Image reconstruction as an inverse problem

2005 ◽  
pp. 241-254
Author(s):  
Frank P. Pijpers
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction

Image Reconstruction with the Fourier Coefficients for Magnetic Induction Tomography

2020 ◽  
Vol 16 (2) ◽  
pp. 156-163
Author(s):  
Jingwen Wang ◽  
Xu Wang ◽  
Dan Yang ◽  
Kaiyang Wang
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Magnetic Induction ◽  
Fourier Coefficients ◽  
Signal Reconstruction ◽  
Reconstruction Algorithm ◽  
Reconstruction Method ◽  
Measurement Equation ◽  
Image Reconstruction Method ◽  
Magnetic Induction Tomography

Background: Image reconstruction of magnetic induction tomography (MIT) is a typical ill-posed inverse problem, which means that the measurements are always far from enough. Thus, MIT image reconstruction results using conventional algorithms such as linear back projection and Landweber often suffer from limitations such as low resolution and blurred edges. Methods: In this paper, based on the recent finite rate of innovation (FRI) framework, a novel image reconstruction method with MIT system is presented. Results: This is achieved through modeling and sampling the MIT signals in FRI framework, resulting in a few new measurements, namely, fourier coefficients. Because each new measurement contains all the pixel position and conductivity information of the dense phase medium, the illposed inverse problem can be improved, by rebuilding the MIT measurement equation with the measurement voltage and the new measurements. Finally, a sparsity-based signal reconstruction algorithm is presented to reconstruct the original MIT image signal, by solving this new measurement equation. Conclusion: Experiments show that the proposed method has better indicators such as image error and correlation coefficient. Therefore, it is a kind of MIT image reconstruction method with high accuracy.

scholarly journals Quantitative imaging and automated fuel pin identification for passive gamma emission tomography

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ming Fang ◽  
Yoann Altmann ◽  
Daniele Della Latta ◽  
Massimiliano Salvatori ◽  
Angela Di Fulvio
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Image Resolution ◽  
Emission Tomography ◽  
Nuclear Safeguards ◽  
Activity Levels ◽  
Spent Fuel ◽  
Gamma Emission ◽  
Cross Sectional ◽  
Fuel Rods

AbstractCompliance of member States to the Treaty on the Non-Proliferation of Nuclear Weapons is monitored through nuclear safeguards. The Passive Gamma Emission Tomography (PGET) system is a novel instrument developed within the framework of the International Atomic Energy Agency (IAEA) project JNT 1510, which included the European Commission, Finland, Hungary and Sweden. The PGET is used for the verification of spent nuclear fuel stored in water pools. Advanced image reconstruction techniques are crucial for obtaining high-quality cross-sectional images of the spent-fuel bundle to allow inspectors of the IAEA to monitor nuclear material and promptly identify its diversion. In this work, we have developed a software suite to accurately reconstruct the spent-fuel cross sectional image, automatically identify present fuel rods, and estimate their activity. Unique image reconstruction challenges are posed by the measurement of spent fuel, due to its high activity and the self-attenuation. While the former is mitigated by detector physical collimation, we implemented a linear forward model to model the detector responses to the fuel rods inside the PGET, to account for the latter. The image reconstruction is performed by solving a regularized linear inverse problem using the fast-iterative shrinkage-thresholding algorithm. We have also implemented the traditional filtered back projection (FBP) method based on the inverse Radon transform for comparison and applied both methods to reconstruct images of simulated mockup fuel assemblies. Higher image resolution and fewer reconstruction artifacts were obtained with the inverse-problem approach, with the mean-square-error reduced by 50%, and the structural-similarity improved by 200%. We then used a convolutional neural network (CNN) to automatically identify the bundle type and extract the pin locations from the images; the estimated activity levels finally being compared with the ground truth. The proposed computational methods accurately estimated the activity levels of the present pins, with an associated uncertainty of approximately 5%.

scholarly journals DeepPET: A deep encoder–decoder network for directly solving the PET image reconstruction inverse problem

2019 ◽  
Vol 54 ◽  
pp. 253-262 ◽  
Author(s):  
Ida Häggström ◽  
C. Ross Schmidtlein ◽  
Gabriele Campanella ◽  
Thomas J. Fuchs
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Pet Image Reconstruction

scholarly journals Approximate Image Reconstruction in Landscape Reflection Imaging

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Rémi Régnier ◽  
Gaël Rigaud ◽  
Maï K. Nguyen
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Inversion Formula ◽  
Imaging Modality ◽  
Reconstruction Algorithm ◽  
Reflectivity Function ◽  
Reconstruction Kernel ◽  
Simulation Results ◽  
Reflection Imaging ◽  
Present Simulation

Simple reflection imaging of landscape (scenery or extended objects) poses the inverse problem of reconstructing the landscape reflectivity function from its integrals on some particular family of spheres. Such data acquisition is encoded in the framework of a Radon transform on this family of spheres. In spite of the existence of an exact inversion formula, the numerical landscape reflectivity function reconstitution is best obtained with an approximate but judiciously chosen reconstruction kernel. We describe the working of this reflection imaging modality and its theoretical handling, introduce an efficient and stable image reconstruction algorithm, and present simulation results to prove the validity of this choice as well as to demonstrate the feasibility of this imaging process.

scholarly journals Logistic Regression with Wave Preprocessing to Solve Inverse Problem in Industrial Tomography for Technological Process Control

Energies ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 8116
Author(s):  
Tomasz Rymarczyk ◽  
Konrad Niderla ◽  
Edward Kozłowski ◽  
Krzysztof Król ◽  
Joanna Maria Wyrwisz ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Logistic Regression ◽  
Image Reconstruction ◽  
Tap Water ◽  
Machine Learning Algorithms ◽  
Data Sets ◽  
Impedance Tomography ◽  
The Subject ◽  
Vector Images ◽  
Selection Of

The research presented here concerns the analysis and selection of logistic regression with wave preprocessing to solve the inverse problem in industrial tomography. The presented application includes a specialized device for tomographic measurements and dedicated algorithms for image reconstruction. The subject of the research was a model of a tank filled with tap water and specific inclusions. The research mainly targeted the study of developing and comparing models and methods for data reconstruction and analysis. The application allows choosing the appropriate method of image reconstruction, knowing the specifics of the solution. The novelty of the presented solution is the use of original machine learning algorithms to implement electrical impedance tomography. One of the features of the presented solution was the use of many individually trained subsystems, each of which produces a unique pixel of the final image. The methods were trained on data sets generated by computer simulation and based on actual laboratory measurements. Conductivity values for individual pixels are the result of the reconstruction of vector images within the tested object. By comparing the results of image reconstruction, the most efficient methods were identified.

scholarly journals Ultrafast Ultrasound Imaging as an Inverse Problem: Matrix-Free Sparse Image Reconstruction

2018 ◽  
Vol 65 (3) ◽  
pp. 339-355 ◽  
Author(s):  
Adrien Besson ◽  
Dimitris Perdios ◽  
Florian Martinez ◽  
Zhouye Chen ◽  
Rafael E. Carrillo ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Ultrasound Imaging ◽  
Sparse Image Reconstruction ◽  
Matrix Free

Real-time ultrasound image reconstruction as an inverse problem on a GPU

2018 ◽  
Vol 17 (3) ◽  
pp. 543-554
Author(s):  
Paulo R. Bueno ◽  
Marcelo V. W. Zibetti ◽  
Joaquim M. Maia
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Real Time ◽  
Ultrasound Image
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