Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation

Endorectal Digital Prostate Tomosynthesis

Several areas of prostate cancer (PCa) management, such as imaging permanent brachytherapy implants or small, aggressive lesions, benefit from high image resolution. Current PCa imaging methods can have inadequate resolution for imaging these areas. Endorectal digital prostate tomosynthesis (endoDPT), an imaging method that combines an external x-ray source and an endorectal x-ray sensor, can produce three-dimensional images of the prostate region that have high image resolution compared to typical methods. This high resolution may improve PCa management and increase positive outcomes in affected men. This dissertation presents the initial development of endoDPT, including system design, image quality assessment, and examples of possible applications to prostate imaging. Experiments using computational phantoms, physical phantoms, and canine prostate specimens were conducted. Initial system design was performed computationally and three methods of endoDPT image reconstruction were developed: shift and add (SAA), backprojection (BP), and filtered BP (FBP). A physical system was developed using an XDR intraoral x-ray sensor and a GE radiography unit. The resolution and radiation dose of endoDPT were measured and compared to a GE CT scanner. Canine prostate specimens that approximated clinical cases of PCa management were imaged and compared using endoDPT, the above CT scanner, and a GE MRI scanner. This study found that the resolution of endoDPT was significantly higher than CT. The radiation dose of endoDPT was significantly lower than CT in the regions of the phantom that were not in the endoDPT field of view (FoV). Inside the endoDPT FoV, the radiation dose ranged from significantly less than to significantly greater than CT. The endoDPT images of the canine prostate specimens demonstrated qualitative improvements in resolution compared to CT and MRI, but endoDPT had difficulty in visualizing larger structures, such as the prostate border. Overall, this study has demonstrated endoDPT has high image resolution compared to typical methods of PCa imaging. Future work will be focused on development of a prototype system that improves scanning efficiency that can be used to optimize endoDPT and perform pre-clinical studies

Numerical Approaches for Solving the Combined Reconstruction and Registration of Digital Breast Tomosynthesis

Heavy demands on the development of medical imaging modalities for breast cancer detection have been witnessed in the last three decades in an attempt to reduce the mortality associated with the disease. Recently, Digital Breast Tomosynthesis (DBT) shows its promising in the early diagnosis when lesions are small. In particular, it offers potential benefits over X-ray mammography - the current modality of choice for breast screening - of increased sensitivity and specificity for comparable X-ray dose, speed, and cost. An important feature of DBT is that it provides a pseudo-3D image of the breast. This is of particular relevance for heterogeneous dense breasts of young women, which can inhibit detection of cancer using conventional mammography. In the same way that it is difficult to see a bird from the edge of the forest, detecting cancer in a conventional 2D mammogram is a challenging task. Three-dimensional DBT, however, enables us to step through the forest, i.e., the breast, reducing the confounding effect of superimposed tissue and so (potentially) increasing the sensitivity and specificity of cancer detection. The workflow in which DBT would be used clinically, involves two key tasks: reconstruction, to generate a 3D image of the breast, and registration, to enable images from different visits to be compared as is routinely performed by radiologists working with conventional mammograms. Conventional approaches proposed in the literature separate these steps, solving each task independently. This can be effective if reconstructing using a complete set of data. However, for ill-posed limited-angle problems such as DBT, estimating the deformation is difficult because of the significant artefacts associated with DBT reconstructions, leading to severe inaccuracies in the registration. The aim of my work is to find and evaluate methods capable of allying these two tasks, which will enhance the performance of each process as a result. Consequently, I prove that the processes of reconstruction and registration of DBT are not independent but reciprocal. This thesis proposes innovative numerical approaches combining reconstruction of a pair of temporal DBT acquisitions with their registration iteratively and simultaneously. To evaluate the performance of my methods I use synthetic images, breast MRI, and DBT simulations with in-vivo breast compressions. I show that, compared to the conventional sequential method, jointly estimating image intensities and transformation parameters gives superior results with respect to both reconstruction fidelity and registration accuracy

A scalable neural network architecture for self-supervised tomographic image reconstruction

We present a lightweight and scalable artificial neural network architecture which is used to reconstruct a tomographic image from a given sinogram. A self-supervised learning approach is used where the network iteratively generates an image that is then converted into a sinogram using the Radon transform; this new sinogram is then compared with the sinogram from the experimental dataset using a combined mean absolute error and structural similarity index measure loss function to update the weights of the network accordingly. We demonstrate that the network is able to reconstruct images that are larger than 1024 × 1024. Furthermore, it is shown that the new network is able to reconstruct images of higher quality than conventional reconstruction algorithms, such as the filtered back projection and iterative algorithms (SART, SIRT, CGLS), when sinograms with angular undersampling are used. The network is tested with simulated data as well as experimental synchrotron X-ray micro-tomography and X-ray diffraction computed tomography data

