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Mossa-Basha M, Zhu C, Pandhi T, Mendoza S, Azadbakht J, Safwat A, Homen D, Zamora C, Gnanasekaran DK, Peng R, Cen S, Duddalwar V, Alger JR, Wang DJJ. Deep Learning Denoising Improves CT Perfusion Image Quality in the Setting of Lower Contrast Dosing: A Feasibility Study. AJNR Am J Neuroradiol 2024; 45:1468-1474. [PMID: 38844370 PMCID: PMC11448976 DOI: 10.3174/ajnr.a8367] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2024] [Accepted: 05/24/2024] [Indexed: 08/11/2024]
Abstract
BACKGROUND AND PURPOSE Considering recent iodinated contrast shortages and a focus on reducing waste, developing protocols with lower contrast dosing while maintaining image quality through artificial intelligence is needed. This study compared reduced iodinated contrast media and standard dose CTP acquisitions, and the impact of deep learning denoising on CTP image quality in preclinical and clinical studies. The effect of reduced X-ray mAs dose was also investigated in preclinical studies. MATERIALS AND METHODS Twelve swine underwent 9 CTP examinations each, performed at combinations of 3 different x-ray (37, 67, and 127 mAs) and iodinated contrast media doses (10, 15, and 20 mL). Clinical CTP acquisitions performed before and during the iodinated contrast media shortage and protocol change (from 40 to 30 mL) were retrospectively included. Eleven patients with reduced iodinated contrast media dosages and 11 propensity-score-matched controls with the standard iodinated contrast media dosages were included. A residual encoder-decoder convolutional neural network (RED-CNN) was trained for CTP denoising using k-space-weighted image average filtered CTP images as the target. The standard, RED-CNN-denoised, and k-space-weighted image average noise-filtered images for animal and human studies were compared for quantitative SNR and qualitative image evaluation. RESULTS The SNR of animal CTP images decreased with reductions in iodinated contrast media and milliampere-second doses. Contrast dose reduction had a greater effect on SNR than milliampere-second reduction. Noise-filtering by k-space-weighted image average and RED-CNN denoising progressively improved the SNR of CTP maps, with RED-CNN resulting in the highest SNR. The SNR of clinical CTP images was generally lower with a reduced iodinated contrast media dose, which was improved by the k-space-weighted image average and RED-CNN denoising (P < .05). Qualitative readings consistently rated RED-CNN denoised CTP as the best quality, followed by k-space-weighted image average and then standard CTP images. CONCLUSIONS Deep learning-denoising can improve image quality for low iodinated contrast media CTP protocols, and could approximate standard iodinated contrast media dose CTP, in addition to potentially improving image quality for low milliampere-second acquisitions.
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Affiliation(s)
- Mahmud Mossa-Basha
- From the Department of Radiology (M.M.-B., C.Z., A.S), University of Washington, Seattle, Washington
| | - Chengcheng Zhu
- From the Department of Radiology (M.M.-B., C.Z., A.S), University of Washington, Seattle, Washington
| | - Tanya Pandhi
- Mark and Mary Stevens Neuroimaging and Informatics Institute (T.P., S.M., D.K.G., D.J.J.W.), Keck School of Medicine, University of Southern California, Los Angeles, California
| | - Steve Mendoza
- Mark and Mary Stevens Neuroimaging and Informatics Institute (T.P., S.M., D.K.G., D.J.J.W.), Keck School of Medicine, University of Southern California, Los Angeles, California
| | | | - Ahmed Safwat
- From the Department of Radiology (M.M.-B., C.Z., A.S), University of Washington, Seattle, Washington
| | - Dean Homen
- Department of Radiology (D.H., C.Z.), University of North Carolina, Chapel Hill, North Carolina
| | - Carlos Zamora
- Department of Radiology (D.H., C.Z.), University of North Carolina, Chapel Hill, North Carolina
| | - Dinesh Kumar Gnanasekaran
- Mark and Mary Stevens Neuroimaging and Informatics Institute (T.P., S.M., D.K.G., D.J.J.W.), Keck School of Medicine, University of Southern California, Los Angeles, California
| | - Ruiyue Peng
- Hura Imaging Inc (R.P., J.R.A.), Los Angeles, California
| | - Steven Cen
- Department of Radiology (S.C., V.D., D.J.J.W.), Keck School of Medicine, University of Southern California, Los Angeles, California
| | - Vinay Duddalwar
- Department of Radiology (S.C., V.D., D.J.J.W.), Keck School of Medicine, University of Southern California, Los Angeles, California
| | - Jeffry R Alger
- Hura Imaging Inc (R.P., J.R.A.), Los Angeles, California
| | - Danny J J Wang
- Mark and Mary Stevens Neuroimaging and Informatics Institute (T.P., S.M., D.K.G., D.J.J.W.), Keck School of Medicine, University of Southern California, Los Angeles, California
