Automatic alignment for three-dimensional tomographic reconstruction

In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to reconstruct the object. Given noisy and incomplete measurements, the inverse problem is typically solved through a regularized least-squares approach. A challenge for both approaches is that in practice the exact directions and offsets of the x-rays are only known approximately due to, e.g. calibration errors. Such errors lead to artifacts in the reconstructed image. In the case of sufficient sampling and geometrically simple misalignment, the measurements can be corrected by exploiting so-called consistency conditions. In other cases, such conditions may not apply and we have to solve an additional inverse problem to retrieve the angles and shifts. In this paper we propose a general algorithmic framework for retrieving these parameters in conjunction with an algebraic reconstruction technique. The proposed approach is illustrated by numerical examples for both simulated data and an electron tomography dataset

Flexible Attenuation Fields: Tomographic Reconstruction From Heterogeneous Datasets

Traditional reconstruction methods for X-ray computed tomography (CT) are highly constrained in the variety of input datasets they admit. Many of the imaging settings -- the incident energy, field-of-view, effective resolution -- remain fixed across projection images, and the only real variance is in the detector\u27s position and orientation with respect to the scene. In contrast, methods for 3D reconstruction of natural scenes are extremely flexible to the geometric and photometric properties of the input datasets, readily accepting and benefiting from images captured under varying lighting conditions, with different cameras, and at disparate points in time and space. Extending CT to support similar degrees of flexibility would significantly enhance what can be learned from tomographic datasets. We propose that traditionally complicated or time-consuming tomographic tasks, such as multi-resolution and multi-energy analysis, can be more readily achieved with a reconstruction framework which explicitly accepts datasets with varied imaging settings. This work presents a CT reconstruction framework specifically designed for datasets with heterogeneous capture properties which we call Flexible Attenuation Fields (FlexAF). Built on differentiable ray tracing and continuous neural volumes, FlexAF accepts X-ray images captured from any position and orientation in the world coordinate frame, including images which differ in size, resolution, field-of-view, and photometric settings. This method produces reconstructions for regular CT scans which are comparable to those produced by filtered backprojection, demonstrating that additional flexibility does not fundamentally hinder the ability to reconstruct high-quality volumes. Our experiments test the expanded capabilities of FlexAF for addressing challenging reconstruction tasks, including automatic camera calibration and reconstruction of multi-resolution and multi-energy volumes

Geometrical Calibration and Filter Optimization for Cone-Beam Computed Tomography

This thesis will discuss the requirements of a software library for tomography and will derive a framework which can be used to realize various applications in cone-beam computed tomography (CBCT). The presented framework is self-contained and is realized using the MATLAB environment in combination with native low-level technologies (C/C++ and CUDA) to improve its computational performance, while providing accessibility and extendability through to use of a scripting language environment. On top of this framework, the realization of Katsevich’s algorithm on multicore hardware will be explained and the resulting implementation will be compared to the Feldkamp, Davis and Kress (FDK) algorithm. It will also be shown that this helical reconstruction method has the potential to reduce the measurement uncertainty. However, misalignment artifacts appear more severe in the helical reconstructions from real data than in the circular ones. Especially for helical CBCT (H-CBCT), this fact suggests that a precise calibration of the computed tomography (CT) system is inevitable. As a consequence, a self-calibration method will be designed that is able to estimate the misalignment parameters from the cone-beam projection data without the need of any additional measurements. The presented method employs a multi-resolution 2D-3D registration technique and a novel volume update scheme in combination with a stochastic reprojection strategy to achieve a reasonable runtime performance. The presented results will show that this method reaches sub-voxel accuracy and can compete with current state-of-the-art online- and offline-calibration approaches. Additionally, for the construction of filters in the area of limited-angle tomography a general scheme which uses the Approximate Inverse (AI) to compute an optimized set of 2D angle-dependent projection filters will be derived. Optimal sets of filters are then precomputed for two angular range setups and will be reused to perform various evaluations on multiple datasets with a filtered backprojection (FBP)-type method. This approach will be compared to the standard FDK algorithm and to the simultaneous iterative reconstruction technique (SIRT). The results of the study show that the introduced filter optimization produces results comparable to those of SIRT with respect to the reduction of reconstruction artifacts, whereby its runtime is comparable to that of the FDK algorithm

