Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction

2018 ◽  
Vol 25 (1) ◽  
pp. 248-256
Author(s):  
Camila de Lima ◽  
Elias Salomão Helou
Keyword(s):  
Projection Operator ◽  
Tomographic Reconstruction ◽  
Computational Cost ◽  
Iterative Algorithms ◽  
Incremental Algorithm ◽  
Back Projection ◽  
Tomographic Images ◽  
Incremental Methods ◽  
Order Of Magnitude ◽  
Synchrotron Light

Iterative methods for tomographic image reconstruction have the computational cost of each iteration dominated by the computation of the (back)projection operator, which take roughlyO(N3) floating point operations (flops) forN×Npixels images. Furthermore, classical iterative algorithms may take too many iterations in order to achieve acceptable images, thereby making the use of these techniques unpractical for high-resolution images. Techniques have been developed in the literature in order to reduce the computational cost of the (back)projection operator toO(N2logN) flops. Also, incremental algorithms have been devised that reduce by an order of magnitude the number of iterations required to achieve acceptable images. The present paper introduces an incremental algorithm with a cost ofO(N2logN) flops per iteration and applies it to the reconstruction of very large tomographic images obtained from synchrotron light illuminated data.

THE BACK-PROJECTION METHOD FOR CONSTRUCTING 3D NON-TENSOR PRODUCT MOTHER WAVELETS AND THE APPLICATION IN IMAGE EDGE DETECTION

2012 ◽  
Vol 10 (03) ◽  
pp. 1250026 ◽  
Author(s):  
LI ZENG ◽  
JIQIANG GUO ◽  
CHENCHENG HUANG
Keyword(s):  
Tensor Product ◽  
Computational Cost ◽  
Three Dimension ◽  
Back Projection ◽  
Mother Wavelet ◽  
3D Images ◽  
Mexican Hat Wavelet ◽  
Mexican Hat ◽  
Directional Wavelets ◽  
Mother Wavelets

In this paper, a non-tensor product method for constructing three-dimension (3D) mother wavelets by back-projecting two dimension (2D) mother wavelets is presented. We have proved that if a 2D mother wavelet satisfies certain conditions, the back-projection of the 2D mother wavelet is a 3D mother wavelet. And the construction instances of 3D Mexican-hat wavelet and 3D Meyer wavelet are given. These examples imply that we can get some new 3D mother wavelets from known 1D or 2D mother wavelets by using back-projecting method. This method inaugurates a new approach for constructing non-tensor product 3D wavelet. In addition, the non-tensor product 3D Mexican-hat wavelet is used for detecting the edge of two 3D images in our experimental section. Compared with the Mallat's maximum wavelet module approach which uses 3D directional wavelets, experimental results show it can obtain better outcome especial for the edge which the orientation is not along the coordinate axis. Furthermore, the edge is more fine, and the computational cost is much smaller. The non-tensor product mother wavelets constructed by using the method of this paper also can be widely used for compression, filtering and denoising of 3D images.

scholarly journals Beam image-shift accelerated data acquisition for near-atomic resolution single-particle cryo-electron tomography

2020 ◽  
Author(s):  
Jonathan Bouvette ◽  
Hsuan-Fu Liu ◽  
Xiaochen Du ◽  
Ye Zhou ◽  
Andrew P. Sikkema ◽  
...  
Keyword(s):  
Data Collection ◽  
Electron Tomography ◽  
Tomographic Reconstruction ◽  
Beam Image ◽  
Geometrical Constraints ◽  
Order Of Magnitude ◽  
Biological Environment ◽  
Map Resolution ◽  
Resolution Single

ABSTRACTTomographic reconstruction of cryopreserved specimens imaged in an electron microscope followed by extraction and averaging of sub-volumes has been successfully used to derive atomic models of macromolecules in their biological environment. Eliminating biochemical isolation steps required by other techniques, this method opens up the cell to in-situ structural studies. However, the need to compensate for errors in targeting introduced during mechanical navigation of the specimen significantly slows down tomographic data collection thus limiting its practical value. Here, we introduce protocols for tilt-series acquisition and processing that accelerate data collection speed by an order of magnitude and improve map resolution by ~1-3 Å compared to existing approaches. We achieve this by using beam-image shift to multiply the number of areas imaged at each stage position, by integrating geometrical constraints during imaging to achieve high precision targeting, and by performing per-tilt astigmatic CTF estimation and data-driven exposure weighting to improve final map resolution. We validated our beam image-shift electron cryo-tomography (BISECT) approach by determining the structure of a low molecular weight target (~300kDa) at 3.6 Å resolution where density for individual side chains is clearly resolved.

scholarly journals A Survey of the Use of Iterative Reconstruction Algorithms in Electron Microscopy

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
C. O. S. Sorzano ◽  
J. Vargas ◽  
J. Otón ◽  
J. M. de la Rosa-Trevín ◽  
J. L. Vilas ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Electron Tomography ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
Iterative Algorithms ◽  
Projection Methods ◽  
Particle Analysis ◽  
Reconstruction Algorithms ◽  
Large Families ◽  
Key Steps

One of the key steps in Electron Microscopy is the tomographic reconstruction of a three-dimensional (3D) map of the specimen being studied from a set of two-dimensional (2D) projections acquired at the microscope. This tomographic reconstruction may be performed with different reconstruction algorithms that can be grouped into several large families: direct Fourier inversion methods, back-projection methods, Radon methods, or iterative algorithms. In this review, we focus on the latter family of algorithms, explaining the mathematical rationale behind the different algorithms in this family as they have been introduced in the field of Electron Microscopy. We cover their use in Single Particle Analysis (SPA) as well as in Electron Tomography (ET).

