The effect of overabundant projection directions on 3D reconstruction algorithms

The experimental process of collecting images from macromolecules in an electron microscope is such that it does not allow for prior specification of the angular distribution of the projection images. As a consequence, an uneven distribution of projection directions may occur. Concerns have been raised recently about the behavior of 3D reconstruction algorithms for the case of unevenly distributed projections. It has been illustrated on experimental data that in the case of a heavily uneven distribution of projection directions some algorithms tend to elongate the reconstructed volumes along the overloaded direction so much as to make a quantitative biological analysis impossible. In answer to these concerns we have developed a strategy for quantitative comparison and optimization of 3D reconstruction algorithms. We apply this strategy to quantitatively analyze algebraic reconstruction techniques (ART) with blobs, simultaneous iterative reconstruction techniques (SIRT) with voxels, and weighted backprojection (WBP). We show that the elongation artifacts that had been previously reported can be strongly reduced. With our specific choices for the free parameters of the three algorithms, WBP reconstructions tend to be inferior to those obtained with either SIRT or ART and the results obtained with ART are comparable to those with SIRT, but at a very small fraction of the computational cost of SIRT.     

Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography

Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3-5nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimental demonstration of equally-sloped tomography (EST) to alleviate these problems. As a proof of principle, we applied EST to reconstructing frozen-hydrated keyhole limpet hemocyanin molecules from a tilt-series taken with constant slope increments. In comparison with weighted back-projection (WBP), the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), EST reconstructions exhibited higher contrast, less peripheral noise, more easily detectable molecular boundaries and reduced missing wedge effects. More importantly, EST reconstructions including only two-thirds the original images appeared to have the same resolution as full WBP reconstructions, suggesting that EST can either reduce the dose required to reach a given resolution or allow higher resolutions to be achieved with a given dose. EST was also applied to reconstructing a frozen-hydrated bacterial cell from a tilt-series taken with constant angular increments. The results confirmed similar benefits when standard tilts are utilized.     

An Effective CUDA Parallelization of Projection in Iterative Tomography Reconstruction

Projection and back-projection are the most computationally intensive parts in Computed Tomography (CT) reconstruction, and are essential to acceleration of CT reconstruction algorithms. Compared to back-projection, parallelization efficiency in projection is highly limited by racing condition and thread unsynchronization. In this paper, a strategy of Fixed Sampling Number Projection (FSNP) is proposed to ensure the operation synchronization in the ray-driven projection with Graphical Processing Unit (GPU). Texture fetching is also used utilized to further accelerate the interpolations in both projection and back-projection. We validate the performance of this FSNP approach using both simulated and real cone-beam CT data. Experimental results show that compare to the conventional approach, the proposed FSNP method together with texture fetching is 10~16 times faster than the conventional approach based on global memory, and thus leads to more efficient iterative algorithm in CT reconstruction.     

染色体三维结构重建方法研究

染色体三维结构重构问题是近年生物领域中基因组学的热点研究问题,是以二维交互频率数据为基础来预测其三维空间结构。最新相关实验表明染色质的三维空间结构对于基因表达、调控等方面都具有重要意义。而Hi-c数据能利用染色质交互信息形成二维接触矩阵重构出染色体三维结构。本综述以染色体三维结构重建方法为研究对象,通过对染色体三维结构重建方法进行比较分析,综述了目前基于Hi-c数据在染色体三维结构重建中的经典方法,系统介绍了染色体三维结构重建技术的发展脉络,以促进染色体三维结构重建的进一步研究。     

ART: mathematics and applications. A report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques

Some properties of the algebraic reconstruction techniques (ART) for reconstructing objects from their projections (e.g. electron micrographs) are discussed. Some generalizations of previously published ART algorithms are given. In particular, ART is extended to handle weighted projection data. An early conjecture about ART is proved for one of the algorithms: it converges to the most uniform solution of the constraint equations provided by the projection data. Other convergence properties of the ART algorithms are discussed and proved. Some new ART algorithms are described. These are believed to converge to optimal reconstructions consistent with the projection data. The importance of choosing the correct ray widths in case of real projection data is demonstrated, and a method for calculating correct ray widths is given. A method is proposed for estimating the optimal number of iterations in a reconstruction. The performance of ART on real data is demonstrated both in the absence of and in the presence of noise.     

