Denoising of Electron Tomographic Reconstructions Using Multiscale Transformations

The visualization of volume maps obtained by electron tomographic reconstruction is severely hampered by noise. As electron tomography is usually applied to individual, nonrepeatable structures, e.g., cell sections or cell organelles, the noise cannot be removed by averaging as is done implicitly in electron crystallography or explicitly in single particle analysis. In this paper, an approach for noise reduction is presented, based on a multiscale transformation, e.g., the wavelet transformation, in conjunction with a nonlinear filtration of the transform coefficients. After a brief introduction to the theoretical background, the effect of this type of noise reduction is demonstrated by test calculations as well as by applications to tomographic reconstructions of ice-embedded specimens. Regarding noise reduction and structure preservation, the method turns out to be superior to conventional filter techniques, such as the median filter or the Wiener filter. Results obtained with the use of different types of multiscale transformations are compared and the choice of suitable filter parameters is discussed.     

Analysis of Video-Based Microscopic Particle Trajectories Using Kalman Filtering

The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes.     

The discriminative bilateral filter: an enhanced denoising filter for electron microscopy data

Advances in three-dimensional (3D) electron microscopy (EM) and image processing are providing considerable improvements in the resolution of subcellular volumes, macromolecular assemblies and individual proteins. However, the recovery of high-frequency information from biological samples is hindered by specimen sensitivity to beam damage. Low dose electron cryo-microscopy conditions afford reduced beam damage but typically yield images with reduced contrast and low signal-to-noise ratios (SNRs). Here, we describe the properties of a new discriminative bilateral (DBL) filter that is based upon the bilateral filter implementation of Jiang et al. (Jiang, W., Baker, M.L., Wu, Q., Bajaj, C., Chiu, W., 2003. Applications of a bilateral denoising filter in biological electron microscopy. J. Struc. Biol. 128, 82-97.). In contrast to the latter, the DBL filter can distinguish between object edges and high-frequency noise pixels through the use of an additional photometric exclusion function. As a result, high frequency noise pixels are smoothed, yet object edge detail is preserved. In the present study, we show that the DBL filter effectively reduces noise in low SNR single particle data as well as cellular tomograms of stained plastic sections. The properties of the DBL filter are discussed in terms of its usefulness for single particle analysis and for pre-processing cellular tomograms ahead of image segmentation.     

Bilateral edge filter: photometrically weighted, discontinuity based edge detection

Edge-detection algorithms have the potential to play an increasingly important role both in single particle analysis (for the detection of randomly oriented particles), and in tomography (for the segmentation of 3D volumes). However, the majority of traditional linear filters are significantly affected by noise as well as artefacts, and offer limited selectivity. The Bilateral edge filter presented here is an adaptation of the Bilateral filter [Jiang, W., Baker, M.L., Wu, Q., Bajaj, C., Chiu, W., 2003. Applications of a bilateral denoising filter in biological electron microscopy. J. Struct. Biol. 144, 114-122] designed for enhanced edge detection. It uses photometric weighting to identify significant discontinuities (representing edges), minimizing artefacts and noise. Compared with common edge-detectors (LoG, Marr-Hildreth) the Bilateral edge filter yielded significantly better results. Indeed data was of a similar quality to that of the Canny edge-detector, which is considered as a leading standard in edge detection [Basu, M., 2002. Gaussian-based edge-detection methods-a survey. IEEE Trans. Syst. Man Cybern. C Appl. Rev. 32, 252-260]. Compared to the Canny edge-detector the Bilateral edge-detector has the advantages that it only requires the adjustment of a single parameter, is theoretically faster for reasonably sized images, and can be used in selective contrast enhancement of images. The simplicity and speed of the filter for single particle and tomographic analysis are discussed.     

Developing a denoising filter for electron microscopy and tomography data in the cloud

The low radiation conditions and the predominantly phase-object image formation of cryo-electron microscopy (cryo-EM) result in extremely high noise levels and low contrast in the recorded micrographs. The process of single particle or tomographic 3D reconstruction does not completely eliminate this noise and is even capable of introducing new sources of noise during alignment or when correcting for instrument parameters. The recently developed Digital Paths Supervised Variance (DPSV) denoising filter uses local variance information to control regional noise in a robust and adaptive manner. The performance of the DPSV filter was evaluated in this review qualitatively and quantitatively using simulated and experimental data from cryo-EM and tomography in two and three dimensions. We also assessed the benefit of filtering experimental reconstructions for visualization purposes and for enhancing the accuracy of feature detection. The DPSV filter eliminates high-frequency noise artifacts (density gaps), which would normally preclude the accurate segmentation of tomography reconstructions or the detection of alpha-helices in single-particle reconstructions. This collaborative software development project was carried out entirely by virtual interactions among the authors using publicly available development and file sharing tools.     