A 3D Complexity-Adaptive Approach to Exploit Sparsity in Elastic Wave Propagation

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Claudia Haindl ◽  
Kuangdai Leng ◽  
Tarje Nissen-Meyer
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Parameter Tuning ◽  
Performance Limits ◽  
Absorbing Boundary ◽  
Adaptive Approach ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Complex Settings ◽  
Close Fit

We present an adaptive approach to seismic modeling by which the computational cost of a 3D simulation can be reduced while retaining resolution and accuracy. This Azimuthal Complexity Adaptation (ACA) approach relies upon the inherent smoothness of wavefields around the azimuth of a source-centered cylindrical coordinate system. Azimuthal oversampling is thereby detected and eliminated. The ACA method has recently been introduced as part of AxiSEM3D, an open-source solver for global seismology. We employ a generalization of this solver which can handle local-scale Cartesian models, and which features a combination of an absorbing boundary condition and a sponge boundary with automated parameter tuning. The ACA method is benchmarked against an established 3D method using a model featuring bathymetry and a salt body. We obtain a close fit where the models are implemented equally in both solvers and an expectedly poor fit otherwise, with the ACA method running an order of magnitude faster than the classic 3D method. Further, we present maps of maximum azimuthal wavenumbers that are created to facilitate azimuthal complexity adaptation. We show how these maps can be interpreted in terms of the 3D complexity of the wavefield and in terms of seismic resolution. The expected performance limits of the ACA method for complex 3D structures are tested on the SEG/EAGE salt model. In this case, ACA still reduces the overall degrees of freedom by 92% compared to a complexity-blind AxiSEM3D simulation. In comparison with the reference 3D method, we again find a close fit and a speed-up of a factor 7. We explore how the performance of ACA is affected by model smoothness by subjecting the SEG/EAGE salt model to Gaussian smoothing. This results in a doubling of the speed-up. ACA thus represents a convergent, versatile and efficient method for a variety of complex settings and scales.

scholarly journals Accelerating numerical wave propagation using wavefield adapted meshes. Part I: forward and adjoint modelling

2020 ◽  
Vol 221 (3) ◽  
pp. 1580-1590 ◽  
Author(s):  
M van Driel ◽  
C Boehm ◽  
L Krischer ◽  
M Afanasiev
Keyword(s):  
Wave Propagation ◽  
Adaptive Mesh Refinement ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Model Space ◽  
Adaptive Mesh ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Adjoint Modelling ◽  
The Waves

SUMMARY An order of magnitude speed-up in finite-element modelling of wave propagation can be achieved by adapting the mesh to the anticipated space-dependent complexity and smoothness of the waves. This can be achieved by designing the mesh not only to respect the local wavelengths, but also the propagation direction of the waves depending on the source location, hence by anisotropic adaptive mesh refinement. Discrete gradients with respect to material properties as needed in full waveform inversion can still be computed exactly, but at greatly reduced computational cost. In order to do this, we explicitly distinguish the discretization of the model space from the discretization of the wavefield and derive the necessary expressions to map the discrete gradient into the model space. While the idea is applicable to any wave propagation problem that retains predictable smoothness in the solution, we highlight the idea of this approach with instructive 2-D examples of forward as well as inverse elastic wave propagation. Furthermore, we apply the method to 3-D global seismic wave simulations and demonstrate how meshes can be constructed that take advantage of high-order mappings from the reference coordinates of the finite elements to physical coordinates. Error level and speed-ups are estimated based on convergence tests with 1-D and 3-D models.

A Hybrid Approach for Automatic Aorta Segmentation in Abdominal 3D CT Scan Images

2021 ◽  
Vol 11 (3) ◽  
pp. 712-719
Author(s):  
Iftikhar Ahmad ◽  
Sami ur Rehman ◽  
Imran Ullah Khan ◽  
Arfa Ali ◽  
Hussain Rahman ◽  
...  
Keyword(s):  
Medical Imaging ◽  
Ct Scan ◽  
Hybrid Approach ◽  
Computational Cost ◽  
Iterative Algorithms ◽  
Fast Algorithms ◽  
Human Anatomy ◽  
3D Ct Scan ◽  
Segmentation Accuracy ◽  
Segmentation Algorithms

Due to rapid advancement in medical imaging, human anatomy is now observable in finer details bringing new dimensions to diagnosis and treatment. One such area which benefitted from advancement in medical imaging is aorta segmentation. Aorta segmentation is achieved by using anatomical features (shape and position of aorta) using specialized segmentation algorithms. These segmentation algorithms are broadly classified into two categories. The first type comprises of fast algorithms which exploits spatial and intensity properties of images. The second type are iterative algorithms which use optimization of a cost function to track aorta boundaries. Fast algorithms offer lower computation cost, whereas iterative algorithms offer better segmentation accuracy. Therefore, there is a tradeoff between segmentation accuracy and computational cost. In this work, a hybrid approach for aorta segmentation in 3D Computed Tomography (CT) scan images is proposed. The proposed approach produces high segmentation accuracy of intensity based (fast) approaches at reduced computational cost. The proposed technique is evaluated using real world 3D abdominal CT scan images. The proposed approach can either be used as a fast-standalone segmentation procedure, or as a pre-segmentation procedure for iterative and more accurate approaches.

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