- Department of Radiology (S.C., V.D., D.J.J.W.), Keck School of Medicine, University of Southern California, Los Angeles, California
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Shou Q, Zhao C, Shao X, Herting MM, Wang DJ. High Resolution Multi-delay Arterial Spin Labeling with Transformer based Denoising for Pediatric Perfusion MRI. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2024:2024.03.04.24303727. [PMID: 38496517 PMCID: PMC10942515 DOI: 10.1101/2024.03.04.24303727] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2024]
Abstract
Multi-delay arterial spin labeling (MDASL) can quantitatively measure cerebral blood flow (CBF) and arterial transit time (ATT), which is particularly suitable for pediatric perfusion imaging. Here we present a high resolution (iso-2mm) MDASL protocol and performed test-retest scans on 21 typically developing children aged 8 to 17 years. We further proposed a Transformer-based deep learning (DL) model with k-space weighted image average (KWIA) denoised images as reference for training the model. The performance of the model was evaluated by the SNR of perfusion images, as well as the SNR, bias and repeatability of the fitted CBF and ATT maps. The proposed method was compared to several benchmark methods including KWIA, joint denoising and reconstruction with total generalized variation (TGV) regularization, as well as directly applying a pretrained Transformer model on a larger dataset. The results show that the proposed Transformer model with KWIA reference can effectively denoise multi-delay ASL images, not only improving the SNR for perfusion images of each delay, but also improving the SNR for the fitted CBF and ATT maps. The proposed method also improved test-retest repeatability of whole-brain perfusion measurements. This may facilitate the use of MDASL in neurodevelopmental studies to characterize typical and aberrant brain development.
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Affiliation(s)
- Qinyang Shou
- University of Southern California, Los Angeles, California 90033 USA
| | - Chenyang Zhao
- University of Southern California, Los Angeles, California 90033 USA
| | - Xingfeng Shao
- University of Southern California, Los Angeles, California 90033 USA
| | - Megan M Herting
- University of Southern California, Los Angeles, California 90033 USA
| | - Danny Jj Wang
- University of Southern California, Los Angeles, California 90033 USA
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Niu S, Li S, Huang S, Liang L, Tang S, Wang T, Yu G, Niu T, Wang J, Ma J. Adaptive prior image constrained total generalized variation for low-dose dynamic cerebral perfusion CT reconstruction. JOURNAL OF X-RAY SCIENCE AND TECHNOLOGY 2024; 32:1429-1447. [PMID: 39302409 DOI: 10.3233/xst-240104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/22/2024]
Abstract
BACKGROUND Dynamic cerebral perfusion CT (DCPCT) can provide valuable insight into cerebral hemodynamics by visualizing changes in blood within the brain. However, the associated high radiation dose of the standard DCPCT scanning protocol has been a great concern for the patient and radiation physics. Minimizing the x-ray exposure to patients has been a major effort in the DCPCT examination. A simple and cost-effective approach to achieve low-dose DCPCT imaging is to lower the x-ray tube current in data acquisition. However, the image quality of low-dose DCPCT will be degraded because of the excessive quantum noise. OBJECTIVE To obtain high-quality DCPCT images, we present a statistical iterative reconstruction (SIR) algorithm based on penalized weighted least squares (PWLS) using adaptive prior image constrained total generalized variation (APICTGV) regularization (PWLS-APICTGV). METHODS APICTGV regularization uses the precontrast scanned high-quality CT image as an adaptive structural prior for low-dose PWLS reconstruction. Thus, the image quality of low-dose DCPCT is improved while essential features of targe image are well preserved. An alternating optimization algorithm is developed to solve the cost function of the PWLS-APICTGV reconstruction. RESULTS PWLS-APICTGV algorithm was evaluated using a digital brain perfusion phantom and patient data. Compared to other competing algorithms, the PWLS-APICTGV algorithm shows better noise reduction and structural details preservation. Furthermore, the PWLS-APICTGV algorithm can generate more accurate cerebral blood flow (CBF) map than that of other reconstruction methods. CONCLUSIONS PWLS-APICTGV algorithm can significantly suppress noise while preserving the important features of the reconstructed DCPCT image, thus achieving a great improvement in low-dose DCPCT imaging.