Fast and accurate three-dimensional reconstruction from projections with random orientations via radon transforms

A new algorithm for three-dimensional reconstruction from randomly oriented projections has been developed. The algorithm recovers the 3D Radon transform from the 2D Radon transforms (sinograms) of the projections. The structure in direct space is obtained by an inversion of the 3D Radon transform. The mathematical properties of the Radon transform are exploited to design a special filter that can be used to correct inconsistencies in a data set and to fill the gaps in the Radon transform that originate from missing projections. Several versions of the algorithm have been implemented, with and without a filter and with different interpolation methods for merging the sinograms into the 3D Radon transform. The algorithms have been tested on analytical phantoms and experimental data and have been compared with a weighted back projection algorithm (WBP). A quantitative analysis of phantoms reconstructed from noise-free and noise-corrupted projections shows that the new algorithms are more accurate than WBP when the number of projections is small. Experimental structures obtained by the new methods are strictly comparable to those obtained by WBP. Moreover, the algorithm is more than 10 times faster than WPB when applied to a data set of 1000-5000 projections. Copyright 1999 Academic Press.     

Fast tomographic reconstruction on multicore computers

SUMMARY: Tomo3D implements a multithreaded vectorized approach to tomographic reconstruction that takes full advantage of the computer power in modern multicore computers. Full resolution tomograms are generated at high speed on standard computers with no special system requirements. Tomo3D has the most common reconstruction methods implemented, namely weighted Back-projection (WBP) and simultaneous iterative reconstruction technique (SIRT). It proves to be competitive with current graphic processor unit solutions in terms of processing time, in the order of a few seconds with WBP or minutes with SIRT. The program is compatible with standard packages, which easily allows integration in the electron tomography workflow.     

A Novel Weighted Total Difference Based Image Reconstruction Algorithm for Few-View Computed Tomography

In practical applications of computed tomography (CT) imaging, due to the risk of high radiation dose imposed on the patients, it is desired that high quality CT images can be accurately reconstructed from limited projection data. While with limited projections, the images reconstructed often suffer severe artifacts and the edges of the objects are blurred. In recent years, the compressed sensing based reconstruction algorithm has attracted major attention for CT reconstruction from a limited number of projections. In this paper, to eliminate the streak artifacts and preserve the edge structure information of the object, we present a novel iterative reconstruction algorithm based on weighted total difference (WTD) minimization, and demonstrate the superior performance of this algorithm. The WTD measure enforces both the sparsity and the directional continuity in the gradient domain, while the conventional total difference (TD) measure simply enforces the gradient sparsity horizontally and vertically. To solve our WTD-based few-view CT reconstruction model, we use the soft-threshold filtering approach. Numerical experiments are performed to validate the efficiency and the feasibility of our algorithm. For a typical slice of FORBILD head phantom, using 40 projections in the experiments, our algorithm outperforms the TD-based algorithm with more than 60% gains in terms of the root-mean-square error (RMSE), normalized root mean square distance (NRMSD) and normalized mean absolute distance (NMAD) measures and with more than 10% gains in terms of the peak signal-to-noise ratio (PSNR) measure. While for the experiments of noisy projections, our algorithm outperforms the TD-based algorithm with more than 15% gains in terms of the RMSE, NRMSD and NMAD measures and with more than 4% gains in terms of the PSNR measure. The experimental results indicate that our algorithm achieves better performance in terms of suppressing streak artifacts and preserving the edge structure information of the object.     

N4WBP5, a potential target for ubiquitination by the Nedd4 family of proteins, is a novel Golgi-associated protein.

Nedd4 belongs to a family of ubiquitin-protein ligases that is characterized by 2--4 WW domains, a carboxyl-terminal Hect (homologous to E6-AP Carboxyl terminus)domain and in most cases an amino-terminal C2 domain. We had previously identified a series of proteins that associates with the WW domains of Nedd4. In this paper, we demonstrate that one of the Nedd4-binding proteins, N4WBP5, belongs to a small group of evolutionarily conserved proteins with three transmembrane domains. N4WBP5 binds Nedd4 WW domains via the two PPXY motifs present in the amino terminus of the protein. In addition to Nedd4, N4WBP5 can interact with the WW domains of a number of Nedd4 family members and is ubiquitinated. Endogenous N4WBP5 localizes to the Golgi complex. Ectopic expression of the protein disrupts the structure of the Golgi, suggesting that N4WBP5 forms part of a family of integral Golgi membrane proteins. Based on previous observations in yeast, we propose that N4WBP5 may act as an adaptor for Nedd4-like proteins and their putative targets to control ubiquitin-dependent protein sorting and trafficking.     

