Wavelet transform filtering and nonlinear anisotropic diffusion assessed for signal reconstruction performance on multidimensional biomedical data

Detection of quadratic phase coupling by cross-bicoherence and spectral Granger causality in bifrequencies interactions

Quadratic Phase Coupling (QPC) serves as an essential statistical instrument for evaluating nonlinear synchronization within multivariate time series data, especially in signal processing and neuroscience fields. This study explores the precision of QPC detection using numerical estimates derived from cross-bicoherence and bivariate Granger causality within a straightforward, yet noisy, instantaneous multiplier model. It further assesses the impact of accidental statistically significant bifrequency interactions, introducing new metrics such as the ratio of bispectral quadratic phase coupling and the ratio of bivariate Granger causality quadratic phase coupling. Ratios nearing 1 signify a high degree of accuracy in detecting QPC. The coupling strength between interacting channels is identified as a key element that introduces nonlinearities, influencing the signal-to-noise ratio in the output channel. The model is tested across 59 experimental conditions of simulated recordings, with each condition evaluated against six coupling strength values, covering a wide range of carrier frequencies to examine a broad spectrum of scenarios. The findings demonstrate that the bispectral method outperforms bivariate Granger causality, particularly in identifying specific QPC under conditions of very weak couplings and in the presence of noise. The detection of specific QPC is crucial for neuroscience applications aimed at better understanding the temporal and spatial coordination between different brain regions.

It's noisy out there! A review of denoising techniques in cryo-electron tomography

Cryo-electron tomography is the only technique that can provide sub-nanometer resolved images of cell regions or even whole cells, without the need of labeling or staining methods. Technological advances over the past decade in electron microscope stability, cameras, stage precision and software have resulted in faster acquisition speeds and considerably improved resolution. In pursuit of even better image resolution, researchers seek to reduce noise - a crucial factor affecting the reliability of the tomogram interpretation and ultimately limiting the achieved resolution. Sub-tomogram averaging is the method of choice for reducing noise in repetitive objects. However, when averaging is not applicable, a trade-off between reducing noise and conserving genuine image details must be achieved. Thus, denoising is an important process that improves the interpretability of the tomogram not only directly but also by facilitating other downstream tasks, such as segmentation and 3D visualization. Here, I review contemporary denoising techniques for cryo-electron tomography by taking into account noise-specific properties of both reconstruction and detector noise. The outcomes of different techniques are compared, in order to help researchers select the most appropriate for each dataset and to achieve better and more reliable interpretation of the tomograms.

Methods for segmentation and interpretation of electron tomographic reconstructions

Electron tomography has become a powerful tool for revealing the molecular architecture of biological cells and tissues. In principle, electron tomography can provide high-resolution mapping of entire proteomes. The achievable resolution (3-8 nm) is capable of bridging the gap between live-cell imaging and atomic resolution structures. However, the relevant information is not readily accessible from the data and needs to be identified, extracted, and processed before it can be used. Because electron tomography imaging and image acquisition technologies have enjoyed major advances in the last few years and continue to increase data throughput, the need for approaches that allow automatic and objective interpretation of electron tomograms becomes more and more urgent. This chapter provides an overview of the state of the art in this field and attempts to identify the major bottlenecks that prevent approaches for interpreting electron tomography data to develop their full potential.

Structure enhancement diffusion and contour extraction for electron tomography of mitochondria

The interpretation and measurement of the architectural organization of mitochondria depend heavily upon the availability of good software tools for filtering, segmenting, extracting, measuring, and classifying the features of interest. Images of mitochondria contain many flow-like patterns and they are usually corrupted by large amounts of noise. Thus, it is necessary to enhance them by denoising and closing interrupted structures. We introduce a new approach based on anisotropic nonlinear diffusion and bilateral filtering for electron tomography of mitochondria. It allows noise removal and structure closure at certain scales, while preserving both the orientation and magnitude of discontinuities without the need for threshold switches. This technique facilitates image enhancement for subsequent segmentation, contour extraction, and improved visualization of the complex and intricate mitochondrial morphology. We perform the extraction of the structure-defining contours by employing a variational level set formulation. The propagating front for this approach is an approximate signed distance function which does not require expensive re-initialization. The behavior of the combined approach is tested for visualizing the structure of a HeLa cell mitochondrion and the results we obtain are very promising.