Application of template matching technique to particle detection in electron micrographs

Template matching together with the comprehensive theory of image formation in electron microscope provides an optimal (in Bayesian sense) tool for solving one of the outstanding problems in single particle analysis, i.e., automatic selection of particle views from noisy micrograph fields. The method is based on the assumption that the reference three-dimensional structure is known and that the relevant parameters of the model of the image formation process can be estimated. In the first stage of the procedure, a set of possible particle views is generated using the available reference structure. The template images are constructed as linear combinations of available particle views using a clustering technique. Next, the micrograph noise characteristic is established using an automated contrast transfer function (CTF) estimation procedure. Finally, the CTF parameters calculated are used to construct a matched filter and correlation functions corresponding to the available template images are calculated. In order to alleviate the problem of the biased caused by varying image formation conditions, a decision making strategy based on the predicted distribution of correlation coefficients is proposed. It is demonstrated that due to the inclusion of CTF considerations, the template matching method performed very well in a broad range of microscopy conditions.     

空间频率通道中噪声对体视匹配的影响

本工作希望了解噪声在各空间频率通道中对体视的影响.产生从5%至35%每隔5%的七个等级的随机点噪声图象,参照Wilson四通道模型的频率分别用两种不同滤波器对随机点立体图对(RDS)及噪声图象进行滤波,然后在各通道图对中加入不同通道噪声进行匹配观察.得到:1.高频通道的体视抗干扰能力高于低频通道.2.Gabor函数滤波后图对的体视抗干扰能力高于Butterworth滤波器滤波后的,但均低于未滤波的.3.当噪声大于15%时,低频噪声对低频图对及高频噪声对高、低频图对的体视匹配有抑制作用,而低频噪声对高频图对则影响很小.4.未滤波及各通道图对的最大噪声容限均不超过25%.     

A Local Agreement Filtering Algorithm for Transmission EM Reconstructions

We present LAFTER, an algorithm for de-noising single particle reconstructions from cryo-EM.Single particle analysis entails the reconstruction of high-resolution volumes from tens of thousands of particle images with low individual signal-to-noise. Imperfections in this process result in substantial variations in the local signal-to-noise ratio within the resulting reconstruction, complicating the interpretation of molecular structure. An effective local de-noising filter could therefore improve interpretability and maximise the amount of useful information obtained from cryo-EM maps.LAFTER is a local de-noising algorithm based on a pair of serial real-space filters. It compares independent half-set reconstructions to identify and retain shared features that have power greater than the noise. It is capable of recovering features across a wide range of signal-to-noise ratios, and we demonstrate recovery of the strongest features at Fourier shell correlation (FSC) values as low as 0.144 over a 256³-voxel cube. A fast and computationally efficient implementation of LAFTER is freely available.We also propose a new way to evaluate the effectiveness of real-space filters for noise suppression, based on the correspondence between two FSC curves: 1) the FSC between the filtered and unfiltered volumes, and 2) C_ref, the FSC between the unfiltered volume and a hypothetical noiseless volume, which can readily be estimated from the FSC between two half-set reconstructions.     

Optimal noise filtering in the chemotactic response of Escherichia coli

Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.     

Improved processing of the steady-state evoked potential

Two related procedures for estimating the parameters of steady-state evoked potentials (SSEPs) are introduced. The first procedure involves an initial stage of digital bandpass filtering followed by a Discrete Fourier Transform analysis. In the second method, a high resolution method based on parametric modelling is applied to the filtered data. The digital pre-filter consists of a non-phase shifting Chebychev bandpass filter. The parametric modelling method considers the evoked-response-plus-noise distribution to consist of a set of exponentially damped sinusoids. The frequency, amplitude, phase and damping factors of these components are estimated by calculating the mean of the forward and backward prediction filters and linear regression.We compared the signal-to-noise ratio (SNR) of the new procedures to the conventional Discrete Fourier Transform method for Monte Carlo simulations utilizing known sinusoids buried in white noise, known sinusoids buried in human EEG noise and for a sample of visual evoked potential data. Both of the new methods produce substantially more accurate and less variable estimates of test sinusoid amplitude. For VEP recording, the EEG background noise level is reduced by 5–6 dB over that obtained with the DFT. The new methods also provide approximately 5 dB better SNR than the DFT for detection of sinusoids based on the Rayleigh statistic. The parametric modelling approach is particularly suited for the analysis of very short data records including cycle-by-cycle analysis of the SSEP.     