Maximum-Entropy Three-Dimensional Reconstruction with Deconvolution of the Contrast Transfer Function: A Test Application with Adenovirus

We have developed an objective, quantitative, and general algorithm to improve the fidelity of three-dimensional reconstructions made from electron micrographs while at the same time filtering much of the noise present in the recorded data. The new technique is called constrained maximum entropy tomography (COMET). The essence of the method is that it will produce the most featureless reconstruction that fits the projection data within their observational accuracy. In particular, the COMET procedure will minimise the detrimental effects of errors in the measured data and deconvolute the effects of the contrast transfer function. An objective test has been performed using COMET on a conventional image reconstruction obtained from cryo-electron micrographs of adenovirus. The density for hexon, the major coat protein of the virus, which is known to high resolution from X-ray crystallography, provided a known high-resolution control. The COMET reconstruction is in considerably better agreement with the crystallographic electron density than the original reconstruction, throughout the entire resolution range.     

Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging

In dynamic Positron Emission Tomography (PET), an estimate of the radio activity concentration is obtained from a series of frames of sinogram data taken at ranging in duration from 10 seconds to minutes under some criteria. So far, all the well-known reconstruction algorithms require known data statistical properties. It limits the speed of data acquisition, besides, it is unable to afford the separated information about the structure and the variation of shape and rate of metabolism which play a major role in improving the visualization of contrast for some requirement of the diagnosing in application. This paper presents a novel low rank-based activity map reconstruction scheme from emission sinograms of dynamic PET, termed as SLCR representing Sparse/Low Rank Constrained Reconstruction for Dynamic PET Imaging. In this method, the stationary background is formulated as a low rank component while variations between successive frames are abstracted to the sparse. The resulting nuclear norm and l ₁ norm related minimization problem can also be efficiently solved by many recently developed numerical methods. In this paper, the linearized alternating direction method is applied. The effectiveness of the proposed scheme is illustrated on three data sets.     

microRNA-485-5p inhibits the progression of hepatocellular carcinoma through blocking the WBP2/Wnt signaling pathway

microRNA-485-5p (miR-485-5p) has been shown to act as a tumor-suppressor gene in some cancers, such as ovarian epithelial tumors and oral tongue squamous cell carcinoma. However, with regard to the anti-tumor role of miR-485-5p in hepatocellular carcinoma (HCC), evidence is unexpectedly limited. In the present study, we investigated the expression and the role of miR-485-5p in the progression of HCC. Microarray analysis revealed that miR-485-5p was downregulated and WBP2 was upregulated in HCC, which was consistent with RT-qPCR and immunohistochemistry assays in the HCC tissues we collected. A negative correlation between the expression of miR-485-5p and WBP2 was also found in HCC tissues. It was predicted and confirmed that miR-485-5p could bind to WW domain binding protein 2 (WBP2) through in silico analysis of genetic sequences and an in vitro dual-luciferase reporter gene assay. Next, gain- or loss-of-function studies were applied in the HCC cell line (Huh7) to examine the effects of miR-485-5p and WBP2 on HCC cell behavior. The effects of miR-485-5p and WBP2 on the Wnt/β-catenin signaling pathway were determined by TOP/FOP flash luciferase assays. miR-485-5p was shown to downregulate WBP2 and block the Wnt/β-catenin signaling pathway. As expected, elevated miR-485-5p levels and inhibition of WBP2 protein expression exerted inhibitory effects on HCC cell proliferation, migration and invasion and, induced apoptosis. In vivo experiments were finally conducted, which confirmed that upregulation of miR-485-5p or depletion of WBP2 attenuated tumor growth. Collectively, our results suggest miR-485-5p can downregulate WBP2 to inhibit the development of HCC by the blockade of the Wnt/β-catenin signaling, providing a novel molecular target for HCC treatment.     