Fast noise reduction in computed tomography for improved 3-D visualization

Computed tomography (CT) has a trend towards higher resolution and higher noise. This development has increased the interest in anisotropic smoothing techniques for CT, which aim to reduce noise while preserving structures of interest. However, existing smoothing techniques are slow, which makes clinical application difficult. Furthermore, the published methods have limitations with respect to preserving small details in CT data. This paper presents a widely applicable speed optimized framework for anisotropic smoothing techniques. A second contribution of this paper is an extension to an existing smoothing technique aimed at better preserving small structures of interest in CT data. Based on second-order image structure, the method first determines an importance map, which indicates potentially relevant structures that should be preserved. Subsequently an anisotropic diffusion process is started. The diffused data is used in most parts of the images, while structures with significant second-order information are preserved. The method is qualitatively evaluated against an anisotropic diffusion method without structure preservation in an observer study to assess the improvement of 3-D visualizations of CT series and quantitatively by determining the reduction of the difference between low and high dose CT scans of in vitro carotid plaques.

Evaluation of denoising algorithms for biological electron tomography

Tomograms of biological specimens derived using transmission electron microscopy can be intrinsically noisy due to the use of low electron doses, the presence of a "missing wedge" in most data collection schemes, and inaccuracies arising during 3D volume reconstruction. Before tomograms can be interpreted reliably, for example, by 3D segmentation, it is essential that the data be suitably denoised using procedures that can be individually optimized for specific data sets. Here, we implement a systematic procedure to compare various nonlinear denoising techniques on tomograms recorded at room temperature and at cryogenic temperatures, and establish quantitative criteria to select a denoising approach that is most relevant for a given tomogram. We demonstrate that using an appropriate denoising algorithm facilitates robust segmentation of tomograms of HIV-infected macrophages and Bdellovibrio bacteria obtained from specimens at room and cryogenic temperatures, respectively. We validate this strategy of automated segmentation of optimally denoised tomograms by comparing its performance with manual extraction of key features from the same tomograms.

Template matching as a tool for annotation of tomograms of stained biological structures

In recent years, electron tomography has improved our three-dimensional (3D) insight in the structural architecture of cells and organelles. For studies that involve the 3D imaging of stained sections, manual annotation of tomographic data has been an important method to help understand the overall 3D morphology of cellular compartments. Here, we postulate that template matching can provide a tool for more objective annotation and contouring of cellular structures. Also, this technique can extract information hitherto unharvested in tomographic studies. To evaluate the performance of template matching on tomograms of stained sections, we generated several templates representing a piece of microtubule or patches of membranes of different staining-thicknesses. These templates were matched to tomograms of stained electron microscopy sections. Both microtubules and ER-Golgi membranes could be detected using this method. By matching cuboids of different thicknesses, we were able to distinguish between coated and non-coated endosomal membrane-domains. Finally, heterogeneity in staining-thickness of endosomes could be observed. Template matching can be a useful addition to existing annotation-methods, and provide additional insights in cellular architecture.

Efficient automatic noise reduction of electron tomographic reconstructions based on iterative median filtering

A simple, fast and efficient noise-reduction protocol for three-dimensional electron tomographic reconstructions of biological material is presented. The approach is based on iterative application of median filtering and shows promise for automatic noise reduction as a pre-processor for automated data analysis tools which aim at segmentation, feature extraction and pattern recognition. The application of this algorithm produces encouraging results for a wide variety of experimental and synthetic electron tomographic reconstructions.

Model-based automated extraction of microtubules from electron tomography volume

We propose a model-based automated approach to extracting microtubules from noisy electron tomography volume. Our approach consists of volume enhancement, microtubule localization, and boundary segmentation to exploit the unique geometric and photometric properties of microtubules. The enhancement starts with an anisotropic invariant wavelet transform to enhance the microtubules globally, followed by a three-dimensional (3-D) tube-enhancing filter based on Weingarten matrix to further accentuate the tubular structures locally. The enhancement ends with a modified coherence-enhancing diffusion to complete the interruptions along the microtubules. The microtubules are then localized with a centerline extraction algorithm adapted for tubular objects. To perform segmentation, we novelly modify and extend active shape model method. We first use 3-D local surface enhancement to characterize the microtubule boundary and improve shape searching by relating the boundary strength with the weight matrix of the searching error. We then integrate the active shape model with Kalman filtering to utilize the longitudinal smoothness along the microtubules. The segmentation improved in this way is robust against missing boundaries and outliers that are often present in the tomography volume. Experimental results demonstrate that our automated method produces results close to those by manual process and uses only a fraction of the time of the latter.

