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Hehn L, Tilley S, Pfeiffer F, Stayman JW. Blind deconvolution in model-based iterative reconstruction for CT using a normalized sparsity measure. Phys Med Biol 2019; 64:215010. [PMID: 31561247 DOI: 10.1088/1361-6560/ab489e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Model-based iterative reconstruction techniques for CT that include a description of the noise statistics and a physical forward model of the image formation process have proven to increase image quality for many applications. Specifically, including models of the system blur into the physical forward model and thus implicitly performing a deconvolution of the projections during tomographic reconstruction, could demonstrate distinct improvements, especially in terms of resolution. However, the results strongly rely on an exact characterization of all components contributing to the system blur. Such characterizations can be laborious and even a slight mismatch can diminish image quality significantly. Therefore, we introduce a novel objective function, which enables us to jointly estimate system blur parameters during tomographic reconstruction. Conventional objective functions are biased in terms of blur and can yield lowest cost to blurred reconstructions with low noise levels. A key feature of our objective function is a new normalized sparsity measure for CT based on total-variation regularization, constructed to be less biased in terms of blur. We outline a solving strategy for jointly recovering low-dimensional blur parameters during tomographic reconstruction. We perform an extensive simulation study, evaluating the performance of the regularization and the dependency of the different parts of the objective function on the blur parameters. Scenarios with different regularization strengths and system blurs are investigated, demonstrating that we can recover the blur parameter used for the simulations. The proposed strategy is validated and the dependency of the objective function with the number of iterations is analyzed. Finally, our approach is experimentally validated on test-bench data of a human wrist phantom, where the estimated blur parameter coincides well with visual inspection. Our findings are not restricted to attenuation-based CT and may facilitate the recovery of more complex imaging model parameters.
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Affiliation(s)
- Lorenz Hehn
- Chair of Biomedical Physics, Department of Physics and Munich School of BioEngineering, Technical University of Munich, 85748 Garching, Germany. Department of Diagnostic and Interventional Radiology, School of Medicine & Klinikum rechts der Isar, Technical University of Munich, 81675 München, Germany. Author to whom correspondence should be addressed
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Tilley S, Jacobson M, Cao Q, Brehler M, Sisniega A, Zbijewski W, Stayman JW. Penalized-Likelihood Reconstruction With High-Fidelity Measurement Models for High-Resolution Cone-Beam Imaging. IEEE TRANSACTIONS ON MEDICAL IMAGING 2018; 37:988-999. [PMID: 29621002 PMCID: PMC5889122 DOI: 10.1109/tmi.2017.2779406] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
We present a novel reconstruction algorithm based on a general cone-beam CT forward model, which is capable of incorporating the blur and noise correlations that are exhibited in flat-panel CBCT measurement data. Specifically, the proposed model may include scintillator blur, focal-spot blur, and noise correlations due to light spread in the scintillator. The proposed algorithm (GPL-BC) uses a Gaussian Penalized-Likelihood objective function, which incorporates models of blur and correlated noise. In a simulation study, GPL-BC was able to achieve lower bias as compared with deblurring followed by FDK as well as a model-based reconstruction method without integration of measurement blur. In the same study, GPL-BC was able to achieve better line-pair reconstructions (in terms of segmented-image accuracy) as compared with deblurring followed by FDK, a model-based method without blur, and a model-based method with blur but not noise correlations. A prototype extremities quantitative cone-beam CT test-bench was used to image a physical sample of human trabecular bone. These data were used to compare reconstructions using the proposed method and model-based methods without blur and/or correlation to a registered CT image of the same bone sample. The GPL-BC reconstructions resulted in more accurate trabecular bone segmentation. Multiple trabecular bone metrics, including trabecular thickness (Tb.Th.) were computed for each reconstruction approach as well as the CT volume. The GPL-BC reconstruction provided the most accurate Tb.Th. measurement, 0.255 mm, as compared with the CT derived value of 0.193 mm, followed by the GPL-B reconstruction, the GPL-I reconstruction, and then the FDK reconstruction (0.271 mm, 0.309 mm, and 0.335 mm, respectively).