The Estimation and Correction of Rigid Motion in Helical Computed Tomography

X-ray CT is a tomographic imaging tool used in medicine and industry. Although technological developments have significantly improved the performance of CT systems, the accuracy of images produced by state-of-the-art scanners is still often limited by artefacts due to object motion. To tackle this problem, a number of motion estimation and compensation methods have been proposed. However, no methods with the demonstrated ability to correct for rigid motion in helical CT scans appear to exist. The primary aims of this thesis were to develop and evaluate effective methods for the estimation and correction of arbitrary six degree-of-freedom rigid motion in helical CT. As a first step, a method was developed to accurately estimate object motion during CT scanning with an optical tracking system, which provided sub-millimetre positional accuracy. Subsequently a motion correction method, which is analogous to a method previously developed for SPECT, was adapted to CT. The principle is to restore projection consistency by modifying the source-detector orbit in response to the measured object motion and reconstruct from the modified orbit with an iterative reconstruction algorithm. The feasibility of this method was demonstrated with a rapidly moving brain phantom, and the efficacy of correcting for a range of human head motions acquired from healthy volunteers was evaluated in simulations. The methods developed were found to provide accurate and artefact-free motion corrected images with most types of head motion likely to be encountered in clinical CT imaging, provided that the motion was accurately known. The method was also applied to CT data acquired on a hybrid PET/CT scanner demonstrating its versatility. Its clinical value may be significant by reducing the need for repeat scans (and repeat radiation doses), anesthesia and sedation in patient groups prone to motion, including young children

Ultrasound and photoacoustic methods for anatomic and functional imaging in image guided radiation therapy

(MATERIAL and METHODS) First, we define the physical principals and optimal protocols that provide contrast when imaging with US and the transducer properties contributing to resolution limits. The US field of view (FOV) was characterized to determine the optimal settings with regard to imaging depth, focal region, with and without harmonic imaging, and artifact identification. This will allow us to determine the minimum errors expected when registering multimodal volumes (CT, US, CBCT). Next, we designed an in-house integrated US manipulator and platform to relate CT, 3D-US and linear accelerator coordinate systems. To validate our platform, an agar-based phantom with measured densities and speed-of-sound consistent with tissues surrounding the bladder was fabricated. This phantom was rotated relative to the CT and US coordinate systems and imaged with both modalities. These CT and 3D-US images were imported into the treatment planning system, where US-to-US and US-to-CT images were co-registered and the registration matrix used to re-align the phantom relative to the linear accelerator. The measured precision in the phantom setup, which is defined by the standard deviation of the transformation matrix components, was consistent with and exceeding acceptable clinical patient re-alignments (2 mm). Statistical errors from US-US registrations for different patient orientations ranged from 0.06-1.66 mm for x, y, and z translational components, and 0.00-1.05 degrees for rotational components. Statistical errors from US-CT registrations were 0.23-1.18 mm for the x, y and z translational components, and 0.08-2.52 degrees for the rotational components. The high precision in the multimodal registrations suggest the ability to use US for patient positioning when targeting abdominal structures. We are now testing this on a dog patient to obtain both inter and intra-fractional positional errors. The objective of this experiment is to confirm Hill’s equation describing the relationship between hemoglobin saturation (SaO2) and the partial pressure of dissolved oxygen (pO2). The relationship is modeled as a sigmoidal curve that is a function of two parameters – the Hill coefficient, n, and the net association constant of HbO2, K (or pO2 at 50% SaO2). The goal is to noninvasively measure SaO2 in breast tumors in mice using photoacoustic computed tomographic (PCT) imaging and compare those measurements to a gold standard for pO2 using the OxyLite probe. First, a calibration study was performed to measure the SaO2 (co-oximeter) and pO2 (Oxylite probe) in blood using Hill’s equation (P50=23.2 mmHg and n=2.26). Next, non-invasive localized measurements of SaO2 in MDA-MD-231 and MCF7 breast tumors using PCT spectroscopic methods were compared to pO 2 levels using Oxylite probe. The fitted results for MCF7 and MDA-MD-231 data resulted in a P50 of 17.2 mmHg and 20.7 mmHg and a n of 1.76 and 1.63, respectively. The lower value of the P50 is consistent with tumors being more acidic than healthy tissue. Current work applying photon fluence corrections and image artifact reduction is expected to improve the quality of the results. In summary, this study demonstrates that photoacoustic imaging can be used to monitor tumor oxygenation, and its potential use to investigate the effectiveness of radiation therapy and the ability to adapt therapeutic protocols