Three-Dimensional Reconstruction of Three-Way FRET Microscopy Improves Imaging of Multiple Protein-Protein Interactions

Fluorescence resonance energy transfer (FRET) microscopy is a powerful tool for imaging the interactions between fluorescently tagged proteins in two-dimensions. For FRET microscopy to reach its full potential, it must be able to image more than one pair of interacting molecules and image degradation from out-of-focus light must be reduced. Here we extend our previous work on the application of maximum likelihood methods to the 3-dimensional reconstruction of 3-way FRET interactions within cells. We validated the new method (3D-3Way FRET) by simulation and fluorescent protein test constructs expressed in cells. In addition, we improved the computational methods to create a 2-log reduction in computation time over our previous method (3DFSR). We applied 3D-3Way FRET to image the 3D subcellular distributions of HIV Gag assembly. Gag fused to three different FPs (CFP, YFP, and RFP), assembled into viral-like particles and created punctate FRET signals that become visible on the cell surface when 3D-3Way FRET was applied to the data. Control experiments in which YFP-Gag, RFP-Gag and free CFP were expressed, demonstrated localized FRET between YFP and RFP at sites of viral assembly that were not associated with CFP. 3D-3Way FRET provides the first approach for quantifying multiple FRET interactions while improving the 3D resolution of FRET microscopy data without introducing bias into the reconstructed estimates. This method should allow improvement of widefield, confocal and superresolution FRET microscopy data.     

A Dictionary Learning Approach with Overlap for the Low Dose Computed Tomography Reconstruction and Its Vectorial Application to Differential Phase Tomography

X-ray based Phase-Contrast Imaging (PCI) techniques have been demonstrated to enhance the visualization of soft tissues in comparison to conventional imaging methods. Nevertheless the delivered dose as reported in the literature of biomedical PCI applications often equals or exceeds the limits prescribed in clinical diagnostics. The optimization of new computed tomography strategies which include the development and implementation of advanced image reconstruction procedures is thus a key aspect. In this scenario, we implemented a dictionary learning method with a new form of convex functional. This functional contains in addition to the usual sparsity inducing and fidelity terms, a new term which forces similarity between overlapping patches in the superimposed regions. The functional depends on two free regularization parameters: a coefficient multiplying the sparsity-inducing norm of the patch basis functions coefficients, and a coefficient multiplying the norm of the differences between patches in the overlapping regions. The solution is found by applying the iterative proximal gradient descent method with FISTA acceleration. The gradient is computed by calculating projection of the solution and its error backprojection at each iterative step. We study the quality of the solution, as a function of the regularization parameters and noise, on synthetic data for which the solution is a-priori known. We apply the method on experimental data in the case of Differential Phase Tomography. For this case we use an original approach which consists in using vectorial patches, each patch having two components: one per each gradient component. The resulting algorithm, implemented in the European Synchrotron Radiation Facility tomography reconstruction code PyHST, has proven to be efficient and well-adapted to strongly reduce the required dose and the number of projections in medical tomography.     

High-performance electron tomography of complex biological specimens

We have evaluated reconstruction methods using smooth basis functions in the electron tomography of complex biological specimens. In particular, we have investigated series expansion methods, with special emphasis on parallel computation. Among the methods investigated, the component averaging techniques have proven to be most efficient and have generally shown fast convergence rates. The use of smooth basis functions provides the reconstruction algorithms with an implicit regularization mechanism, very appropriate for noisy conditions. Furthermore, we have applied high-performance computing (HPC) techniques to address the computational requirements demanded by the reconstruction of large volumes. One of the standard techniques in parallel computing, domain decomposition, has yielded an effective computational algorithm which hides the latencies due to interprocessor communication. We present comparisons with weighted back-projection (WBP), one of the standard reconstruction methods in the areas of computational demand and reconstruction quality under noisy conditions. These techniques yield better results, according to objective measures of quality, than the weighted backprojection techniques after a very few iterations. As a consequence, the combination of efficient iterative algorithms and HPC techniques has proven to be well suited to the reconstruction of large biological specimens in electron tomography, yielding solutions in reasonable computation times.     

Reconstruction of pedigrees in clonal plant populations

We present a Bayesian method for the reconstruction of pedigrees in clonal populations using co-dominant genomic markers such as microsatellites and single nucleotide polymorphisms (SNPs). The accuracy of the algorithm is demonstrated for simulated data. We show that the joint estimation of parameters of interest such as the rate of self-fertilization is possible with high accuracy even with marker panels of moderate power. Classical methods can only assign a very limited number of statistically significant parentages in this case and would therefore fail. Statistical confidence is estimated by Markov Chain Monte Carlo (MCMC) sampling. The method is implemented in a fast and easy to use open source software that scales to large datasets with many thousand individuals.