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Tilley S, Siewerdsen JH, Zbijewski W, Stayman JW. Nonlinear Statistical Reconstruction for Flat-Panel Cone-Beam CT with Blur and Correlated Noise Models. PROCEEDINGS OF SPIE--THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING 2016; 9783. [PMID: 27110051 DOI: 10.1117/12.2216126] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
Flat-panel cone-beam CT (FP-CBCT) is a promising imaging modality, partly due to its potential for high spatial resolution reconstructions in relatively compact scanners. Despite this potential, FP-CBCT can face difficulty resolving important fine scale structures (e.g, trabecular details in dedicated extremities scanners and microcalcifications in dedicated CBCT mammography). Model-based methods offer one opportunity to improve high-resolution performance without any hardware changes. Previous work, based on a linearized forward model, demonstrated improved performance when both system blur and spatial correlations characteristics of FP-CBCT systems are modeled. Unfortunately, the linearized model relies on a staged processing approach that complicates tuning parameter selection and can limit the finest achievable spatial resolution. In this work, we present an alternative scheme that leverages a full nonlinear forward model with both system blur and spatially correlated noise. A likelihood-based objective function is derived from this forward model and we derive an iterative optimization algorithm for its solution. The proposed approach is evaluated in simulation studies using a digital extremities phantom and resolution-noise trade-offs are quantitatively evaluated. The correlated nonlinear model outperformed both the uncorrelated nonlinear model and the staged linearized technique with up to a 86% reduction in variance at matched spatial resolution. Additionally, the nonlinear models could achieve finer spatial resolution (correlated: 0.10 mm, uncorrelated: 0.11 mm) than the linear correlated model (0.15 mm), and traditional FDK (0.40 mm). This suggests the proposed nonlinear approach may be an important tool in improving performance for high-resolution clinical applications.
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Affiliation(s)
- Steven Tilley
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD
| | | | - Wojciech Zbijewski
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD
| | - J Webster Stayman
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD
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Tilley S, Siewerdsen JH, Stayman JW. Model-based iterative reconstruction for flat-panel cone-beam CT with focal spot blur, detector blur, and correlated noise. Phys Med Biol 2015; 61:296-319. [PMID: 26649783 DOI: 10.1088/0031-9155/61/1/296] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
While model-based reconstruction methods have been successfully applied to flat-panel cone-beam CT (FP-CBCT) systems, typical implementations ignore both spatial correlations in the projection data as well as system blurs due to the detector and focal spot in the x-ray source. In this work, we develop a forward model for flat-panel-based systems that includes blur and noise correlation associated with finite focal spot size and an indirect detector (e.g. scintillator). This forward model is used to develop a staged reconstruction framework where projection data are deconvolved and log-transformed, followed by a generalized least-squares reconstruction that utilizes a non-diagonal statistical weighting to account for the correlation that arises from the acquisition and data processing chain. We investigate the performance of this novel reconstruction approach in both simulated data and in CBCT test-bench data. In comparison to traditional filtered backprojection and model-based methods that ignore noise correlation, the proposed approach yields a superior noise-resolution tradeoff. For example, for a system with 0.34 mm FWHM scintillator blur and 0.70 FWHM focal spot blur, using the correlated noise model instead of an uncorrelated noise model increased resolution by 42% (with variance matched at 6.9 × 10(-8) mm(-2)). While this advantage holds across a wide range of systems with differing blur characteristics, the improvements are greatest for systems where source blur is larger than detector blur.
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Affiliation(s)
- Steven Tilley
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21205, USA
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Liu H, Guo M, Hu Z, Shi P, Hu H. Nonlinear dual reconstruction of SPECT activity and attenuation images. PLoS One 2014; 9:e106951. [PMID: 25225796 PMCID: PMC4167322 DOI: 10.1371/journal.pone.0106951] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2014] [Accepted: 08/08/2014] [Indexed: 11/22/2022] Open
Abstract
In single photon emission computed tomography (SPECT), accurate attenuation maps are needed to perform essential attenuation compensation for high quality radioactivity estimation. Formulating the SPECT activity and attenuation reconstruction tasks as coupled signal estimation and system parameter identification problems, where the activity distribution and the attenuation parameter are treated as random variables with known prior statistics, we present a nonlinear dual reconstruction scheme based on the unscented Kalman filtering (UKF) principles. In this effort, the dynamic changes of the organ radioactivity distribution are described through state space evolution equations, while the photon-counting SPECT projection data are measured through the observation equations. Activity distribution is then estimated with sub-optimal fixed attenuation parameters, followed by attenuation map reconstruction given these activity estimates. Such coupled estimation processes are iteratively repeated as necessary until convergence. The results obtained from Monte Carlo simulated data, physical phantom, and real SPECT scans demonstrate the improved performance of the proposed method both from visual inspection of the images and a quantitative evaluation, compared to the widely used EM-ML algorithms. The dual estimation framework has the potential to be useful for estimating the attenuation map from emission data only and thus benefit the radioactivity reconstruction.
