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Konovalov AB. Compressed-sensing-inspired reconstruction algorithms in low-dose computed tomography: A review. Phys Med 2024; 124:104491. [PMID: 39079308 DOI: 10.1016/j.ejmp.2024.104491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/02/2024] [Revised: 07/13/2024] [Accepted: 07/23/2024] [Indexed: 08/10/2024] Open
Abstract
BACKGROUND Optimization of the dose the patient receives during scanning is an important problem in modern medical X-ray computed tomography (CT). One of the basic ways to its solution is to reduce the number of views. Compressed sensing theory helped promote the development of a new class of effective reconstruction algorithms for limited data CT. These compressed-sensing-inspired (CSI) algorithms optimize the Lp (0 ≤ p ≤ 1) norm of images and can accurately reconstruct CT tomograms from a very few views. The paper presents a review of the CSI algorithms and discusses prospects for their further use in commercial low-dose CT. METHODS Many literature references with the CSI algorithms have been were searched. To structure the material collected the author gives a classification framework within which he describes Lp regularization methods, the basic CSI algorithms that are used most often in few-view CT, and some of their derivatives. Lots of examples are provided to illustrate the use of the CSI algorithms in few-view and low-dose CT. RESULTS A list of the CSI algorithms is compiled from the literature search. For better demonstrativeness they are summarized in a table. The inference is done that already today some of the algorithms are capable of reconstruction from 20 to 30 views with acceptable quality and dose reduction by a factor of 10. DISCUSSION In conclusion the author discusses how soon the CSI reconstruction algorithms can be introduced in the practice of medical diagnosis and used in commercial CT scanners.
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Affiliation(s)
- Alexander B Konovalov
- FSUE "Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics", Snezhinsk, Chelyabinsk Region 456770, Russia.
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Iovea M, Stanciulescu A, Hermann E, Neagu M, Duliu OG. Multi-Energy and Fast-Convergence Iterative Reconstruction Algorithm for Organic Material Identification Using X-ray Computed Tomography. MATERIALS (BASEL, SWITZERLAND) 2023; 16:1654. [PMID: 36837279 PMCID: PMC9962467 DOI: 10.3390/ma16041654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Revised: 01/16/2023] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
In order to significantly reduce the computing time while, at the same time, keeping the accuracy and precision when determining the local values of the density and effective atomic number necessary for identifying various organic material, including explosives and narcotics, a specialized multi-stage procedure based on a multi-energy computed tomography investigation within the 20-160 keV domain was elaborated. It consisted of a compensation for beam hardening and other non-linear effects that affect the energy dependency of the linear attenuation coefficient (LAC) in the chosen energy domain, followed by a 3D fast reconstruction algorithm capable of reconstructing the local LAC values for 64 energy values from 19.8 to 158.4 keV, and, finally, the creation of a set of algorithms permitting the simultaneous determination of the density and effective atomic number of the investigated materials. This enabled determining both the density and effective atomic number of complex objects in approximately 24 s, with an accuracy and precision of less than 3%, which is a significantly better performance with respect to the reported literature values.
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Affiliation(s)
- Mihai Iovea
- Accent Pro 2000 srl, 25A, Mărășești Str., 077125 Magurele (Ilfov), Romania
| | | | - Edward Hermann
- Accent Pro 2000 srl, 25A, Mărășești Str., 077125 Magurele (Ilfov), Romania
| | - Marian Neagu
- Accent Pro 2000 srl, 25A, Mărășești Str., 077125 Magurele (Ilfov), Romania
| | - Octavian G. Duliu
- Accent Pro 2000 srl, 25A, Mărășești Str., 077125 Magurele (Ilfov), Romania
- Department of Structure of Matter, Earth and Atmospheric Physics, Astrophysics, Faculty of Physics, University of Bucharest, 405, Atomistilor Str., 077125 Magurele (Ilfov), Romania
- Geological Institute of Romania, 1, Caransebes Str., 012271 Bucharest, Romania
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Konovalov AB, Vlasov VV, Samarin SI, Soloviev ID, Savitsky AP, Tuchin VV. Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study. JOURNAL OF BIOMEDICAL OPTICS 2022; 27:126001. [PMID: 36519075 PMCID: PMC9743783 DOI: 10.1117/1.jbo.27.12.126001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
SIGNIFICANCE Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons. AIM The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry. APPROACH The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method. RESULTS 3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object. CONCLUSIONS Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.
