Statistical Reconstruction Methods For Insufficient X-ray CT Projection Data

X-ray computed tomography (CT) technique can provide a cross-section image and has beenextensively applied to a large number of applications in biomedical imaging andnon-destructive detection. However, x-ray is a kind of ionizing radiation, which is harmful tohuman health. As a result, the ALARA (As Low As Reasonably Achievalbe) principle hasbeen proposed by medical community. There are two ways for dose reduction: one is toweaken the x-ray flux towards each detector element via adjusting the operating current andtime of an x-ray tube, and the other is to decrease the number of x-ray attenuation measuresacross a whole object to be reconstructed. These ways will lead to noisy, truncated,down-sampled and other insufficient projection data. In addition, the limitations in scanninggeometry, such as the limitation of detector size, usually lead to the truncated projection datain practice. In above situations, because the insufficient projection data dissatisfies the exactreconstruction condition, conventional reconstruction methods will result in images withpoor quality. Therefore, the research about the reconstruction method for insufficientprojection data is very useful not only for reducing radiation dose while maintaining thediagnostic performance but also for reducing the limitations in system geometry.Iterative reconstruction method which reconstructs the image through optimizing theobjective function iteratively is an effective way to solve the reconstruction problem ofinsufficient projection data. It has a lower demand on the completeness of projection dataand is easier to take into account the physical model and prior information in thereconstruction than analytical reconstruction method. In practice, the measured data followssome kinds of statistical distributions. Statistical reconstruction method considering this kindof statistical property of projection data in the process of developing its objective functionhas a better performance on suppressing noise and artifacts in the result, especially for noisydata. On the other hand, compressive sensing (CS) theory proved that a sparse signal can berecovered from the samples much less than the requirement of Shannon/Nyquist theory,which provides a way to solve the reconstruction problem of insufficient projection data.Based on the CS theory, iterative reconstruction with a sparse constraint can be used toobtain decent results for the interior problem, few-view tomography and other insufficient data reconstruction problems. Hence, prior information and constraints are necessary forinsufficient data reconstruction, and statistical iterative reconstruction framework whichconsiders the statistical property of data can combine these prior constraints with projectiondata fidelity better.As above, this dissertation focuses on incorporating suitable prior information andconstraints into the statistical iterative reconstruction framework for the reconstruction ofinsufficient projection data, especially for the interior problem, few-view tomography andhighly noisy data. The goal pursued by this work is to develop advanced reconstructionmethods which have a better performance on the insufficient data in practice. The details areas follows:1. The improved total variation (TV) method based CT reconstruction. Based on the CStheory, the iterative reconstruction with a TV minimization constraint can lead to decentresult from insufficient projection data. In order to make a better balance betweensuppressing noise and preserving edge, an improved variation is proposed. An anisotropicstrategy is developed to effectively preserve the edges of imaging objects and an amplitudedependent weight is used to suppress the smaller variations. The simulation results show thatthis method performs better than its original TV counterpart.2. Statistical interior tomography. Interior problem is to reconstruct an interior region ofinterest (ROI) from the truncated projection data along the lines only through the ROI. Thisscanning mode can not only greatly reduce the x-ray dose outside the ROI but also reducethe detector size. The current interior tomography methods did not take into account thestatistical nature of projection data, and will not work well in the case of low count data. Toimprove interior tomography for further radiation dose reduction and faster data acquisition,it is natural to consider the statistical property of local projection data. Therefore, thisdissertation presents a statistical interior tomography method making use of CS theory. A TVregularization term is formulated in the maximization of a posteriori (MAP) frameworkincorporating other constraints to solve the interior problem. Numerical simulation and realdata experiments extensively validate the proposed method for the interior tomography ofnoisy and few-view data.3. Interior tomography associated with Hilbert data statistically. Further studies onstatistical interior tomography are carried out. Two kinds of statistical interior tomographyare developed considering the statistical property of Hilbert data. One is the statisticalinterior tomography associated with the optimized THT data, which optimizes the THT datastatistically in each iteration of statistical iterative reconstruction. Another is the faststatistical interior tomography, which incorporates the statistical property of THT data andthe TV minimization constraint into the THT based interior tomography framework. Thesetwo methods are validated by numerical simulation. 4. Hybrid true-color micro-CT system design and image reconstruction. Micro-CT has ahigher spatial resolution and is very useful for biomedical research. To improve its contrastresolution with lower system cost and radiation dose, a hybrid true-color micro-CT system isdesigned and the related image reconstruction method is developed. This systemincorporates an energy-resolved photon-counting detector into the conventional micro-CT,which provides both a global gray-scale reconstruction and a true-color ROI reconstruction.The proposed system and algorithm are extensively validated by numerical simulation,physical phantom experiment and animal studies.5. Dictionary learning based low-dose CT reconstruction. A dictionary is an over-completebasis learned from patches extracted from training images, so that it is expected to have abetter sparsifying capability than any generic sparse transform. This dissertation introducesdictionary learning into CT reconstruction. The sparsity constraint in terms of either a globalor adaptive dictionary has been introduced into the statistical iterative reconstructionframework. Numerical simulation and real data experiments validate the proposed methodcan produce promising results in terms of preserving details and suppressing noise.Especially, it outperforms the TV minimization method for low-dose CT.