Three-Dimensional Reconstruction from Reduced Sets of Very Noisy Images Acquired Following a Single-Axis Tilt Schema: Application of a New Three-Dimensional Reconstruction Algorithm and Objective Comparison with Weighted Backprojection

In this work we propose a reconstruction algorithm (ART with blobs) that has not been previously used in electron Tomography and we compare it with the standard method in the field (weighted back projection, WBP). We assume that only a limited set of very noisy images, collected around a single axis tilt, is available; which is a typical situation in Electron Tomography. In general, the reconstruction problem is underdetermined (due to the limited number of projections) and the data are inconsistent (due to the high level of noise). The evaluation of the results is performed in a rigorous way by a task-oriented approach which makes use of numerical observers. ART with blobs outperforms WBP for a number of key tasks. Results are presented both for simplified line integral data and for realistic simulations of macromolecular structures embedded in amorphous ice.     

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.     

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.     

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

Three-dimensional (3D) electron microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. The 3D reconstruction of a macromolecule using single-particle techniques involves thousands of 2D projections. One of the key parameters required to perform such a 3D reconstruction is the orientation of each projection image as well as its in-plane orientation. This information is unknown experimentally and must be determined using image-processing techniques. We propose the use of wavelets to match the experimental projections with those obtained from a reference 3D model. The wavelet decomposition of the projection images provides a framework for a multiscale matching algorithm in which speed and robustness to noise are gained. Furthermore, this multiresolution approach is combined with a novel orientation selection strategy. Results obtained from computer simulations as well as experimental data encourage the use of this approach.     

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.     

XMIPP: a new generation of an open-source image processing package for electron microscopy

X-windows based microscopy image processing package (Xmipp) is a specialized suit of image processing programs, primarily aimed at obtaining the 3D reconstruction of biological specimens from large sets of projection images acquired by transmission electron microscopy. This public-domain software package was introduced to the electron microscopy field eight years ago, and since then it has changed drastically. New methodologies for the analysis of single-particle projection images have been added to classification, contrast transfer function correction, angular assignment, 3D reconstruction, reconstruction of crystals, etc. In addition, the package has been extended with functionalities for 2D crystal and electron tomography data. Furthermore, its current implementation in C++, with a highly modular design of well-documented data structures and functions, offers a convenient environment for the development of novel algorithms. In this paper, we present a general overview of a new generation of Xmipp that has been re-engineered to maximize flexibility and modularity, potentially facilitating its integration in future standardization efforts in the field. Moreover, by focusing on those developments that distinguish Xmipp from other packages available, we illustrate its added value to the electron microscopy community.     

A Novel Iterative CT Reconstruction Approach Based on FBP Algorithm

The Filtered Back-Projection (FBP) algorithm and its modified versions are the most important techniques for CT (Computerized tomography) reconstruction, however, it may produce aliasing degradation in the reconstructed images due to projection discretization. The general iterative reconstruction (IR) algorithms suffer from their heavy calculation burden and other drawbacks. In this paper, an iterative FBP approach is proposed to reduce the aliasing degradation. In the approach, the image reconstructed by FBP algorithm is treated as the intermediate image and projected along the original projection directions to produce the reprojection data. The difference between the original and reprojection data is filtered by a special digital filter, and then is reconstructed by FBP to produce a correction term. The correction term is added to the intermediate image to update it. This procedure can be performed iteratively to improve the reconstruction performance gradually until certain stopping criterion is satisfied. Some simulations and tests on real data show the proposed approach is better than FBP algorithm or some IR algorithms in term of some general image criteria. The calculation burden is several times that of FBP, which is much less than that of general IR algorithms and acceptable in the most situations. Therefore, the proposed algorithm has the potential applications in practical CT systems.     

Detecting consistent common lines in cryo-EM by voting

The single-particle reconstruction problem of electron cryo-microscopy (cryo-EM) is to find the three-dimensional structure of a macromolecule given its two-dimensional noisy projection images at unknown random directions. Ab initio estimates of the 3D structure are often obtained by the “Angular Reconstitution” method, in which a coordinate system is established from three projections, and the orientation of the particle giving rise to each image is deduced from common lines among the images. However, a reliable detection of common lines is difficult due to the low signal-to-noise ratio of the images. In this paper we describe a global self-correcting voting procedure in which all projection images participate to decide the identity of the consistent common lines. The algorithm determines which common line pairs were detected correctly and which are spurious. We show that the voting procedure succeeds at relatively low detection rates and that its performance improves as the number of projection images increases. We demonstrate the algorithm for both simulative and experimental images of the 50S ribosomal subunit.     