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Affiliation(s)
- Alexander B. Konovalov
- Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics,” Snezhinsk, Russia
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Vitaly V. Vlasov
- Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics,” Snezhinsk, Russia
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Sergei I. Samarin
- Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics,” Snezhinsk, Russia
| | - Ilya D. Soloviev
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Alexander P. Savitsky
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Valery V. Tuchin
- Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
- Saratov State University, Saratov, Russia
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Konovalov A, Vlasov V, Kolchugin S, Malyshkin G, Mukhamadiyev R. Monte Carlo simulation of sensitivity functions for few-view computed tomography of strongly absorbing media. MONTE CARLO METHODS AND APPLICATIONS 2022; 28:269-278. [DOI: 10.1515/mcma-2022-2120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/10/2023]
Abstract
Abstract
The paper describes a sensitivity function calculation method for few-view X-ray computed tomography of strongly absorbing objects. It is based on a probabilistic interpretation of energy transport through the object from a source to a detector. A PRIZMA code package is used to track photons. The code is developed at FSUE “RFNC–VNIITF named after Academ. E. I. Zababakhin” and implements a stochastic Monte Carlo method. The value of the sensitivity function in a discrete cell of the reconstruction region is assumed to be directly proportional to the fraction of photon trajectories which cross the cell from all those recorded by the detector. The method’s efficiency is validated through a numerical experiment on the reconstruction of a section of a spherical heavy-metal phantom with an air cavity and a density difference of 25 Ṫhe proposed method is shown to outperform the method based on projection approximation in case of reconstruction from 9 views.
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Affiliation(s)
- Alexander Konovalov
- Computational Center , Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All–Russia Research Institute of Technical Physics” , Snezhinsk , Chelyabinsk Region, 456770 , Russia
| | - Vitaly Vlasov
- Computational Center , Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All–Russia Research Institute of Technical Physics” , Snezhinsk , Chelyabinsk Region, 456770 , Russia
| | - Sergey Kolchugin
- Computational Center , Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All–Russia Research Institute of Technical Physics” , Snezhinsk , Chelyabinsk Region, 456770 , Russia
| | - Gennady Malyshkin
- Department of Mathematics , Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All–Russia Research Institute of Technical Physics” , Snezhinsk , Chelyabinsk Region, 456770 , Russia
| | - Rim Mukhamadiyev
- Department of Mathematics , Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All–Russia Research Institute of Technical Physics” , Snezhinsk , Chelyabinsk Region, 456770 , Russia
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Konovalov AB, Vlasov VV, Kiselev AN. Development of Image Reconstruction Algorithms for Few-View Computed Tomography at RFNC–VNIITF: History, State of the Art, and Prospects. RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING 2022; 58:455-465. [DOI: 10.1134/s1061830922060067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2022] [Revised: 04/22/2022] [Accepted: 04/22/2022] [Indexed: 09/10/2023]
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Vlasov VV, Konovalov AB. Minimizing the Number of Views in Few-View Computed Tomography: a Deep Learning Approach. 2022 INTERNATIONAL CONFERENCE ON INDUSTRIAL ENGINEERING, APPLICATIONS AND MANUFACTURING (ICIEAM) 2022. [DOI: 10.1109/icieam54945.2022.9787247] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/10/2023]
Affiliation(s)
- V. V. Vlasov
- Computational Center Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics”,Snezhinsk,Russia
| | - A. B. Konovalov
- Computational Center Federal State Unitary Enterprise “Russian Federal Nuclear Center – Zababakhin All-Russia Research Institute of Technical Physics”,Snezhinsk,Russia
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Konovalov AB, Mukhamadiyev RF, Kiselev AN. Monte Carlo Based Estimation of Weight Functions for Few-View Computed Tomography of Strongly Absorbing Objects. 2022 INTERNATIONAL CONFERENCE ON INDUSTRIAL ENGINEERING, APPLICATIONS AND MANUFACTURING (ICIEAM) 2022. [DOI: 10.1109/icieam54945.2022.9787270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/10/2023]
