Joint Estimation of Image and Deformation Parameters in Tomographic Image Reconstruction

We consider an emission tomography reconstruction problem in which projection measurements from several successive time frames are available. Two strategies for doing motion-corrected image reconstruction are compared. In the first strategy, separate images are reconstructed from the measurements at each time frame. They are then consolidated by post-registration and averaging procedures. In the second strategy, parameters to describe the effects of motion are added to the statistical model of the projections. Joint maximum likelihood estimation of image and motion parameters is then carried out.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85809/1/Fessler184.pd

Reconstruction Algorithms for Novel Joint Imaging Techniques in PET

Positron emission tomography (PET) is an important functional in vivo imaging modality with many clinical applications. Its enormously wide range of applications has made both research and industry combine it with other imaging modalities such as X-ray computed tomography (CT) or magnetic resonance imaging (MRI). The general purpose of this work is to study two cases in PET where the goal is to perform image reconstruction jointly on two data types. The first case is the Beta-Gamma image reconstruction. Positron emitting isotopes, such as 11C, 13N, and 18F, can be used to label molecules, and tracers, such as 11CO2, are delivered to plants to study their biological processes, particularly metabolism and photosynthesis, which may contribute to the development of plants that have higher yield of crops and biomass. Measurements and resulting images from PET scanners are not quantitative in young plant structures or in plant leaves due to low positron annihilation in thin objects. To address this problem we have designed, assembled, modeled, and tested a nuclear imaging system (Simultaneous Beta-Gamma Imager). The imager can simultaneously detect positrons (β+) and coincidence-gamma rays (γ). The imaging system employs two planar detectors; one is a regular gamma detector which has a LYSO crystal array, and the other is a phoswich detector which has an additional BC-404 plastic scintillator for beta detection. A forward model for positrons is proposed along with a joint image reconstruction formulation to utilize the beta and coincidence-gamma measurements for estimating radioactivity distribution in plant leaves. The joint reconstruction algorithm first reconstructs the beta and gamma images independently to estimate the thickness component of the beta forward model, and then jointly estimates the radioactivity distribution in the object. We have validated the physics model and the reconstruction framework through a phantom imaging study and imaging a tomato leaf that has absorbed 11CO2. The results demonstrate that the simultaneously acquired beta and coincidence-gamma data, combined with our proposed joint reconstruction algorithm, improved the quantitative accuracy of estimating radioactivity distribution in thin objects such as leaves. We used the Structural Similarity (SSIM) index for comparing the leaf images from the Simultaneous Beta-Gamma Imager with the ground truth image. The jointly reconstructed images yield SSIM indices of 0.69 and 0.63, whereas the separately reconstructed beta alone and gamma alone images had indices of 0.33 and 0.52, respectively. The second case is the virtual-pinhole PET technology, which has shown that higher resolution and contrast recovery can be gained by adding a high resolution PET insert with smaller crystals to a conventional PET scanner. Such enhancements are obtained when the insert is placed in proximity of the region of interest (ROI) and in coincidence with the conventional PET scanner. Intuitively, the insert may be positioned within the scanner\u27s axial field-of-view (FOV) and radially closer to the ROI than the scanner\u27s ring. One of the complicating factors of this design is the insert\u27s blocking the scanner\u27s lines-of-response (LORs). Such data may be compensated through attenuation and scatter correction in image reconstruction. However, a potential solution is to place the insert outside of the scanner\u27s axial FOV and to move the body to be in proximity of the insert. We call this imaging strategy the surveillance mode. As the main focus of this work, we have developed an image reconstruction framework for the surveillance mode imaging. The preliminary results show improvement in spatial resolution and contrast recovery. Any improvement in contrast recovery should result in enhancement in tumor detectability, which will be of high clinical significance