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Affiliation(s)
- Huafeng Liu
- State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou, China
| | - Min Guo
- State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou, China
| | - Zhenghui Hu
- State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou, China
| | - Pengcheng Shi
- B. Thomas Golisano College of Computing and Information Sciences, Rochester Institute of Technology, Rochester, New York, United States of America
| | - Hongjie Hu
- Department of Radiology, Sir Run Run Shaw Hospital, College of Medicine, Zhejiang University, Hangzhou, China
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Stayman JW, Zbijewski W, Tilley S, Siewerdsen J. Generalized Least-Squares CT Reconstruction with Detector Blur and Correlated Noise Models. PROCEEDINGS OF SPIE--THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING 2014; 9033:903335. [PMID: 25328638 DOI: 10.1117/12.2043067] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
The success and improved dose utilization of statistical reconstruction methods arises, in part, from their ability to incorporate sophisticated models of the physics of the measurement process and noise. Despite the great promise of statistical methods, typical measurement models ignore blurring effects, and nearly all current approaches make the presumption of independent measurements - disregarding noise correlations and a potential avenue for improved image quality. In some imaging systems, such as flat-panel-based cone-beam CT, such correlations and blurs can be a dominant factor in limiting the maximum achievable spatial resolution and noise performance. In this work, we propose a novel regularized generalized least-squares reconstruction method that includes models for both system blur and correlated noise in the projection data. We demonstrate, in simulation studies, that this approach can break through the traditional spatial resolution limits of methods that do not model these physical effects. Moreover, in comparison to other approaches that attempt deblurring without a correlation model, superior noise-resolution trade-offs can be found with the proposed approach.
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Affiliation(s)
- J Webster Stayman
- Dept. of Biomedical Eng., Johns Hopkins University, Baltimore, MD USA 21205
| | - Wojciech Zbijewski
- Dept. of Biomedical Eng., Johns Hopkins University, Baltimore, MD USA 21205
| | - Steven Tilley
- Dept. of Biomedical Eng., Johns Hopkins University, Baltimore, MD USA 21205
| | - Jeffrey Siewerdsen
- Dept. of Biomedical Eng., Johns Hopkins University, Baltimore, MD USA 21205
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Stayman JW, Dang H, Ding Y, Siewerdsen JH. PIRPLE: a penalized-likelihood framework for incorporation of prior images in CT reconstruction. Phys Med Biol 2013; 58:7563-82. [PMID: 24107545 PMCID: PMC3868341 DOI: 10.1088/0031-9155/58/21/7563] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Over the course of diagnosis and treatment, it is common for a number of imaging studies to be acquired. Such imaging sequences can provide substantial patient-specific prior knowledge about the anatomy that can be incorporated into a prior-image-based tomographic reconstruction for improved image quality and better dose utilization. We present a general methodology using a model-based reconstruction approach including formulations of the measurement noise that also integrates prior images. This penalized-likelihood technique adopts a sparsity enforcing penalty that incorporates prior information yet allows for change between the current reconstruction and the prior image. Moreover, since prior images are generally not registered with the current image volume, we present a modified model-based approach that seeks a joint registration of the prior image in addition to the reconstruction of projection data. We demonstrate that the combined prior-image- and model-based technique outperforms methods that ignore the prior data or lack a noise model. Moreover, we demonstrate the importance of registration for prior-image-based reconstruction methods and show that the prior-image-registered penalized-likelihood estimation (PIRPLE) approach can maintain a high level of image quality in the presence of noisy and undersampled projection data.
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Affiliation(s)
- J Webster Stayman
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21205, USA
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Nuyts J, De Man B, Fessler JA, Zbijewski W, Beekman FJ. Modelling the physics in the iterative reconstruction for transmission computed tomography. Phys Med Biol 2013. [PMID: 23739261 DOI: 10.1088/0031‐9155/58/12/r63] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.
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Affiliation(s)
- Johan Nuyts
- Department of Nuclear Medicine and Medical Imaging Research Center, KU Leuven, Leuven, Belgium.
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Nuyts J, De Man B, Fessler JA, Zbijewski W, Beekman FJ. Modelling the physics in the iterative reconstruction for transmission computed tomography. Phys Med Biol 2013; 58:R63-96. [PMID: 23739261 PMCID: PMC3725149 DOI: 10.1088/0031-9155/58/12/r63] [Citation(s) in RCA: 97] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.
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Affiliation(s)
- Johan Nuyts
- Department of Nuclear Medicine and Medical Imaging Research Center, KU Leuven, Leuven, Belgium.
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Development and evaluation of QSPECT open-source software for the iterative reconstruction of SPECT images. Nucl Med Commun 2010; 31:558-66. [DOI: 10.1097/mnm.0b013e32833841e8] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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