Automatic particle pickup method using a neural network has high accuracy by applying an initial weight derived from eigenimages: a new reference free method for single-particle analysis

The single-particle analysis is a structure-determining method for electron microscope (EM) images which does not require crystal. In this method, the projections are picked up and averaged by the images of similar Euler angles to improve the signal to noise ratio, and then create a 3-D reconstruction. The selection of a large number of particles from the cryo-EM micrographs is a pre-requisite for obtaining a high resolution. To pickup a low-contrast cryo-EM protein image, we have recently found that a three-layer pyramidal-type neural network is successful in detecting such a faint image, which had been difficult to detect by other methods. The connection weights between the input and hidden layers, which work as a matching filter, have revealed that they reflect characters of the particle projections in the training data. The images stored in terms of the connection weights were complex, more similar to the eigenimages which are created by the principal component analysis of the learning images rather than to the averages of the particle projections. When we set the initial learning weights according to the eigenimages in advance, the learning period was able to be shortened to less than half the time of the NN whose initial weights had been set randomly. Further, the pickup accuracy increased from 90 to 98%, and a combination of the matching filters were found to work as an integrated matching filter there. The integrated filters were amazingly similar to averaged projections and can be used directly as references for further two-dimensional averaging. Therefore, this research also presents a brand-new reference-free method for single-particle analysis.     

一种滤除医学影像噪声的混合滤波算法

目的：医学影像在获取、存储、传输过程中会不同程度地受到噪声污染,这极大影像了其在临床诊疗中的应用。为了有效地滤除医学影像噪声,提出了一种混合滤波算法。方法：该算法首先将含有高斯和椒盐噪声的图像进行形态学开运算,然后对开运算后的图像进行二维小波分解,得到高频和低频小波分解系数。保留低频系数不变,将高频系数经过维纳滤波器进行滤波,最后进行小波系数重构。结果：采用该混合滤波算法、小波阚值去噪、中值滤波、维纳滤波分别对含有混合噪声的医学影像分别进行滤除噪声处理,该滤波算法去噪后影像的PSNR值明显高于其他三种方法。结论：该混合滤波算法是一种较为有效的医学影像噪声滤除方法。     

Real time microprocessor-based 50 Hz notch filter for ECG

High performance analogue notch filters are difficult to realize in practice. Their real time digital counterparts, when implemented on an inexpensive microprocessor with no additional hardware, also have limitations of their own. To overcome these limitations, we have developed a new type of 50 Hz notch filter with its poles close to the zeros of the transfer function 1 + Z^−N. This new type of digital notch filter can be used for suppression of 50 Hz noise in the ECG. The filter is simple to design and easy to implement on most 8-bit microprocessors. It has a high execution speed, low analogue to digital noise, low recursive noise and good frequency response with no overshoot or ringing. It is capable of suppressing 50 Hz noise by at least 40 db. Its finite bandwidth of 4 Hz causes about 2% attenuation on the QRS peak, which is acceptable for almost all practical applications. One possible drawback is that multiple notches occur at higher frequencies. However, this has hardly any effect on the ECG because of the limited notch bandwidth.     

Comparison of Deconvolution Filters for Photoacoustic Tomography

In this work, we compare the merits of three temporal data deconvolution methods for use in the filtered backprojection algorithm for photoacoustic tomography (PAT). We evaluate the standard Fourier division technique, the Wiener deconvolution filter, and a Tikhonov L-2 norm regularized matrix inversion method. Our experiments were carried out on subjects of various appearances, namely a pencil lead, two man-made phantoms, an in vivo subcutaneous mouse tumor model, and a perfused and excised mouse brain. All subjects were scanned using an imaging system with a rotatable hemispherical bowl, into which 128 ultrasound transducer elements were embedded in a spiral pattern. We characterized the frequency response of each deconvolution method, compared the final image quality achieved by each deconvolution technique, and evaluated each method’s robustness to noise. The frequency response was quantified by measuring the accuracy with which each filter recovered the ideal flat frequency spectrum of an experimentally measured impulse response. Image quality under the various scenarios was quantified by computing noise versus resolution curves for a point source phantom, as well as the full width at half maximum (FWHM) and contrast-to-noise ratio (CNR) of selected image features such as dots and linear structures in additional imaging subjects. It was found that the Tikhonov filter yielded the most accurate balance of lower and higher frequency content (as measured by comparing the spectra of deconvolved impulse response signals to the ideal flat frequency spectrum), achieved a competitive image resolution and contrast-to-noise ratio, and yielded the greatest robustness to noise. While the Wiener filter achieved a similar image resolution, it tended to underrepresent the lower frequency content of the deconvolved signals, and hence of the reconstructed images after backprojection. In addition, its robustness to noise was poorer than that of the Tikhonov filter. The performance of the Fourier filter was found to be the poorest of all three methods, based on the reconstructed images’ lowest resolution (blurriest appearance), generally lowest contrast-to-noise ratio, and lowest robustness to noise. Overall, the Tikhonov filter was deemed to produce the most desirable image reconstructions.     