High-Resolution Quantitative Cone-Beam Computed Tomography: Systems, Modeling, and Analysis for Improved Musculoskeletal Imaging

This dissertation applies accurate models of imaging physics, new high-resolution imaging hardware, and novel image analysis techniques to benefit quantitative applications of x-ray CT in in vivo assessment of bone health. We pursue three Aims: 1. Characterization of macroscopic joint space morphology, 2. Estimation of bone mineral density (BMD), and 3. Visualization of bone microstructure. This work contributes to the development of extremity cone-beam CT (CBCT), a compact system for musculoskeletal (MSK) imaging. Joint space morphology is characterized by a model which draws an analogy between the bones of a joint and the plates of a capacitor. Virtual electric field lines connecting the two surfaces of the joint are computed as a surrogate measure of joint space width, creating a rich, non-degenerate, adaptive map of the joint space. We showed that by using such maps, a classifier can outperform radiologist measurements at identifying osteoarthritic patients in a set of CBCT scans. Quantitative BMD accuracy is achieved by combining a polyenergetic model-based iterative reconstruction (MBIR) method with fast Monte Carlo (MC) scatter estimation. On a benchtop system emulating extremity CBCT, we validated BMD accuracy and reproducibility via a series of phantom studies involving inserts of known mineral concentrations and a cadaver specimen. High-resolution imaging is achieved using a complementary metal-oxide semiconductor (CMOS)-based x-ray detector featuring small pixel size and low readout noise. A cascaded systems model was used to performed task-based optimization to determine optimal detector scintillator thickness in nominal extremity CBCT imaging conditions. We validated the performance of a prototype scanner incorporating our optimization result. Strong correlation was found between bone microstructure metrics obtained from the prototype scanner and µCT gold standard for trabecular bone samples from a cadaver ulna. Additionally, we devised a multiresolution reconstruction scheme allowing fast MBIR to be applied to large, high-resolution projection data. To model the full scanned volume in the reconstruction forward model, regions outside a finely sampled region-of-interest (ROI) are downsampled, reducing runtime and cutting memory requirements while maintaining image quality in the ROI

Microstructural Quantification, Property Prediction, and Stochastic Reconstruction of Heterogeneous Materials Using Limited X-Ray Tomography Data

abstract: An accurate knowledge of the complex microstructure of a heterogeneous material is crucial for quantitative structure-property relations establishment and its performance prediction and optimization. X-ray tomography has provided a non-destructive means for microstructure characterization in both 3D and 4D (i.e., structural evolution over time). Traditional reconstruction algorithms like filtered-back-projection (FBP) method or algebraic reconstruction techniques (ART) require huge number of tomographic projections and segmentation process before conducting microstructural quantification. This can be quite time consuming and computationally intensive. In this thesis, a novel procedure is first presented that allows one to directly extract key structural information in forms of spatial correlation functions from limited x-ray tomography data. The key component of the procedure is the computation of a “probability map”, which provides the probability of an arbitrary point in the material system belonging to specific phase. The correlation functions of interest are then readily computed from the probability map. Using effective medium theory, accurate predictions of physical properties (e.g., elastic moduli) can be obtained. Secondly, a stochastic optimization procedure that enables one to accurately reconstruct material microstructure from a small number of x-ray tomographic projections (e.g., 20 - 40) is presented. Moreover, a stochastic procedure for multi-modal data fusion is proposed, where both X-ray projections and correlation functions computed from limited 2D optical images are fused to accurately reconstruct complex heterogeneous materials in 3D. This multi-modal reconstruction algorithm is proved to be able to integrate the complementary data to perform an excellent optimization procedure, which indicates its high efficiency in using limited structural information. Finally, the accuracy of the stochastic reconstruction procedure using limited X-ray projection data is ascertained by analyzing the microstructural degeneracy and the roughness of energy landscape associated with different number of projections. Ground-state degeneracy of a microstructure is found to decrease with increasing number of projections, which indicates a higher probability that the reconstructed configurations match the actual microstructure. The roughness of energy landscape can also provide information about the complexity and convergence behavior of the reconstruction for given microstructures and projection number.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201