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.     

Fluorescence lifetime optical projection tomography

We describe a quantitative fluorescence projection tomography technique which measures the 3‐D fluorescence lifetime distribution in optically cleared specimens up 1 cm in diameter. This is achieved by acquiring a series of wide‐field time‐gated images at different relative time delays with respect to a train of excitation pulses, at a number of projection angles. For each time delay, the 3‐D time‐gated intensity distribution is reconstructed using a filtered back projection algorithm and the fluorescence lifetime subsequently determined for each reconstructed horizontal plane by iterative fitting to a mono‐exponential decay. Due to its inherently ratiometric nature, fluorescence lifetime is robust against intensity based artefacts as well as producing a quantitative measure of the fluorescence signal. We present a 3‐D fluorescence lifetime reconstruction of a mouse embryo labelled with an alexa‐488 conjugated antibody targeted to the neurofilament, which clearly differentiates between the extrinsic label and the autofluorescence, particularly from the heart and dorsal aorta. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Image reconstruction of optical computed tomography by using the algebraic reconstruction technique for dose readouts of polymer gel dosimeters

Optical computed tomography (optical CT) has been proven to be a useful tool for dose readouts of polymer gel dosimeters. In this study, the algebraic reconstruction technique (ART) for image reconstruction of gel dosimeters was used to improve the image quality of optical CT. Cylindrical phantoms filled with N-isopropyl-acrylamide polymer gels were irradiated using a medical linear accelerator. A circular dose distribution and a hexagonal dose distribution were produced by applying the VMAT technique and the six-field dose delivery, respectively. The phantoms were scanned using optical CT, and the images were reconstructed using the filtered back-projection (FBP) algorithm and the ART. For the circular dose distribution, the ART successfully reduced the ring artifacts and noise in the reconstructed image. For the hexagonal dose distribution, the ART reduced the hot spots at the entrances of the beams and increased the dose uniformity in the central region. Within 50% isodose line, the gamma pass rates for the 2 mm/3% criteria for the ART and FBP were 99.2% and 88.1%, respectively. The ART could be used for the reconstruction of optical CT images to improve image quality and provide accurate dose conversion for polymer gel dosimeters.     

Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L(2,3) edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell's nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Reprint of "Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)" [J. Struct. Biol. 160 (2007) 35-48

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L_2,3 edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell’s nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Nonlinear Dual Reconstruction of SPECT Activity and Attenuation Images

In single photon emission computed tomography (SPECT), accurate attenuation maps are needed to perform essential attenuation compensation for high quality radioactivity estimation. Formulating the SPECT activity and attenuation reconstruction tasks as coupled signal estimation and system parameter identification problems, where the activity distribution and the attenuation parameter are treated as random variables with known prior statistics, we present a nonlinear dual reconstruction scheme based on the unscented Kalman filtering (UKF) principles. In this effort, the dynamic changes of the organ radioactivity distribution are described through state space evolution equations, while the photon-counting SPECT projection data are measured through the observation equations. Activity distribution is then estimated with sub-optimal fixed attenuation parameters, followed by attenuation map reconstruction given these activity estimates. Such coupled estimation processes are iteratively repeated as necessary until convergence. The results obtained from Monte Carlo simulated data, physical phantom, and real SPECT scans demonstrate the improved performance of the proposed method both from visual inspection of the images and a quantitative evaluation, compared to the widely used EM-ML algorithms. The dual estimation framework has the potential to be useful for estimating the attenuation map from emission data only and thus benefit the radioactivity reconstruction.     

Highly sensitive saturation labeling reveals changes in abundance of cell cycle‐associated proteins and redox enzyme variants during oocyte maturation in vitro

Oocyte maturation is a complex process and a critical issue in assisted reproduction techniques (ART) in humans and other mammals. We used a sensitive 2‐D DIGE saturation labeling approach including an internal pooled standard for quantitative proteome profiling of immature versus in vitro matured bovine oocytes in six independent samples. The study comprised 48 2D gel images representing 24 DIGE experiments. From 250 ng sample analyzed per gel, quantitative analysis revealed an average of 2244 spots in pH 4–7 images and 1291 spots in pH 6–9 images. Thirty‐eight spots with different intensities were detected in total. Spots of a preparative gel from 2200 oocytes were identified by nano‐LC‐MS/MS analysis. The ten spots which could be unambiguously identified include the Ca²⁺‐binding protein translationally controlled tumor protein, enzymes of the Krebs and pentose phosphate cycles, clusterin, 14‐3‐3 ?, elongation factor‐1 gamma, and redox enzymes such as polymorphic forms of GST Mu 5 and peroxiredoxin‐3. The cellular distribution of two proteins was determined by confocal laser scanning microscopy. The interesting protein candidates identified by this study may help to improve the in vitro maturation process in order to increase the rate of successful in vitro fertilization and other ART in cattle and other mammals.     