Reconstruction Algorithms for Novel Joint Imaging Techniques in PET

Positron emission tomography (PET) is an important functional in vivo imaging modality with many clinical applications. Its enormously wide range of applications has made both research and industry combine it with other imaging modalities such as X-ray computed tomography (CT) or magnetic resonance imaging (MRI). The general purpose of this work is to study two cases in PET where the goal is to perform image reconstruction jointly on two data types. The first case is the Beta-Gamma image reconstruction. Positron emitting isotopes, such as 11C, 13N, and 18F, can be used to label molecules, and tracers, such as 11CO2, are delivered to plants to study their biological processes, particularly metabolism and photosynthesis, which may contribute to the development of plants that have higher yield of crops and biomass. Measurements and resulting images from PET scanners are not quantitative in young plant structures or in plant leaves due to low positron annihilation in thin objects. To address this problem we have designed, assembled, modeled, and tested a nuclear imaging system (Simultaneous Beta-Gamma Imager). The imager can simultaneously detect positrons (β+) and coincidence-gamma rays (γ). The imaging system employs two planar detectors; one is a regular gamma detector which has a LYSO crystal array, and the other is a phoswich detector which has an additional BC-404 plastic scintillator for beta detection. A forward model for positrons is proposed along with a joint image reconstruction formulation to utilize the beta and coincidence-gamma measurements for estimating radioactivity distribution in plant leaves. The joint reconstruction algorithm first reconstructs the beta and gamma images independently to estimate the thickness component of the beta forward model, and then jointly estimates the radioactivity distribution in the object. We have validated the physics model and the reconstruction framework through a phantom imaging study and imaging a tomato leaf that has absorbed 11CO2. The results demonstrate that the simultaneously acquired beta and coincidence-gamma data, combined with our proposed joint reconstruction algorithm, improved the quantitative accuracy of estimating radioactivity distribution in thin objects such as leaves. We used the Structural Similarity (SSIM) index for comparing the leaf images from the Simultaneous Beta-Gamma Imager with the ground truth image. The jointly reconstructed images yield SSIM indices of 0.69 and 0.63, whereas the separately reconstructed beta alone and gamma alone images had indices of 0.33 and 0.52, respectively. The second case is the virtual-pinhole PET technology, which has shown that higher resolution and contrast recovery can be gained by adding a high resolution PET insert with smaller crystals to a conventional PET scanner. Such enhancements are obtained when the insert is placed in proximity of the region of interest (ROI) and in coincidence with the conventional PET scanner. Intuitively, the insert may be positioned within the scanner\u27s axial field-of-view (FOV) and radially closer to the ROI than the scanner\u27s ring. One of the complicating factors of this design is the insert\u27s blocking the scanner\u27s lines-of-response (LORs). Such data may be compensated through attenuation and scatter correction in image reconstruction. However, a potential solution is to place the insert outside of the scanner\u27s axial FOV and to move the body to be in proximity of the insert. We call this imaging strategy the surveillance mode. As the main focus of this work, we have developed an image reconstruction framework for the surveillance mode imaging. The preliminary results show improvement in spatial resolution and contrast recovery. Any improvement in contrast recovery should result in enhancement in tumor detectability, which will be of high clinical significance

Reduction of Limited Angle Artifacts in Medical Tomography via Image Reconstruction

