scholarly journals X-rays Image reconstruction using Proximal Algorithm and adapted TV Regularization

2021 ◽  
Vol 348 ◽  
pp. 01011
Author(s):  
Aicha Allag ◽  
Redouane Drai ◽  
Tarek Boutkedjirt ◽  
Abdessalam Benammar ◽  
Wahiba Djerir
Keyword(s):  
Structural Information ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
Tv Regularization ◽  
Object Based ◽  
Suggested Technique ◽  
Reconstruction Image ◽  
Ill Posed

Computed tomography (CT) aims to reconstruct an internal distribution of an object based on projection measurements. In the case of a limited number of projections, the reconstruction problem becomes significantly ill-posed. Practically, reconstruction algorithms play a crucial role in overcoming this problem. In the case of missing or incomplete data, and in order to improve the quality of the reconstruction image, the choice of a sparse regularisation by adding l1 norm is needed. The reconstruction problem is then based on using proximal operators. We are interested in the Douglas-Rachford method and employ total variation (TV) regularization. An efficient technique based on these concepts is proposed in this study. The primary goal is to achieve high-quality reconstructed images in terms of PSNR parameter and relative error. The numerical simulation results demonstrate that the suggested technique minimizes noise and artifacts while preserving structural information. The results are encouraging and indicate the effectiveness of the proposed strategy.

scholarly journals A FIRST ORDER PREDICATE LOGIC FORMULATION OF THE 3D RECONSTRUCTION PROBLEM AND ITS SOLUTION SPACE

2005 ◽  
Vol 19 (01) ◽  
pp. 45-62 ◽  
Author(s):  
MARTIN ROBINSON ◽  
KURT KUBIK ◽  
BRIAN LOVELL
Keyword(s):  
3D Reconstruction ◽  
Predicate Logic ◽  
Solution Space ◽  
Color Variation ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
First Order ◽  
Ill Posed ◽  
3D Scene ◽  
Logic Formulation

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 × 5 voxel space gives 10 to 107 solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

A non-smooth and non-convex regularization method for limited-angle CT image reconstruction

2018 ◽  
Vol 26 (6) ◽  
pp. 799-820 ◽  
Author(s):  
Lingli Zhang ◽  
Li Zeng ◽  
Chengxiang Wang ◽  
Yumeng Guo
Keyword(s):  
Regularization Method ◽  
State Of The Art ◽  
Projection Data ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
Practical Applications ◽  
Splitting Technique ◽  
Ill Posed ◽  
Convex Regularization ◽  
Limited Angle

Abstract Restricted by the practical applications and radiation exposure of computed tomography (CT), the obtained projection data is usually incomplete, which may lead to a limited-angle reconstruction problem. Whereas reconstructing an object from limited-angle projection views is a challenging and ill-posed inverse problem. Fortunately, the regularization methods offer an effective way to deal with that. Recently, several researchers are absorbed in {\ell_{1}} regularization to address such problem, but it has some problems for suppressing the limited-angle slope artifacts around edges due to incomplete projection data. In this paper, in order to surmount the ill-posedness, a non-smooth and non-convex method that is based on {\ell_{0}} and {\ell_{1}} regularization is presented to better deal with the limited-angle problem. Firstly, the splitting technique is utilized to deal with the presented approach called LWPC-ST-IHT. Afterwards, some propositions and convergence analysis of the presented approach are established. Numerical implementations show that our approach is more capable of suppressing the slope artifacts compared with the classical and state of the art iterative reconstruction algorithms.

Structural studies of small amorphous volumes by electron diffraction

1990 ◽  
Vol 48 (4) ◽  
pp. 122-123
Author(s):  
Pierre Moine
Keyword(s):  
Electron Diffraction ◽  
Born Approximation ◽  
Structural Information ◽  
Fundamental Relation ◽  
X Rays ◽  
Structural Studies ◽  
Diffraction Experiment ◽  
Transmission Electron ◽  
Amorphous Structures ◽  
Diffraction Patterns

