors to precise imaging and measurements of tiny structures. This paper develops a new method to correct drift and distortion aberrations of scanning electron microscope images, and evaluates the effect of correction by comparing corrected images with scanning electron microscope image of a standard sample. The drift correction is based on the interpolation scheme, where a series of images are captured at one location of the sample and perform image correlation between the first image and the consequent images to interpolate the drift–time relationship of scanning electron microscope images. The distortion correction employs the axial symmetry model of charged particle imaging theory to two images sharing with the same location of one object under different imaging fields of view. The difference apart from rigid displacement between the mentioned two images will give distortion parameters. Three‐order precision is considered in the model and experiment shows that one pixel maximum correction is obtained for the employed high‐resolution electron microscopic system.     

Effect of the phase shift due to dynamical scattering on the contrast of crystal structure images

The contrast of through-focus images of a niobium tungsten bronze, 2Nb₂O₅·7WO₃, taken by a 1 MV high resolution electron microscope, is discussed in terms of the transfer function, in which, in addition to the conventional phase aberration, the phase shift due to the dynamical scattering is taken into account. It is found that the phase shift may be advantagous in the formation of structure images, as long as the crystal very thin, i.e., a few nanometers in thickness. It is also made clear why the best defocus for optimum structure images differs from the Scherzer defocus, depending on the crystal thickness. An almost exact contrast reversal occurs at overfocus only in the images of extremely thin crystals, because the positive range of the transfer function is made narrower due to the above phase shift. The discussion is supported by the computer simulation of the image contrast.     

Digitally collected cryo-electron micrographs for single particle reconstruction

Several advantages and disadvantages have been cited for image collection with a slow-scan CCD camera. Here we explore its use for cryo-EM single particle reconstruction and present two practical examples. The icosahedral adenovirus (Ad) type 2 ( approximately 150 MDa) was reconstructed from 396 particle images. The Fourier shell correlation (FSC) 0.5 threshold and the Fourier shell phase residual (FSPR) 45 degrees criterion yielded 17 AA resolution for the ordered viral capsid. Visual comparison with the filtered Ad2 crystallographic hexon confirmed a resolution range of 15-17 A. The asymmetric DNA-PKcs protein (470 kDa) was reconstructed from 9,473 particle images, using a previously published reconstruction based on class-sum images as an orientational search model [Chiu et al. (1998) J. Mol. Biol. 284:1075-1081]. FSC and FSPR methods yielded 17 A resolution for the new DNA-PKcs reconstruction, indicating a small but noticeable improvement over that of the class-sum based reconstruction. Despite the lack of symmetry for DNA-PKcs and its lower image contrast compared to Ad2 (0.8% vs. 2.5%), the same resolution was obtained for both particles by averaging significantly more DNA-PKcs images. Use of the CCD camera enables the microscopist to adjust the electron beam strength interactively and thereby maximize the image contrast for beam sensitive samples. On-line Fourier transformation also allows routine monitoring of drift and astigmatism during image collection, resulting in a high percentage of micrographs suitable for image processing. In conclusion, our results show that digital image collection with the YAG-scintillator slow-scan CCD camera is a viable approach for 3D reconstruction of both symmetric and asymmetric particles.     

Super-Resolution Reconstruction via Multi-frame Defocused Images Based on PSF Estimation and Compressive Sensing

Image super-resolution reconstruction is an effective method to improve image resolution, but most reconstruction methods rely on the clear low resolution images ignoring the blurred images which are also effective observations of the scene. Aiming at the problem, a super-resolution reconstruction (SRR) method via multi-frame defocused images is proposed. Firstly, according to the image degraded model, we establish the cost function of the point spread function (PSF) and utilize the particle swarm optimization algorithm to estimate it. Then, based on the multi-frame defocused images and PSFs, a joint reconstruction model is established to realize SRR by compressive sensing (CS) theory. In the CS framework, only the interpolated version of the low-resolution image is used for training purpose and the K-Singular Value Decomposition method is used for dictionary training. In addition, to solve the edge effect problem, an internal blur matrix is constructed according to the image blurring process, and a weight coefficient is introduced in the patch splicing process. Experiments show that the proposed algorithm can accurately estimate the defocused image PSF and achieve a good reconstruction effect.     

基于滤光轮双相机系统的高光谱分辨率成像

滤光轮光谱成像系统在光谱成像领域应用广泛,空间分辨率高,但是光谱分辨率较低。针对这一问题,提出了基于滤光轮双相机系统的高光谱分辨率成像,设计了一种基于插分补偿的多光谱计算重构方法,实现系统的高光谱分辨率、高空间分辨率成像。首先利用滤光轮双相机成像系统采集多光谱图像以及RGB图像,然后从多光谱图像获取离散的光谱响应曲线,最后根据RGB三通道数据与光谱高维数据之间的映射关系以及能量守恒定理,进行光谱响应曲线的插分补偿并实现高光谱分辨率成像。实验结果表明,本文方法能够在保持空间分辨率的情况下,高效地实现光谱分辨率为5 nm甚至更高光谱分辨率的成像,重建结果与真实值的均方根误差为0.017 1,具有较好的准确性和鲁棒性。     

Out‐of‐focus background subtraction for fast structured illumination super‐resolution microscopy of optically thick samples

We propose a structured illumination microscopy method to combine super resolution and optical sectioning in three‐dimensional (3D) samples that allows the use of two‐dimensional (2D) data processing. Indeed, obtaining super‐resolution images of thick samples is a difficult task if low spatial frequencies are present in the in‐focus section of the sample, as these frequencies have to be distinguished from the out‐of‐focus background. A rigorous treatment would require a 3D reconstruction of the whole sample using a 3D point spread function and a 3D stack of structured illumination data. The number of raw images required, 15 per optical section in this case, limits the rate at which high‐resolution images can be obtained. We show that by a succession of two different treatments of structured illumination data we can estimate the contrast of the illumination pattern and remove the out‐of‐focus content from the raw images. After this cleaning step, we can obtain super‐resolution images of optical sections in thick samples using a two‐beam harmonic illumination pattern and a limited number of raw images. This two‐step processing makes it possible to obtain super resolved optical sections in thick samples as fast as if the sample was two‐dimensional.