3D Forward and Back-Projection for X-Ray CT Using Separable Footprints

Iterative methods for 3D image reconstruction have the potential to improve image quality over conventional filtered back projection (FBP) in X-ray computed tomography (CT). However, the computation burden of 3D cone-beam forward and back-projectors is one of the greatest challenges facing practical adoption of iterative methods for X-ray CT. Moreover, projector accuracy is also important for iterative methods. This paper describes two new separable footprint (SF) projector methods that approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. The SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction, whereas the SF-TT projector uses trapezoid functions in both directions. Simulations and experiments showed that both SF projector methods are more accurate than the distance-driven (DD) projector, which is a current state-of-the-art method in the field. The SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. The SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85876/1/Fessler5.pd

High Fidelity System Modeling for High Quality Image Reconstruction in Clinical CT

Today, while many researchers focus on the improvement of the regularization term in IR algorithms, they pay less concern to the improvement of the fidelity term. In this paper, we hypothesize that improving the fidelity term will further improve IR image quality in low-dose scanning, which typically causes more noise. The purpose of this paper is to systematically test and examine the role of high-fidelity system models using raw data in the performance of iterative image reconstruction approach minimizing energy functional. We first isolated the fidelity term and analyzed the importance of using focal spot area modeling, flying focal spot location modeling, and active detector area modeling as opposed to just flying focal spot motion. We then compared images using different permutations of all three factors. Next, we tested the ability of the fidelity terms to retain signals upon application of the regularization term with all three factors. We then compared the differences between images generated by the proposed method and Filtered-Back-Projection. Lastly, we compared images of low-dose in vivo data using Filtered-Back-Projection, Iterative Reconstruction in Image Space, and the proposed method using raw data. The initial comparison of difference maps of images constructed showed that the focal spot area model and the active detector area model also have significant impacts on the quality of images produced. Upon application of the regularization term, images generated using all three factors were able to substantially decrease model mismatch error, artifacts, and noise. When the images generated by the proposed method were tested, conspicuity greatly increased, noise standard deviation decreased by 90% in homogeneous regions, and resolution also greatly improved. In conclusion, the improvement of the fidelity term to model clinical scanners is essential to generating higher quality images in low-dose imaging

Quantifying admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT

Iterative image reconstruction (IIR) with sparsity-exploiting methods, such as total variation (TV) minimization, investigated in compressive sensing (CS) claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is non-trivial, because both full sampling in the discrete-to-discrete imaging model and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. The present article proposes definitions of full sampling by introducing four sufficient-sampling conditions (SSCs). The SSCs are based on the condition number of the system matrix of a linear imaging model and address invertibility and stability. In the example application of breast CT, the SSCs are used as reference points of full sampling for quantifying the undersampling admitted by reconstruction through TV-minimization. In numerical simulations, factors affecting admissible undersampling are studied. Differences between few-view and few-detector bin reconstruction as well as a relation between object sparsity and admitted undersampling are quantified.Comment: Revised version that was submitted to IEEE Transactions on Medical Imaging on 8/16/201

Theoretical and Experimental Evaluation of Spatial Resolution in a Variable Resolution X-Ray Computed Tomography Scanner

A variable resolution x-ray (VRX) computed tomography (CT) scanner can image objects of various sizes with greatly improved spatial resolution. The scanner employs an angulated discrete detector and achieves the resolution boost by matching the detector angulation to the scanner field of view (FOV) determined by the size of an object being imaged. A comprehensive evaluation of spatial resolution in an experimental version of the VRX CT scanner is presented in this dissertation. Two components of this resolution were evaluated – the pre-reconstruction spatial resolution, described by the detector presampling modulation transfer function (MTF), and the post-reconstruction spatial resolution, given by the scanner reconstruction MTF. The detector presampling MTF was modeled by the Monte Carlo simulation and measured by the moving-slit method. The modeled results showed the increase in the maximum cutoff frequency (in the detector plane) from 1.53 to 53.64 cycles per mm (cy/mm) as the scanner FOV decreased from 32 to 1 cm. The measured results supported the modeling, except for the small FOVs (below 8 cm), where the MTF could not be measured up to the cutoff frequency due to the focal-spot limitation. The scanner reconstruction MTF was measured by the special-phantom method. The measured results demonstrated the increase in the average cutoff frequency (in the object plane) from 2.44 to 4.13 cy/mm as the scanner FOV decreased from 16 to 8 cm. The MTF could not be measured at the FOVs other than 8 and 16 cm, due to the calibration-reconstruction inaccuracies and, again, the focal-spot limitation. Overall, the evaluation confirmed the potential value of the VRX CT scanner and produced results important for its further development