High-resolution,High-speed,Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Digital fringe projection (DFP) techniques provide dense 3D measurements of dynamically changing surfaces. Like the human eyes and brain, DFP uses triangulation between matching points in two views of the same scene at different angles to compute depth. However, unlike a stereo-based method, DFP uses a digital video projector to replace one of the cameras¹. The projector rapidly projects a known sinusoidal pattern onto the subject, and the surface of the subject distorts these patterns in the camera’s field of view. Three distorted patterns (fringe images) from the camera can be used to compute the depth using triangulation.Unlike other 3D measurement methods, DFP techniques lead to systems that tend to be faster, lower in equipment cost, more flexible, and easier to develop. DFP systems can also achieve the same measurement resolution as the camera. For this reason, DFP and other digital structured light techniques have recently been the focus of intense research (as summarized in^1-5). Taking advantage of DFP, the graphics processing unit, and optimized algorithms, we have developed a system capable of 30 Hz 3D video data acquisition, reconstruction, and display for over 300,000 measurement points per frame^6,7. Binary defocusing DFP methods can achieve even greater speeds⁸.Diverse applications can benefit from DFP techniques. Our collaborators have used our systems for facial function analysis⁹, facial animation¹⁰, cardiac mechanics studies¹¹, and fluid surface measurements, but many other potential applications exist. This video will teach the fundamentals of DFP techniques and illustrate the design and operation of a binary defocusing DFP system.     

Development of a novel algorithm for metal artifact reduction in digital tomosynthesis using projection-based dual-energy material decomposition for arthroplasty: A phantom study

In this study, a novel dual-energy (DE) material decomposition reconstruction algorithm (DEMDRA) was developed using projection data with the aim of reducing metal artifacts during digital tomosynthesis (DT) for implants. Using the three-material decomposition method and decomposition projection data specific for each material, a novel DEMDRA was implemented to reduce metal artifacts via weighted hybrid reconstructed images [maximum likelihood expectation maximization (MLEM) and shift-and-add (SAA)]. Pulsed X-ray exposures with rapid switching between low and high tube potential kVp were used for DE-DT imaging, and the images were compared using conventional filtered back projection (FBP), MLEM, the simultaneous algebraic reconstruction technique total variation (SART-TV), virtual monochromatic processing, and metal artifact reduction (MAR)-processing algorithms. The reductions in metal artifacts were compared using an artifact index (AI), Gumbel distribution of the largest variations, and the artifact spread functions (ASFs) for prosthesis phantom. The novel DEMDRA yielded an adequately effective overall performance in terms of the AI, and the resulting images yielded good results independently of the type of metal used in the prosthetic phantom, as well as good noise artifact removal, particularly at greater distances from metal objects. Furthermore, the DEMDRA represented the minimum in the model of largest variations. Regarding the ASF analysis, the novel DEMDRA yielded superior metal artifact reduction when compared with conventional reconstruction algorithms with and without MAR processing. Finally, the DEMDRA was particularly useful for reducing high-frequency artifacts.     

Digital holographic microtomography for high‐resolution refractive index mapping of live cells

Quantification of three‐dimensional (3D) refractive index (RI) with sub‐cellular resolution is achieved by digital holographic microtomography (DHμT) using quantitative phase images measured at multiple illumination angles. The DHμT system achieves sensitive and fast phase measurements based on iterative phase extraction algorithm and asynchronous phase shifting interferometry without any phase monitoring or active control mechanism. A reconstruction algorithm, optical diffraction tomography with projection on convex sets and total variation minimization, is implemented to substantially reduce the number of angular scattered fields needed for reconstruction without sacrificing the accuracy and quality of the reconstructed 3D RI distribution. Tomogram of a living CA9‐22 cell is presented to demonstrate the performance of the method. Further, a statistical analysis of the average RI of the nucleoli, the nucleus excluding the nucleoli and the cytoplasm of twenty CA9‐22 cells is performed. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)