Assessing and Improving 4D-CT Imaging for Radiotherapy Applications

Lung cancer has both a high incidence and death rate. A contributing factor to these high rates comes from the difficulty of treating lung cancers due to the inherent mobility of the lung tissue and the tumour. 4D-CT imaging has been developed to image lung tumours as they move during respiration. Most 4D-CT imaging methods rely on data from an external respiratory surrogate to sort the images according to respiratory phase. However, it has been shown that respiratory surrogate 4D-CT methods can suffer from imaging artifacts that degrade the image quality of the 4D-CT volumes that are used to plan a patient\u27s radiation therapy. In Chapter 2 of this thesis a method to investigate the correlation between an external respiratory surrogate and the internal anatomy was developed. The studies were performed on ventilated pigs with an induced inconsistent amplitude of breathing. The effect of inconsistent breathing on the correlation between the external marker and the internal anatomy was tested using a linear regression. It was found in 10 of the 12 studies performed that there were significant changes in the slope of the regression line as a result of inconsistent breathing. From this study we conclude that the relationship between an external marker and the internal anatomy is not stable and can be perturbed by inconsistent breathing amplitudes. Chapter 3 describes the development of a image based 4D-CT imaging algorithm based on the concept of normalized cross correlation (NCC) between images. The volumes produced by the image based algorithm were compared to volumes produced using a clinical external marker 4D-CT algorithm. The image based method produced 4D-CT volumes that had a reduced number of imaging artifacts when compared to the external marker produced volumes. It was shown that an image based 4D-CT method could be developed and perform as well or better than external marker methods that are currently in clinical use. In Chapter 4 a method was developed to assess the uncertainties of the locations of anatomical structures in the volumes produced by the image based 4D-CT algorithm developed in Chapter 3. The uncertainties introduced by using NCC to match a pair of images according to respiratory phase were modeled and experimentally determined. Additionally, the assumption that two subvolumes could be matched in respiratory phase using a single pair of 2D overlapping images was experimentally validated. It was shown that when the image based 4D-CT algorithm developed in Chapter 3 was applied to data acquired from a ventilated pig with induced inconsistent breathing the displacement uncertainties were on the order of 1.0 millimeter. The results of this thesis show that there exists the possibility of a miscorrelation between the motion of a respiratory surrogate (marker) and the internal anatomy under inconsistent breathing amplitude. Additionally, it was shown that an image based 4D-CT method that operates without the need of one or more external respiratory surrogate(s) could produce artifact free volumes synchronous with respiratory phase. The spatial uncertainties of the volumes produced by the image based 4D-CT method were quantified and shown to be small (~ 1mm) which is an acceptable accuracy for radiation treatment planning. The elimination of the external respiratory surrogates simplifies the implementation and increases the throughput of the image based 4D-CT method as well

Zero-shot Medical Image Translation via Frequency-Guided Diffusion Models

Recently, the diffusion model has emerged as a superior generative model that can produce high quality and realistic images. However, for medical image translation, the existing diffusion models are deficient in accurately retaining structural information since the structure details of source domain images are lost during the forward diffusion process and cannot be fully recovered through learned reverse diffusion, while the integrity of anatomical structures is extremely important in medical images. For instance, errors in image translation may distort, shift, or even remove structures and tumors, leading to incorrect diagnosis and inadequate treatments. Training and conditioning diffusion models using paired source and target images with matching anatomy can help. However, such paired data are very difficult and costly to obtain, and may also reduce the robustness of the developed model to out-of-distribution testing data. We propose a frequency-guided diffusion model (FGDM) that employs frequency-domain filters to guide the diffusion model for structure-preserving image translation. Based on its design, FGDM allows zero-shot learning, as it can be trained solely on the data from the target domain, and used directly for source-to-target domain translation without any exposure to the source-domain data during training. We evaluated it on three cone-beam CT (CBCT)-to-CT translation tasks for different anatomical sites, and a cross-institutional MR imaging translation task. FGDM outperformed the state-of-the-art methods (GAN-based, VAE-based, and diffusion-based) in metrics of Frechet Inception Distance (FID), Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index Measure (SSIM), showing its significant advantages in zero-shot medical image translation