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Affiliation(s)
- Shanzhou Niu
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
- Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou, China
| | - Shuo Li
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
| | - Shuyan Huang
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
| | - Lijing Liang
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
| | - Sizhou Tang
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
| | - Tinghua Wang
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China
| | - Gaohang Yu
- School of Science, Hangzhou Dianzi University, Hangzhou, China
| | - Tianye Niu
- Institute of Biomedical Engineering, Shenzhen Bay Laboratory, Shenzhen, China
| | - Jing Wang
- Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, TX, USA
| | - Jianhua Ma
- School of Biomedical Engineering, Southern Medical University, Guangzhou, China
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Xin Y, Kim T, Winkler T, Brix G, Gaulton T, Gerard SE, Herrmann J, Martin KT, Victor M, Reutlinger K, Amato M, Berra L, Kalra MK, Cereda M. Improving pulmonary perfusion assessment by dynamic contrast-enhanced computed tomography in an experimental lung injury model. J Appl Physiol (1985) 2023; 134:1496-1507. [PMID: 37167261 PMCID: PMC10228674 DOI: 10.1152/japplphysiol.00159.2023] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Revised: 04/24/2023] [Accepted: 05/11/2023] [Indexed: 05/13/2023] Open
Abstract
Pulmonary perfusion has been poorly characterized in acute respiratory distress syndrome (ARDS). Optimizing protocols to measure pulmonary blood flow (PBF) via dynamic contrast-enhanced (DCE) computed tomography (CT) could improve understanding of how ARDS alters pulmonary perfusion. In this study, comparative evaluations of injection protocols and tracer-kinetic analysis models were performed based on DCE-CT data measured in ventilated pigs with and without lung injury. Ten Yorkshire pigs (five with lung injury, five healthy) were anesthetized, intubated, and mechanically ventilated; lung injury was induced by bronchial hydrochloric acid instillation. Each DCE-CT scan was obtained during a 30-s end-expiratory breath-hold. Reproducibility of PBF measurements was evaluated in three pigs. In eight pigs, undiluted and diluted Isovue-370 were separately injected to evaluate the effect of contrast viscosity on estimated PBF values. PBF was estimated with the peak-enhancement and the steepest-slope approach. Total-lung PBF was estimated in two healthy pigs to compare with cardiac output measured invasively by thermodilution in the pulmonary artery. Repeated measurements in the same animals yielded a good reproducibility of computed PBF maps. Injecting diluted isovue-370 resulted in smaller contrast-time curves in the pulmonary artery (P < 0.01) and vein (P < 0.01) without substantially diminishing peak signal intensity (P = 0.46 in the pulmonary artery) compared with the pure contrast agent since its viscosity is closer to that of blood. As compared with the peak-enhancement model, PBF values estimated by the steepest-slope model with diluted contrast were much closer to the cardiac output (R2 = 0.82) as compared with the peak-enhancement model. DCE-CT using the steepest-slope model and diluted contrast agent provided reliable quantitative estimates of PBF.NEW & NOTEWORTHY Dynamic contrast-enhanced CT using a lower-viscosity contrast agent in combination with tracer-kinetic analysis by the steepest-slope model improves pulmonary blood flow measurements and assessment of regional distributions of lung perfusion.