Artifacts are unwanted effects in tomographic images that do not reflect the nature of the object. Their widespread occurrence makes their reduction and if possible removal an important subject in the development of tomographic image reconstruction algorithms. Limited angle artifacts are caused by the limited angular measurements, constraining the available tomographic information. This thesis focuses on reducing these artifacts via image reconstruction in two cases of incomplete measurements from: (1) the gaps left after the removal of high density objects such as dental fillings, screws and implants in computed tomography (CT) and (2) partial ring scanner configurations in positron emission tomography (PET). In order to include knowledge about the measurement and noise, prior terms were used within the reconstruction methods. Careful consideration was given to the trade-off between image blurring and noise reduction upon reconstruction of low-dose measurements.Development of reconstruction methods is an incremental process starting with testing on simple phantoms towards more clinically relevant ones by modeling the respective physical processes involved. In this work, phantoms were constructed to ensure that the proposed reconstruction methods addressed to the limited angle problem. The reconstructed images were assessed qualitatively and quantitatively in terms of noise reduction, edge sharpness and contrast recovery.Maximum a posteriori (MAP) estimation with median root prior (MRP) was selected for the reconstruction of limited angle measurements. MAP with MRP successfully reduced the artifacts caused by limited angle data in various datasets, tested with the reconstruction of both list-mode and projection data. In all cases, its performance was found to be superior to conventional reconstruction methods such as total-variation (TV) prior, maximum likelihood expectation maximization (MLEM) and filtered backprojection (FBP). MAP with MRP was also more robust with respect to parameter selection than MAP with TV prior.This thesis demonstrates the wide-range applicability of MAP with MRP in medical tomography, especially in low-dose imaging. Furthermore, we emphasize the importance of developing and testing reconstruction methods with application-specific phantoms, together with the properties and limitations of the measurements in mind

Non-uniform resolution and partial volume recovery in tomographic image reconstruction methods

Acquired data in tomographic imaging systems are subject to physical or detector based image degrading effects. These effects need to be considered and modeled in order to optimize resolution recovery. However, accurate modeling of the physics of data and acquisition processes still lead to an ill-posed reconstruction problem, because real data is incomplete and noisy. Real images are always a compromise between resolution and noise; therefore, noise processes also need to be fully considered for optimum bias variance trade off. Image degrading effects and noise are generally modeled in the reconstruction methods, while, statistical iterative methods can better model these effects, with noise processes, as compared to the analytical methods. Regularization is used to condition the problem and explicit regularization methods are considered better to model various noise processes with an extended control over the reconstructed image quality. Emission physics through object distribution properties are modeled in form of a prior function. Smoothing and edge-preserving priors have been investigated in detail and it has been shown that smoothing priors over-smooth images in high count areas and result in spatially non-uniform and nonlinear resolution response. Uniform resolution response is desirable for image comparison and other image processing tasks, such as segmentation and registration. This work proposes methods, based on MRPs in MAP estimators, to obtain images with almost uniform and linear resolution characteristics, using nonlinearity of MRPs as a correction tool. Results indicate that MRPs perform better in terms of response linearity, spatial uniformity and parameter sensitivity, as compared to QPs and TV priors. Hybrid priors, comprised of MRPs and QPs, have been developed and analyzed for their activity recovery performance in two popular PVC methods and for an analysis of list-mode data reconstruction methods showing that MPRs perform better than QPs in different situations

Tomographic Reconstruction of 2-D Atmospheric Trace Gas Distributions from Active DOAS Measurements

Applying the tomographic principle to active DOAS remote sensing leads to a novel technique for the measurement of atmospheric trace gas distributions. Standard analytical methods for the reconstruction of a scalar field from its line integrals cannot be used due to low numbers of light paths (10-50) and their irregular arrangement, so that the concentration field is expanded into a limited number of local (piecewise constant or linear) basis functions instead. The resulting discrete linear inverse problem is solved by a least squares-minimum norm principle. For sharp 2-D concentration peaks it is shown systematically with respect to their extension how the optimal choice of parametrisation (in terms of number and kind of basis functions) and a priori can tremendously improve the reconstruction. Regularisation plays a minor role. Proposals for retrieving peak distributions by combining different parametrisations are again examined systematically showing that their usefulness heavily depends on the features one is most interested in. Comparison of different 2-D light path geometries reveals that linear independency within the associated systems is pivotal. A detailed analysis of the reconstruction error points out special issues of tomography with only few integration paths and argues that a complete error estimation is not possible without a priori assumptions. Based on this discussion a numerical scheme for calculating the reconstruction error is suggested. The findings are applied to an indoor experiment simulating narrow emission puffs and 2-D model distributions above a street canyon, respectively. For the latter case it is demonstrated how model evaluation can be possible even with a relatively small number of light paths. Contrary to the reconstruction of peak distributions regularisation becomes crucial