Automated extraction of fine features of kinetochore microtubules and plus-ends from electron tomography volume

Kinetochore microtubules (KMTs) and the associated plus-ends have been areas of intense investigation in both cell biology and molecular medicine. Though electron tomography opens up new possibilities in understanding their function by imaging their high-resolution structures, the interpretation of the acquired data remains an obstacle because of the complex and cluttered cellular environment. As a result, practical segmentation of the electron tomography data has been dominated by manual operation, which is time consuming and subjective. In this paper, we propose a model-based automated approach to extracting KMTs and the associated plus-ends with a coarse-to-fine scale scheme consisting of volume preprocessing, microtubule segmentation and plus-end tracing. In volume preprocessing, we first apply an anisotropic invariant wavelet transform and a tube-enhancing filter to enhance the microtubules at coarse level for localization. This is followed with a surface-enhancing filter to accentuate the fine microtubule boundary features. The microtubule body is then segmented using a modified active shape model method. Starting from the segmented microtubule body, the plus-ends are extracted with a probabilistic tracing method improved with rectangular window based feature detection and the integration of multiple cues. Experimental results demonstrate that our automated method produces results comparable to manual segmentation but using only a fraction of the manual segmentation time.

Lessons from tomographic studies of the mammalian Golgi

Basic structure studies of the biosynthetic machinery of the cell by electron microscopy (EM) have underpinned much of our fundamental knowledge in the areas of molecular cell biology and membrane traffic. Driven by our collective desire to understand how changes in the complex and dynamic structure of this enigmatic organelle relate to its pivotal roles in the cell, the comparatively high-resolution glimpses of the Golgi and other compartments of the secretory pathway offered to us through EM have helped to inspire the development and application of some of our most informative, complimentary (molecular, biochemical and genetic) approaches. Even so, no one has yet even come close to relating the basic molecular mechanisms of transport, through and from the Golgi, to its ultrastructure, to everybody's satisfaction. Over the past decade, EM tomography has afforded new insights into structure-function relationships of the Golgi and provoked a re-evaluation of older paradigms. By providing a set of tools for structurally dissecting cells at high-resolution in three-dimensions (3D), EM tomography has emerged as a method for studying molecular cell biology in situ. As we move rapidly toward the establishment of molecular atlases of organelles through advances in proteomics and genomics, tomographic studies of the Golgi offer the tantalizing possibility that one day, we will be able to map the spatio-temporal coordinates of Golgi-related proteins and lipids accurately in the context of 4D cellular space.

Opacity transfer function optimization for volume-rendered computed tomography images of the prostate

RATIONALE AND OBJECTIVES

The selection of an opacity transfer function is essential for volume visualization. Computed tomography (CT) scans of the pelvis were used to determine an optimal opacity transfer function for use in radiotherapy.

MATERIALS AND METHODS

On sample datasets (a mathematical phantom and a patient pelvis CT scan), standard viewing orientations were selected to render the prostate. Opacity functions were selected via (1) trapezoidal manual selection, (2) trapezoidal semiautomatic selection, and (3) histogram volume-based selection. Using an established metric, the errors using each of these methods were computed.

RESULTS

Trapezoidal manual opacity function optimization resulted in visually acceptable images, but the errors were considerable (6.3-9.1 voxel units). These errors could be reduced with the use of trapezoidal semiautomatic selection (4.9-6.2 voxel units) or with histogram volume-based selection (4.8-7.9 voxel units). As each visualization algorithm focused on enhancing the boundary of the prostate using a different approach, the scene information was considerably different using the three techniques.

CONCLUSION

Improved volume visualization of soft tissue interfaces was achieved using automated optimal opacity function determination, compared with manual selection.

An improved algorithm for anisotropic nonlinear diffusion for denoising cryo-tomograms

Cryo-electron tomography is an imaging technique with an unique potential for visualizing large complex biological specimens. It ensures preservation of the biological material but the resulting cryotomograms are extremely noisy. Sophisticated denoising techniques are thus essential for allowing the visualization and interpretation of the information contained in the cryotomograms. Here a software tool based on anisotropic nonlinear diffusion is described for filtering cryotomograms. The approach reduces local noise and meanwhile enhances both curvilinear and planar structures. In the program a novel solution of the partial differential equation has been implemented, which allows a reliable estimation of derivatives and, furthermore, reduces computation time and memory requirements. Several criteria have been included to automatically select the optimal stopping time. The behaviour of the denoising approach is tested for visualizing filamentous structures in cryotomograms.

Computational exploration of structural information from cryo-electron tomograms

Cryo-electron tomography aims to act as an interface between in vivo cell imaging and techniques achieving atomic resolution. This attempt to bridge the resolution gap is facilitated by recent software and hardware advances. Information provided by atomically resolved macromolecules and molecular interaction data need to be put into a common framework in order to create a hybrid multidimensional cellular image. A major partner in this enterprise is the development of regularization and pattern recognition techniques, which try to identify macromolecular complexes as a function of their structural signature in cryo-electron tomograms of living cells.