Qualitatively, amorphous structures can be easily revealed and differentiated from crystalline phases by their Transmission Electron Microscopy (TEM) images and their diffraction patterns (fig.1 and 2) but, for quantitative structural information, electron diffraction pattern intensity analyses are necessary. The parameters describing the structure of an amorphous specimen have been introduced in the context of scattering experiments which have been, so far, the most used techniques to obtain structural information in the form of statistical averages. When only small amorphous volumes (< 1/μm in size or thickness) are available, the much higher scattering of electrons (compared to neutrons or x rays) makes, despite its drawbacks, electron diffraction extremely valuable and often the only feasible technique.In a diffraction experiment, the intensity IN (Q) of a radiation, elastically scattered by N atoms of a sample, is measured and related to the atomic structure, using the fundamental relation (Born approximation) : IN(Q) = |FT[U(r)]|.

Convergence and stability analysis of the half thresholding based few-view CT reconstruction

2020 ◽  
Vol 28 (6) ◽  
pp. 829-847
Author(s):  
Hua Huang ◽  
Chengwu Lu ◽  
Lingli Zhang ◽  
Weiwei Wang
Keyword(s):  
Noise Suppression ◽  
Reconstructed Image ◽  
Reference Image ◽  
Projection Data ◽  
Ct Reconstruction ◽  
Reconstruction Algorithms ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Stability ◽  
Well Posed

AbstractThe projection data obtained using the computed tomography (CT) technique are often incomplete and inconsistent owing to the radiation exposure and practical environment of the CT process, which may lead to a few-view reconstruction problem. Reconstructing an object from few projection views is often an ill-posed inverse problem. To solve such problems, regularization is an effective technique, in which the ill-posed problem is approximated considering a family of neighboring well-posed problems. In this study, we considered the {\ell_{1/2}} regularization to solve such ill-posed problems. Subsequently, the half thresholding algorithm was employed to solve the {\ell_{1/2}} regularization-based problem. The convergence analysis of the proposed method was performed, and the error bound between the reference image and reconstructed image was clarified. Finally, the stability of the proposed method was analyzed. The result of numerical experiments demonstrated that the proposed method can outperform the classical reconstruction algorithms in terms of noise suppression and preserving the details of the reconstructed image.

scholarly journals Measurement of synchrotron-radiation-excited Kossel patterns

2016 ◽  
Vol 23 (1) ◽  
pp. 214-218 ◽  
Author(s):  
G. Bortel ◽  
G. Faigel ◽  
M. Tegze ◽  
A. Chumakov
Keyword(s):  
High Resolution ◽  
Dynamic Range ◽  
Structural Information ◽  
Photon Counting ◽  
Spot Size ◽  
Low Noise ◽  
X Rays ◽  
Technical Problems ◽  
Pixel Detectors ◽  
Exciting Beam

Kossel line patterns contain information on the crystalline structure, such as the magnitude and the phase of Bragg reflections. For technical reasons, most of these patterns are obtained using electron beam excitation, which leads to surface sensitivity that limits the spatial extent of the structural information. To obtain the atomic structure in bulk volumes, X-rays should be used as the excitation radiation. However, there are technical problems, such as the need for high resolution, low noise, large dynamic range, photon counting, two-dimensional pixel detectors and the small spot size of the exciting beam, which have prevented the widespread use of Kossel pattern analysis. Here, an experimental setup is described, which can be used for the measurement of Kossel patterns in a reasonable time and with high resolution to recover structural information.

Processing of Sonar Image Based on Compressive Sensing

2011 ◽  
Vol 301-303 ◽  
pp. 719-723 ◽  
Author(s):  
Zhi Jing Xu ◽  
Huan Lei Dai ◽  
Pei Pei Cao
Keyword(s):  
Wavelet Transform ◽  
Matching Pursuit ◽  
Experimental Result ◽  
Underwater Acoustic Channel ◽  
Sonar Image ◽  
Underwater Image ◽  
Reconstruction Image ◽  
Observation Matrix ◽  
Efficient Transmission