Developments in PET-MRI for Radiotherapy Planning Applications

The hybridization of magnetic resonance imaging (MRI) and positron emission tomography (PET) provides the benefit of soft-tissue contrast and specific molecular information in a simultaneous acquisition. The applications of PET-MRI in radiotherapy are only starting to be realised. However, quantitative accuracy of PET relies on accurate attenuation correction (AC) of, not only the patient anatomy but also MRI hardware and current methods, which are prone to artefacts caused by dense materials. Quantitative accuracy of PET also relies on full characterization of patient motion during the scan. The simultaneity of PET-MRI makes it especially suited for motion correction. However, quality assurance (QA) procedures for such corrections are lacking. Therefore, a dynamic phantom that is PET and MR compatible is required. Additionally, respiratory motion characterization is needed for conformal radiotherapy of lung. 4D-CT can provide 3D motion characterization but suffers from poor soft-tissue contrast. In this thesis, I examine these problems, and present solutions in the form of improved MR-hardware AC techniques, a PET/MRI/CT-compatible tumour respiratory motion phantom for QA measurements, and a retrospective 4D-PET-MRI technique to characterise respiratory motion. Chapter 2 presents two techniques to improve upon current AC methods that use a standard helical CT scan for MRI hardware in PET-MRI. One technique uses a dual-energy computed tomography (DECT) scan to construct virtual monoenergetic image volumes and the other uses a tomotherapy linear accelerator to create CT images at megavoltage energies (1.0 MV) of the RF coil. The DECT-based technique reduced artefacts in the images translating to improved μ-maps. The MVCT-based technique provided further improvements in artefact reduction, resulting in artefact free μ-maps. This led to more AC of the breast coil. In chapter 3, I present a PET-MR-CT motion phantom for QA of motion-correction protocols. This phantom is used to evaluate a clinically available real-time dynamic MR images and a respiratory-triggered PET-MRI protocol. The results show the protocol to perform well under motion conditions. Additionally, the phantom provided a good model for performing QA of respiratory-triggered PET-MRI. Chapter 4 presents a 4D-PET/MRI technique, using MR sequences and PET acquisition methods currently available on hybrid PET/MRI systems. This technique is validated using the motion phantom presented in chapter 3 with three motion profiles. I conclude that our 4D-PET-MRI technique provides information to characterise tumour respiratory motion while using a clinically available pulse sequence and PET acquisition method

Statistical Image Reconstruction and Motion Estimation for Image-Guided Radiotherapy.