Prospects of electron cryotomography to visualize macromolecular complexes inside cellular compartments: implications of crowding

Electron cryotomography has unique potential for three-dimensional visualization of macromolecular complexes at work in their natural environment. This approach is based on reconstructing three-dimensional volumes from tilt series of electron micrographs of cells preserved in their native states by vitrification. Resolutions of 5-8 nm have already been achieved and the prospects for further improvement are good. Since many intracellular activities are conducted by complexes in the megadalton range with dimensions of 20-50 nm, current resolutions should suffice to identify many of them in tomograms. However, residual noise and the dense packing of cellular constituents hamper interpretation. Recently, tomographic data have been collected on vitrified eukaryotic cells (Medalia et al., Science (2002) in press). Their cytoplasm was found to be markedly less crowded than in the prokaryotes previously studied, in accord with differences in crowding between prokaryotic and eukaryotic cells documented by other (indirect) biophysical methods. The implications of this observation are twofold. First, complexes should be more easily identifiable in tomograms of eukaryotic cytoplasm. This applies both to recognizing known complexes and characterizing novel complexes. An example of the latter-a 5-fold symmetric particle is-given. Second, electron cryotomography offers an incisive probe to examine crowding in different cellular compartments.

Identification of macromolecular complexes in cryoelectron tomograms of phantom cells

Electron tomograms of intact frozen-hydrated cells are essentially three-dimensional images of the entire proteome of the cell, and they depict the whole network of macromolecular interactions. However, this information is not easily accessible because of the poor signal-to-noise ratio of the tomograms and the crowded nature of the cytoplasm. Here, we describe a template matching algorithm that is capable of detecting and identifying macromolecules in tomographic volumes in a fully automated manner. The algorithm is based on nonlinear cross correlation and incorporates elements of multivariate statistical analysis. Phantom cells, i.e., lipid vesicles filled with macromolecules, provide a realistic experimental scenario for an assessment of the fidelity of this approach. At the current resolution of approximately 4 nm, macromolecules in the size range of 0.5-1 MDa can be identified with good fidelity.

Three-dimensional reconstructions of extracellular matrix polymers using automated electron tomography

The extracellular matrix is an intricate network of macromolecules which provides support for cells and a framework for tissues. The detailed structure and organisation of most matrix polymers is poorly understood. These polymers have a complex ultrastructure, and it has proved a major challenge both to define their structural organisation and to relate this to their biological function. However, new approaches using automated electron tomography are beginning to reveal important insights into the molecular assembly and structural organisation of two of the most abundant polymer systems in the extracellular matrix. We have generated three-dimensional reconstructions of collagen fibrils from bovine cornea and fibrillin microfibrils from ciliary zonules. Analysis of these data has provided new insights into the organisation and function of these large macromolecular assemblies.

Segmentation of two- and three-dimensional data from electron microscopy using eigenvector analysis

An automatic image segmentation method is used to improve processing and visualization of data obtained by electron microscopy. Exploiting affinity criteria between pixels, e.g., proximity and gray level similarity, in conjunction with an eigenvector analysis, the image is subdivided into areas which correspond to objects or meaningful regions. Extending a proposal by Shi and Malik (1997, Proceedings of the IEEE conference on Computer Vision and Pattern Recognition, pp. 731-737) the approach was adapted to the field of electron microscopy, especially to three-dimensional application as needed by electron tomography. Theory, implementation, parameter setting, and results obtained with a variety of data are presented and discussed. The method turns out to be a powerful tool for visualization with the potential for further improvement by developing and tuning new affinity.

Noise reduction in electron tomographic reconstructions using nonlinear anisotropic diffusion

Electron tomography is a powerful technique capable of giving unique insights into the three-dimensional structural organization of pleomorphic biological objects. However, visualization and interpretation of the resulting volumetric data are hampered by an extremely low signal-to-noise ratio, especially when ice-embedded biological specimens are investigated. Usually, isosurface representation or volume rendering of such data is hindered without any further signal enhancement. We propose a novel technique for noise reduction based on nonlinear anisotropic diffusion. The approach combines efficient noise reduction with excellent signal preservation and is clearly superior to conventional methods (e.g., low-pass and median filtering) and invariant wavelet transform filtering. The gain in the signal-to-noise ratio is verified and demonstrated by means of Fourier shell correlation. Improved visualization performance after processing the 3D images is demonstrated with two examples, tomographic reconstructions of chromatin and of a mitochondrion. Parameter settings and discretization stencils are presented in detail.