The particularity of the underwater acoustic channel has put forward a higher request for collection and efficient transmission of the underwater image. In this paper, based on the characteristics of sonar image, wavelet transform is used to sparse decompose the image, and selecting Gaussian random matrix as the observation matrix and using the orthogonal matching pursuit (OMP) algorithm to reconstruct the image. The experimental result shows that the quality of the reconstruction image and PSNR have gained great ascension compared to the traditional compression and processing of image based on the wavelet transform while they have the same measurement numbers in the coding portion. It provides a convenient for the sonar image’s underwater transmission.

scholarly journals Synergetic Use of Sentinel-1 and Sentinel-2 Data for Soil Moisture Mapping at Plot Scale

2018 ◽  
Vol 10 (8) ◽  
pp. 1285 ◽  
Author(s):  
Reza Attarzadeh ◽  
Jalal Amini ◽  
Claudia Notarnicola ◽  
Felix Greifeneder
Keyword(s):  
Soil Moisture ◽  
Optical Data ◽  
Estimation Accuracy ◽  
Support Vector ◽  
Practical Applications ◽  
Initial Stage ◽  
Object Based ◽  
Single Polarization ◽  
Selection Of

This paper presents an approach for retrieval of soil moisture content (SMC) by coupling single polarization C-band synthetic aperture radar (SAR) and optical data at the plot scale in vegetated areas. The study was carried out at five different sites with dominant vegetation cover located in Kenya. In the initial stage of the process, different features are extracted from single polarization mode (VV polarization) SAR and optical data. Subsequently, proper selection of the relevant features is conducted on the extracted features. An advanced state-of-the-art machine learning regression approach, the support vector regression (SVR) technique, is used to retrieve soil moisture. This paper takes a new look at soil moisture retrieval in vegetated areas considering the needs of practical applications. In this context, we tried to work at the object level instead of the pixel level. Accordingly, a group of pixels (an image object) represents the reality of the land cover at the plot scale. Three approaches, a pixel-based approach, an object-based approach, and a combination of pixel- and object-based approaches, were used to estimate soil moisture. The results show that the combined approach outperforms the other approaches in terms of estimation accuracy (4.94% and 0.89 compared to 6.41% and 0.62 in terms of root mean square error (RMSE) and R2), flexibility on retrieving the level of soil moisture, and better quality of visual representation of the SMC map.

scholarly journals Metaheuristic techniques comparison to optimize robotic end-effector behavior and its workspace

2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880113
Author(s):  
Miguel Angel Funes Lora ◽  
Edgar Alfredo Portilla-Flores ◽  
Raul Rivera Blas ◽  
Emmanuel Alejandro Merchán Cruz ◽  
Manuel Faraón Carbajal Romero
Keyword(s):  
Numerical Technique ◽  
Cuckoo Search ◽  
Optimization Methods ◽  
Metaheuristic Algorithms ◽  
End Effector ◽  
Bee Colony ◽  
Ill Posed ◽  
Metaheuristic Techniques

Many robots are dedicated to replicate trajectories recorded manually; the recorded trajectories may contain singularities, which occur when positions and/or orientations are not achievable by the robot. The optimization of those trajectories is a complex issue and classical optimization methods present a deficient performance when solving them. Metaheuristics are well-known methodologies for solving hard engineering problems. In this case, they are applied to obtain alternative trajectories that pass as closely as possible to the original one, reorienting the end-effector and displacing its position to avoid the singularities caused by limitations of inverse kinematics equations, the task, and the workspace. In this article, alternative solutions for an ill-posed problem concerning the behavior of the robotic end-effector position and orientation are proposed using metaheuristic algorithms such as cuckoo search, differential evolution, and modified artificial bee colony. The case study for this work considers a three-revolute robot (3R), whose trajectories can contain or not singularities, and an optimization problem is defined to minimize the objective function that represents the error of the alternative trajectories. A tournament in combination with a constant of proportionality allows the metaheuristics to modify the gradual orientation and position of the robot when a singularity is present. Consequently, the procedure selects from all the possible elbow-configurations the best that fits the trajectory. A classical numerical technique, Newton’s method, is used to compare the results of the applied metaheuristics, to evaluate their quality. The results of this implementation indicate that metaheuristic algorithms are an efficient tool to solve the problem of optimizing the end-effector behavior, because of the quality of the alternative trajectory produced.

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