Optimization of Low-Dose Tomography via Binary Sensing Matrices

X-ray computed tomography (CT) is one of the most widely used imaging modalities for diagnostic tasks in the clinical application. As X-ray dosage given to the patient has potential to induce undesirable clinical consequences, there is a need for reduction in dosage while maintaining good quality in reconstruction. The present work attempts to address low-dose tomography via an optimization method. In particular, we formulate the reconstruction problem in the form of a matrix system involving a binary matrix. We then recover the image deploying the ideas from the emerging field of compressed sensing (CS). Further, we study empirically the radial and angular sampling parameters that result in a binary matrix possessing sparse recovery parameters. The experimental results show that the performance of the proposed binary matrix with reconstruction using TV minimization by Augmented Lagrangian and ALternating direction ALgorithms (TVAL3) gives comparably better results than Wavelet based Orthogonal Matching Pursuit (WOMP) and the Least Squares solution

Modeling and Development of Iterative Reconstruction Algorithms in Emerging X-ray Imaging Technologies

Many new promising X-ray-based biomedical imaging technologies have emerged over the last two decades. Five different novel X-ray based imaging technologies are discussed in this dissertation: differential phase-contrast tomography (DPCT), grating-based phase-contrast tomography (GB-PCT), spectral-CT (K-edge imaging), cone-beam computed tomography (CBCT), and in-line X-ray phase contrast (XPC) tomosynthesis. For each imaging modality, one or more specific problems prevent them being effectively or efficiently employed in clinical applications have been discussed. Firstly, to mitigate the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods in DPCT, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction. Secondly, to improve image quality in grating-based phase-contrast tomography, we incorporate 2nd order statistical properties of the object property sinograms, including correlations between them, into the formulation of an advanced multi-channel (MC) image reconstruction algorithm, which reconstructs three object properties simultaneously. We developed an advanced algorithm based on the proximal point algorithm and the augmented Lagrangian method to rapidly solve the MC reconstruction problem. Thirdly, to mitigate image artifacts that arise from reduced-view and/or noisy decomposed sinogram data in K-edge imaging, we exploited the inherent sparseness of typical K-edge objects and incorporated the statistical properties of the decomposed sinograms to formulate two penalized weighted least square problems with a total variation (TV) penalty and a weighted sum of a TV penalty and an l1-norm penalty with a wavelet sparsifying transform. We employed a fast iterative shrinkage/thresholding algorithm (FISTA) and splitting-based FISTA algorithm to solve these two PWLS problems. Fourthly, to enable advanced iterative algorithms to obtain better diagnostic images and accurate patient positioning information in image-guided radiation therapy for CBCT in a few minutes, two accelerated variants of the FISTA for PLS-based image reconstruction are proposed. The algorithm acceleration is obtained by replacing the original gradient-descent step by a sub-problem that is solved by use of the ordered subset concept (OS-SART). In addition, we also present efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units (GPUs). Finally, we employed our developed accelerated version of FISTA for dealing with the incomplete (and often noisy) data inherent to in-line XPC tomosynthesis which combines the concepts of tomosynthesis and in-line XPC imaging to utilize the advantages of both for biological imaging applications. We also investigate the depth resolution properties of XPC tomosynthesis and demonstrate that the z-resolution properties of XPC tomosynthesis is superior to that of conventional absorption-based tomosynthesis. To investigate all these proposed novel strategies and new algorithms in these different imaging modalities, we conducted computer simulation studies and real experimental data studies. The proposed reconstruction methods will facilitate the clinical or preclinical translation of these emerging imaging methods

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

Reconstruction of sparse-view tomography via preconditioned Radon sensing matrix

Computed Tomography (CT) is one of the significant research areas in the field of medical image analysis. As X-rays used in CT image reconstruction are harmful to the human body, it is necessary to reduce the X-ray dosage while also maintaining good quality of CT images. Since medical images have a natural sparsity, one can directly employ compressive sensing (CS) techniques to reconstruct the CT images. In CS, sensing matrices having low coherence (a measure providing correlation among columns) provide better image reconstruction. However, the sensing matrix constructed through the incomplete angular set of Radon projections typically possesses large coherence. In this paper, we attempt to reduce the coherence of the sensing matrix via a square and invertible preconditioner possessing a small condition number, which is obtained through a convex optimization technique. The stated properties of our preconditioner imply that it can be used effectively even in noisy cases. We demonstrate empirically that the preconditioned sensing matrix yields better signal recovery than the original sensing matrix

Image reconstruction and processing for stationary digital tomosynthesis systems

Digital tomosynthesis (DTS) is an emerging x-ray imaging technique for disease and cancer screening. DTS takes a small number of x-ray projections to generate pseudo-3D images, it has a lower radiation and a lower cost compared to the Computed Tomography (CT) and an improved diagnostic accuracy compared to the 2D radiography. Our research group has developed a carbon nanotube (CNT) based x-ray source. This technology enables packing multiple x-ray sources into one single x-ray source array. Based on this technology, our group built several stationary digital tomosynthesis (s-DTS) systems, which have a faster scanning time and no source motion blur. One critical step in both tomosynthesis and CT is image reconstruction, which generates a 3D image from the 2D measurement. For tomosynthesis, the conventional reconstruction method runs fast but fails in image quality. A better iterative method exists, however, it is too time-consuming to be used in clinics. The goal of this work is to develop fast iterative image reconstruction algorithm and other image processing techniques for the stationary digital tomosynthesis system, improving the image quality affected by the hardware limitation. Fast iterative reconstruction algorithm, named adapted fan volume reconstruction (AFVR), was developed for the s-DTS. AFVR is shown to be an order of magnitude faster than the current iterative reconstruction algorithms and produces better images over the classical filtered back projection (FBP) method. AFVR was implemented for the stationary digital breast tomosynthesis system (s-DBT), the stationary digital chest tomosynthesis system (s-DCT) and the stationary intraoral dental tomosynthesis system (s-IOT). Next, scatter correction technique for stationary digital tomosynthesis was investigated. A new algorithm for estimating scatter profile was developed, which has been shown to improve the image quality substantially. Finally, the quantitative imaging was investigated, where the s-DCT system was used to assess the coronary artery calcium score.Doctor of Philosoph