Median‐modified Wiener filter provides efficient denoising,preserving spot edge and morphology in 2‐DE image processing

Denoising is a fundamental early stage in 2‐DE image analysis strongly influencing spot detection or pixel‐based methods. A novel nonlinear adaptive spatial filter (median‐modified Wiener filter, MMWF), is here compared with five well‐established denoising techniques (Median, Wiener, Gaussian, and Polynomial‐Savitzky–Golay filters; wavelet denoising) to suggest, by means of fuzzy sets evaluation, the best denoising approach to use in practice. Although median filter and wavelet achieved the best performance in spike and Gaussian denoising respectively, they are unsuitable for contemporary removal of different types of noise, because their best setting is noise‐dependent. Vice versa, MMWF that arrived second in each single denoising category, was evaluated as the best filter for global denoising, being its best setting invariant of the type of noise. In addition, median filter eroded the edge of isolated spots and filled the space between close‐set spots, whereas MMWF because of a novel filter effect (drop‐off‐effect) does not suffer from erosion problem, preserves the morphology of close‐set spots, and avoids spot and spike fuzzyfication, an aberration encountered for Wiener filter. In our tests, MMWF was assessed as the best choice when the goal is to minimize spot edge aberrations while removing spike and Gaussian noise.     

Effect of particle size distribution on filtration performance of cell culture medium

Cell culture media used in CHO-based biologic processes are typically sterile filtered to prevent microbial contamination prior to inoculation. In this study, the impact of common sterile filter throughput on a different, commercially available cell culture media was evaluated from the intermediate-adsorption fouling model of the filtration model. The key particle size range for optimum filter performance was discussed and identified by measuring the submicron order particle size distribution. It may be possible to predict the performance of filter capacity with size-exclusive separation by understanding the media particle counts and size distribution.     

Hybrid filtering to rescue stable oscillations from noise-induced chaos in continuous cultures of budding yeast

In large-scale fermentations with oscillating microbial cultures, noise is commonly present in the feed stream(s). As this can destabilize the oscillations and even generate chaotic behavior, noise filters are employed. Here three types of filters were compared by applying them to a noise-affected continuous culture of Saccharomyces cerevisiae with chaotic oscillations. The aim was to restore the original noise-free stable oscillations. An extended Kalman filter was found to be the least efficient, a neural filter was better and a combined hybrid filter was the best. In addition, better filtering of noise was achieved in the dilution rate than in the oxygen mass transfer coefficient. These results suggest the use of hybrid filters with the dilution rate as the manipulated variable for bioreactor control.     

Removal of ECG interference from surface respiratory electromyography

The signal to noise ratio (SNR) of surface respiratory electromyography signal is very low. Indeed EMG signal is contaminated by different types of noise especially the cardiac artefact ECG. This article explores the problem of removing ECG artefact from respiratory EMG signal. The new method uses an adaptive structure with an electrocardyographic ECG reference signal carried out by wavelet decomposition. The proposed algorithm requires only one channel to both estimating the adaptive filter input reference noise and the respiratory EMG signal. This new technique demonstrates how two steps will be combined: the first step decomposes the signal with forward discrete wavelet transform into sub-bands to get the wavelet coefficients. Then, an improved soft thresholding function was applied. And the ECG input reference signal is reconstructed with the transformed coefficients whereas, the second uses an adaptive filter especially the LMS one to remove the ECG signal. After trying statistical as well as mathematical analysis, the complete investigation ensures that all details and steps make proof that our rigorous method is appropriate. Compared to the results obtained using previous techniques, the results achieved using the new algorithm show a significant improvement in the efficiency of the ECG rejection.     

An adaptation of the Wiener filter suitable for analyzing images of isolated single particles

The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent (“spectral”) signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.     

Exposure to noise pollution across North American passerines supports the noise filter hypothesis

The noise filter hypothesis predicts that species using higher sound frequencies should be more tolerant of noise pollution, because anthropogenic noise is more intense at low frequencies. Recent work analysed continental‐scale data on anthropogenic noise across the USA and found that passerine species inhabiting more noise‐polluted areas do not have higher peak song frequency but have more complex songs. However, this metric of song complexity is of ambiguous interpretation, because it can indicate either diverse syllables or a larger frequency bandwidth. In the latter case, the finding would support the noise filter hypothesis, because larger frequency bandwidths mean that more sound energy spreads to frequencies that are less masked by anthropogenic noise. We reanalysed how passerine song predicts exposure to noise using a more thorough dataset of acoustic song measurements, and showed that it is large frequency bandwidths, rather than diverse syllables, that predict the exposure of species to noise pollution. Given that larger bandwidths often encompass higher maximum frequencies, which are less masked by anthropogenic noise, our result suggests that tolerance to noise pollution might depend mostly on having the high‐frequency parts of song little masked by noise, thus preventing acoustic communication from going entirely unnoticed at long distances.