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Affiliation(s)
- Yi Xin
- Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, United States
- Department of Anesthesia, Critical Care and Pain Medicine, Harvard Medical School, Boston, Massachusetts, United States
| | - Taehwan Kim
- Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, United States
| | - Tilo Winkler
- Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, United States
- Department of Anesthesia, Critical Care and Pain Medicine, Harvard Medical School, Boston, Massachusetts, United States
| | - Gunnar Brix
- Department of Medical and Occupational Radiation Protection, Federal Office for Radiation Protection, Salzgitter, Germany
| | - Timothy Gaulton
- Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, United States
- Department of Anesthesia, Critical Care and Pain Medicine, Harvard Medical School, Boston, Massachusetts, United States
| | - Sarah E Gerard
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa, United States
| | - Jacob Herrmann
- Roy J. Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa, United States
| | - Kevin T Martin
- Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, United States
| | - Marcus Victor
- Disciplina de Pneumologia, Instituto do Coração, Hospital das Clínicas, Faculdade de Medicina, Universidade de São Paulo, São Paulo, Brazil
- Electronics Engineering Division, Aeronautics Institute of Technology, Sao Paulo, Brazil
| | - Kristan Reutlinger
- Department of Anesthesiology and Critical Care, University of Pennsylvania, Philadelphia, Pennsylvania, United States
| | - Marcelo Amato
- Disciplina de Pneumologia, Instituto do Coração, Hospital das Clínicas, Faculdade de Medicina, Universidade de São Paulo, São Paulo, Brazil
| | - Lorenzo Berra
- Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, United States
- Department of Anesthesia, Critical Care and Pain Medicine, Harvard Medical School, Boston, Massachusetts, United States
| | - Mannudeep K Kalra
- Department of Radiology, Massachusetts General Hospital, Boston, Massachusetts, United States
- Department of Radiology, Harvard Medical School, Boston, Massachusetts, United States
| | - Maurizio Cereda
- Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, United States
- Department of Anesthesia, Critical Care and Pain Medicine, Harvard Medical School, Boston, Massachusetts, United States
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牛 善, 刘 宏, 刘 沛, 张 梦, 李 硕, 梁 礼, 李 楠, 刘 国. [Nonlocal low-rank and sparse matrix decomposition for low-dose cerebral perfusion CT image restoration]. NAN FANG YI KE DA XUE XUE BAO = JOURNAL OF SOUTHERN MEDICAL UNIVERSITY 2022; 42:1309-1316. [PMID: 36210703 PMCID: PMC9550540 DOI: 10.12122/j.issn.1673-4254.2022.09.06] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Indexed: 01/24/2023]
Abstract
OBJECTIVE To present a nonlocal low-rank and sparse matrix decomposition (NLSMD) method for low-dose cerebral perfusion CT image restoration. METHODS Low-dose cerebral perfusion CT images were first partitioned into a matrix, and the low- rank and sparse matrix decomposition model was constructed to obtain high-quality low-dose cerebral perfusion CT images. The cerebral hemodynamic parameters were calculated from the restored high-quality CT images. RESULTS In the phantom study, the average structured similarity (SSIM) value of the sequential images obtained by filtered back-projection (FBP) algorithm was 0.9438, which was increased to 0.9765 using the proposed algorithm; the SSIM values of cerebral blood flow (CBF) and cerebral blood volume (CBV) map obtained by FBP algorithm were 0.7005 and 0.6856, respectively, which were increased using the proposed algorithm to 0.7871 and 0.7972, respectively. CONCLUSION The proposed method can effectively suppress noises in low-dose cerebral perfusion CT images to obtain accurate cerebral hemodynamic parameters.
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Affiliation(s)
- 善洲 牛
- 赣南师范大学数学与计算机科学学院,江西 赣州 341000School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
- 赣南师范大学赣州市计算成像重点实验室,江西 赣州 341000Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou 341000, China
| | - 宏 刘
- 赣南师范大学数学与计算机科学学院,江西 赣州 341000School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
- 赣南师范大学赣州市计算成像重点实验室,江西 赣州 341000Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou 341000, China
| | - 沛沄 刘
- 赣南师范大学数学与计算机科学学院,江西 赣州 341000School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
- 赣南师范大学赣州市计算成像重点实验室,江西 赣州 341000Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou 341000, China
| | - 梦真 张
- 赣南师范大学数学与计算机科学学院,江西 赣州 341000School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
- 赣南师范大学赣州市计算成像重点实验室,江西 赣州 341000Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou 341000, China
| | - 硕 李
- 赣南师范大学数学与计算机科学学院,江西 赣州 341000School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
- 赣南师范大学赣州市计算成像重点实验室,江西 赣州 341000Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou 341000, China
| | - 礼境 梁
- 赣南师范大学数学与计算机科学学院,江西 赣州 341000School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
- 赣南师范大学赣州市计算成像重点实验室,江西 赣州 341000Ganzhou Key Laboratory of Computational Imaging, Gannan Normal University, Ganzhou 341000, China