Image reconstruction and motion estimation are very important for image-guided radiotherapy (IGRT). Three-dimensional reconstruction of patient anatomy using X-ray computed tomography (CT) allows identification of the location of a tumor prior to treatment. The locations of tumorsmay change during actual treatment due to movement such as respiratory motion. Motion estimation helps optimize the accuracy and precision of radiotherapy so that more of the normal surrounding tissue can be spared. This dissertation addresses several important issues related to these two core components of IGRT. Firstly, we developed two new separable footprint (SF) projector methods for X-ray conebeam CT. The SF projectors approximate the voxel footprint functions as 2D separable functions. The SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction, whereas the SF-TT projector uses trapezoid functions in both directions. Both SF projector methods are more accurate than the distance-driven (DD) projector, which is a current state-of-the-art method in the field. The SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. In addition, the SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower. Secondly, we proposed a statistical penalized weighted least-squares (PWLS) method with edge-preserving regularization to reconstruct two basis materials from a single-energy CT scan acquired with differential filtration, such as a split filter or a bow-tie filter. It requires only the use of suitable filters between the X-ray tube and the patient. For both filtration methods, the proposed PWLS method reconstructed soft tissue and bone images with lower RMS errors, reduced the beam-hardening artifacts much more effectively and produced lower noise, as compared with the traditional non-iterative Joseph and Spital method. Thirdly, we conducted an objective characterization of the influence of rotational arc length on accuracy of motion estimation for projection-to-volume targeting during rotational therapy. Simulations illustrate the potential accuracy of limited-angle projection-to-volume alignment. Registration accuracy can be sensitive to angular center, tends to be lower along direction of the projection set, and tends to decrease away from the rotation center.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86254/1/yonglong_1.pd

Uniform framework for the objective assessment and optimisation of radiotherapy image quality

Image guidance has rapidly become central to current radiotherapy practice. A uniform framework is developed for evaluating image quality across all imaging modalities by modelling the ‘universal phantom’: breaking any phantom down into its constituent fundamental test objects and applying appropriate analysis techniques to these through the construction of an automated analysis tree. This is implemented practically through the new software package ‘IQWorks’ and is applicable to both radiotherapy and diagnostic imaging. For electronic portal imaging (EPI), excellent agreement was observed with two commercial solutions: the QC-3V phantom and PIPS Pro software (Standard Imaging) and EPID QC phantom and epidSoft software (PTW). However, PIPS Pro’s noise correction strategy appears unnecessary for all but the highest frequency modulation transfer function (MTF) point and its contrast to noise ratio (CNR) calculation is not as described. Serious flaws identified in epid- Soft included erroneous file handling leading to incorrect MTF and signal to noise ratio (SNR) results, and a sensitivity to phantom alignment resulting in overestimation of MTF points by up to 150% for alignment errors of only ±1 pixel. The ‘QEPI1’ is introduced as a new EPI performance phantom. Being a simple lead square with a central square hole it is inexpensive and straightforward to manufacture yet enables calculation of a wide range of performance metrics at multiple locations across the field of view. Measured MTF curves agree with those of traditional bar pattern phantoms to within the limits of experimental uncertainty. An intercomparison of the Varian aS1000 and aS500-II detectors demonstrated an improvement in MTF for the aS1000 of 50–100% over the clinically relevant range 0.4–1 cycles/mm, yet with a corresponding reduction in CNR by a factor of p 2. Both detectors therefore offer advantages for different clinical applications. Characterisation of cone-beam CT (CBCT) facilities on two Varian On-Board Imaging (OBI) units revealed that only two out of six clinical modes had been calibrated by default, leading to errors of the order of 400 HU for some modes and materials – well outside the ±40 HU tolerance. Following calibration, all curves agreed sufficiently for dose calculation accuracy within 2%. CNR and MTF experiments demonstrated that a boost in MTF f50 of 20–30% is achievable by using a 5122 rather than a 3842 matrix, but with a reduction in CNR of the order of 30%. The MTF f50 of the single-pulse half-resolution radiographic mode of the Varian PaxScan 4030CB detector was measured in the plane of the detector as 1.0±0.1 cycles/mm using both a traditional tungsten edge and the new QEPI1 phantom. For digitally reconstructed radiographs (DRRs), a reduction in CT slice thickness resulted in an expected improvement in MTF in the patient scanning direction but a deterioration in the orthogonal direction, with the optimum slice thickness being 1–2 mm. Two general purposes display devices were calibrated against the DICOM Greyscale Standard Display Function (GSDF) to within the ±20% limit for Class 2 review devices. By providing an approach to image quality evaluation that is uniform across all radiotherapy imaging modalities this work enables consistent end-to-end optimisation of this fundamental part of the radiotherapy process, thereby supporting enhanced use of image-guidance at all relevant stages of radiotherapy and better supporting the clinical decisions based on it

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century