Affiliation(s)
- A. B. Konovalov
- Computational Center, Federal State Unitary Enterprise “Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics” (RFNC-VNIITF),Snezhinsk,Russia
| | - R. F. Mukhamadiyev
- Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics” (RFNC-VNIITF),Mathematics Division, Federal State Unitary Enterprise “Russian,Snezhinsk,Russia
| | - A. N. Kiselev
- Computational Center, Federal State Unitary Enterprise “Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics” (RFNC-VNIITF),Snezhinsk,Russia
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Konovalov AB, Vlasov VV, Uglov AS. Early-photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021; 37:e03408. [PMID: 33094558 DOI: 10.1002/cnm.3408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 10/04/2020] [Accepted: 10/17/2020] [Indexed: 06/11/2023]
Abstract
The paper presents an original approach to time-domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state-of-the-art compressed-sensing-like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source-receiver separations which correspond to the macroscopic regime. Two compressed-sensing-like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage-thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.
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Affiliation(s)
- Alexander B Konovalov
- Computational Center, Federal State Unitary Enterprise "Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics,", Snezhinsk, Russia
- Laboratory of Molecular Imaging, Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Vitaly V Vlasov
- Computational Center, Federal State Unitary Enterprise "Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics,", Snezhinsk, Russia
- Laboratory of Molecular Imaging, Bach Institute of Biochemistry, Research Center of Biotechnology of the Russian Academy of Sciences, Moscow, Russia
| | - Alexander S Uglov
- Computational Center, Federal State Unitary Enterprise "Russian Federal Nuclear Center - Zababakhin All-Russia Research Institute of Technical Physics,", Snezhinsk, Russia
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Vlasov V, Konovalov A, Kolchugin S. Joint image reconstruction and segmentation: Comparison of two algorithms for few-view tomography. COMPUTER OPTICS 2019; 43. [DOI: 10.18287/2412-6179-2019-43-6-1008-1020] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/10/2023]
Abstract
Two algorithms of few-view tomography are compared, specifically, the iterative Potts minimization algorithm (IPMA) and the algebraic reconstruction technique with TV-regularization and adaptive segmentation (ART-TVS). Both aim to reconstruct piecewise-constant structures, use the compressed sensing theory, and combine image reconstruction and segmentation procedures. Using a numerical experiment, it is shown that either algorithm can exactly reconstruct the Shepp-Logan phantom from as small as 7 views with noise characteristic of the medical applications of X-ray tomography. However, if an object has a complicated high-frequency structure (QR-code), the minimal number of views required for its exact reconstruction increases to 17–21 for ART-TVS and to 32–34 for IPMA. The ART-TVS algorithm developed by the authors is shown to outperform IPMA in reconstruction accuracy and speed and in resistance to abnormally high noise as well. ART-TVS holds good potential for further improvement.
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Zeng GL. Sparse-view tomography via displacement function interpolation. Vis Comput Ind Biomed Art 2019; 2:13. [PMID: 32240401 PMCID: PMC7099552 DOI: 10.1186/s42492-019-0024-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Accepted: 10/09/2019] [Indexed: 11/10/2022] Open
Abstract
Sparse-view tomography has many applications such as in low-dose computed tomography (CT). Using under-sampled data, a perfect image is not expected. The goal of this paper is to obtain a tomographic image that is better than the naïve filtered backprojection (FBP) reconstruction that uses linear interpolation to complete the measurements. This paper proposes a method to estimate the un-measured projections by displacement function interpolation. Displacement function estimation is a non-linear procedure and the linear interpolation is performed on the displacement function (instead of, on the sinogram itself). As a result, the estimated measurements are not the linear transformation of the measured data. The proposed method is compared with the linear interpolation methods, and the proposed method shows superior performance.
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