| | - 楠 李
- 赣南师范大学经济管理学院,江西 赣州 341000School of Economics and Management, Gannan Normal University, Ganzhou 341000, China
| | - 国良 刘
- 赣南医学院医学信息工程学院,江西 赣州 341000School of Medical Information Engineering, Gannan Medical University, Ganzhou 341000, China
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k-space weighted image average (KWIA) for ASL-based dynamic MR angiography and perfusion imaging. Magn Reson Imaging 2021; 86:94-106. [PMID: 34871715 PMCID: PMC8713133 DOI: 10.1016/j.mri.2021.11.017] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Revised: 10/17/2021] [Accepted: 11/29/2021] [Indexed: 11/23/2022]
Abstract
A novel denoising algorithm termed k-space weighted image average (KWIA) was proposed to improve the signal-to-noise ratio (SNR) of dynamic MRI, such as arterial spin labeling (ASL)-based dynamic magnetic resonance angiography (dMRA) and perfusion imaging. KWIA divides the k-space of each time frame into multiple rings, the central ring of the k-space remains intact to preserve the image contrast and temporal resolution, while outer rings are progressively averaged with neighboring time frames to increase SNR. Simulations and in-vivo dMRA and multi-delay ASL studies were performed to evaluate the performance of KWIA under various MRI acquisition conditions. SNR ratios and temporal signal errors between KWIA-processed and the original data were measured. Visualization of dynamic blood flow signals as well as quantitative parametric maps were evaluated for KWIA-processed images as compared to the original images. KWIA achieved a SNR ratio of 1.73 for dMRA and 2.0 for multi-delay ASL respectively, which were in accordance with the theoretical predictions. Improved visualization of dynamic blood flow signals was demonstrated using KWIA in distal small vessels in dMRA and small brain structures in multi-delay ASL. Approximately 5% temporal errors were observed in both KWIA-processed dMRA and ASL signals. Fine anatomical features were revealed in the quantitative parametric maps of dMRA, and the residuals of model fitting were reduced for multi-delay ASL. Compared to other conventional denoising methods, KWIA is a flexible denoising algorithm that improves the SNR of ASL-based dMRA and perfusion MRI by up to 2-fold without compromising spatial and temporal resolution or quantification accuracy.
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Niu S, Liu H, Zhang M, Wang M, Wang J, Ma J. Iterative reconstruction for low-dose cerebral perfusion computed tomography using prior image induced diffusion tensor. Phys Med Biol 2021; 66. [PMID: 34081027 DOI: 10.1088/1361-6560/ac0290] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 05/18/2021] [Indexed: 11/12/2022]
Abstract
Cerebral perfusion computed tomography (CPCT) can depict the functional status of cerebral circulation at the tissue level; hence, it has been increasingly used to diagnose patients with cerebrovascular disease. However, there is a significant concern that CPCT scanning protocol could expose patients to excessive radiation doses. Although reducing the x-ray tube current when acquiring CPCT projection data is an effective method for reducing radiation dose, this technique usually results in degraded image quality. To enhance the image quality of low-dose CPCT, we present a prior image induced diffusion tensor (PIDT) for statistical iterative reconstruction, based on the penalized weighted least-squares (PWLS) criterion, which we referred to as PWLS-PIDT, for simplicity. Specifically, PIDT utilizes the geometric features of pre-contrast scanned high-quality CT image as a structure prior for PWLS reconstruction; therefore, the low-dose CPCT images are enhanced while preserving important features in the target image. An effective alternating minimization algorithm is developed to solve the associated objective function in the PWLS-PIDT reconstruction. We conduct qualitative and quantitative studies to evaluate the PWLS-PIDT reconstruction with a digital brain perfusion phantom and patient data. With this method, the noise in the reconstructed CPCT images is more substantially reduced than that of other competing methods, without sacrificing structural details significantly. Furthermore, the CPCT sequential images reconstructed via the PWLS-PIDT method can derive more accurate hemodynamic parameter maps than those of other competing methods.
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Affiliation(s)
- Shanzhou Niu
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, 341000, People's Republic of China
| | - Hong Liu
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, 341000, People's Republic of China
| | - Mengzhen Zhang
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, 341000, People's Republic of China
| | - Min Wang
- School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, 341000, People's Republic of China
| | - Jing Wang
- Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, TX 75235, United States of America
| | - Jianhua Ma
- School of Biomedical Engineering, Southern Medical University, Guangzhou, 510515, People's Republic of China
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