Stability estimates for the regularized inversion of the truncated Hilbert transform

In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in L^2(\mathcal F)$, where $\mathcal F$ is a finite interval, from its partial Hilbert transform data. When the Hilbert transform is measured on a finite interval $\mathcal G$ that only overlaps but does not cover $\mathcal F$ this inversion problem is known to be severely ill-posed [1]. In this paper, we study the reconstruction of $f$ restricted to the overlap region $\mathcal F \cap \mathcal G$. We show that with this restriction and by assuming prior knowledge on the $L^2$ norm or on the variation of $f$, better stability with H\"older continuity (typical for mildly ill-posed problems) can be obtained.Comment: added one remark, larger fonts for axis labels in figure

Shearlet-based regularized reconstruction in region-of-interest computed tomography

Region of interest (ROI) tomography has gained increasing attention in recent years due to its potential to reducing radiation exposure and shortening the scanning time. However, tomographic reconstruction from ROI-focused illumination involves truncated projection data and typically results in higher numerical instability even when the reconstruction problem has unique solution. To address this problem, both ad hoc analytic formulas and iterative numerical schemes have been proposed in the literature. In this paper, we introduce a novel approach for ROI tomographic reconstruction, formulated as a convex optimization problem with a regularized term based on shearlets. Our numerical implementation consists of an iterative scheme based on the scaled gradient projection method and it is tested in the context of fan-beam CT. Our results show that our approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.Peer reviewe

Qualitative and quantitative schlieren optical measurement of the human thermal plume

A new large‐field, high‐sensitivity, single‐mirror coincident schlieren optical instrument has been installed at the Bauhaus‐Universität Weimar for the purpose of indoor air research. Its performance is assessed by the non‐intrusive measurement of the thermal plume of a heated manikin. The schlieren system produces excellent qualitative images of the manikin's thermal plume and also quantitative data, especially schlieren velocimetry of the plume's velocity field that is derived from the digital cross‐correlation analysis of a large time sequence of schlieren images. The quantitative results are compared with thermistor and hot‐wire anemometer data obtained at discrete points in the plume. Good agreement is obtained, once the differences between path‐averaged schlieren data and planar anemometry data are reconciled

Synergistic multi-spectral CT reconstruction with directional total variation

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel. We propose to fuse these available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyse the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.</p

Synergistic multi-spectral CT reconstruction with directional total variation

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel. We propose to fuse these available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyse the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.Peer reviewe

Robust and stable region-of-interest tomographic reconstruction using a robust width prior

Region-of-interest computed tomography (ROI CT) aims at reconstructing a region within the field of view by using only ROI-focused projections. The solution of this inverse problem is challenging and methods of tomographic reconstruction that are designed to work with full projection data may perform poorly or fail when applied to this setting. In this work, we study the ROI CT problem in the presence of measurement noise and formulate the reconstruction problem by relaxing data fidelity and consistency requirements. Under the assumption of a robust width prior that provides a form of stability for data satisfying appropriate sparsity-inducing norms, we derive reconstruction performance guarantees and controllable error bounds. Based on this theoretical setting, we introduce a novel iterative reconstruction algorithm from ROI-focused projection data that is guaranteed to converge with controllable error while satisfying predetermined fidelity and consistency tolerances. Numerical tests on experimental data show that our algorithm for ROI CT is competitive with state-of-the-art methods especially when the ROI radius is small

VOXEL-FREE RADON TRANSFORM FOR IMPROVING SURFACE QUALITY IN COMPUTED AXIAL LITHOGRAPHY

Computed axial lithography (CAL) is an additive manufacturing process that projects light patterns onto a rotating vial of photosensitive resin to print the desired object through the superposition of light energy. Currently, these projection patterns are generated by voxelizing a target object from an STL or another 3D file format and applying the Radon transform through an iterative optimization process. In this work, a voxel-free method to generate projection sets is proposed. Here, the Radon transform is performed directly on a non-voxelized target object by calculating intersections between incident rays of light and triangles of the original STL surface mesh. Initial simulated results show a more consistent light dose at the surface of the object, indicating improved surface quality and smoothness. Additionally, simulations show a more uniform object interior using the proposed method as well as the potential for improved speed scaling with object size.Mechanical Engineerin

Kinetics of protein-based in vivo Imaging tracers for positron emission tomography

Within the framework of the “Sel-tag imaging project”, a novel method was used to rapidly label protein tracers and the in vivo targeting abilities of these tracers were studied in animal models of cancer using a preclinical positron emission tomography (PET) camera. To first evaluate and optimize preclinically the use of PET tracers can facilitate their translation to and implementation in human patient studies. The ultimate goal of the different projects within the Sel-tag imaging project was to find imaging biomarkers that could potentially be used for individualizing cancer treatment and thereby improve the therapeutic results. This thesis focuses on methods employed to describe the distribution of these protein-based tracers in human xenografts. Many of the techniques used had been developed for other imaging circumstances. Therefore verification for these imaging applications was an important aspect of these papers. Paper I examined the distribution in a tumour of a medium-sized AnnexinA5-based tracer that targeted phosphatidylserine externalised during cell death in tumours in two cases; first, with no pre-treatment (baseline) and, second, after pre-treatment with a chemotherapeutic agent. Small differences between tracer uptakes in the two cases required a macro parameter analysis method for quantifications. Evaluations of the influence of the enhanced permeability and retention effect by using a size-matched control were introduced. The AnnexinA5 results were compared to those of the metabolic tracer [18F]FDG and complemented with circulating serum markers to increase sensitivity. Paper II extended the analysis in paper I to incorporate more verifications that were also more thorough. The choice of input (blood or reference tissue) and the statistical significance of intergroup comparisons when using conventional uptake measurements and the more involved macro parameter analyses like in paper I were compared. We also proposed that distribution volume ratio was a more appropriate quantification parameter concept for these protein-based tracers with relatively large non-specific uptake. Paper III assessed the smaller Affibody™ tracer ZHER2:342 as an imaging biomarker for human epidermal growth factor 2 (HER2), whose overexpressions are associated with a poor prognosis for breast cancer patients. In order to demonstrate specific binding to HER2, pre-treatment of the tumour with unlabelled protein and uptake in xenografts with low HER2 expression was evaluated. Ex vivo immunohistochemistry of expression levels supported the imaging results. Paper IV examined a radiopharmaceutical that targeted the epidermal growth factor receptor (EGFR), whose overexposure in tumours is associated with a negative prognosis. Again an Affibody™ molecule, (ZEGFR:2377), was used and, as in in paper I, a size-matched control was also used to estimate the non-specific uptake. Uptakes, quantified by conventional uptake methods, varied in tumours with different EGFR expression levels. Ex vivo analyses of expression levels were also performed. Paper V addressed the non-uniform (heterogeneous) uptake of different tracers in a tumour tissue. An algorithm was written that aimed at incorporating all relevant aspects that will influence non-uniformity. Histograms were generated that visualized how the frequency and spread of deviations contributed to the heterogeneity. These aspects could not always be attended in a direct manner, but instead had to be handled in an indirect way. The effect of varying imaging parameters was examined as part of the validation procedure. The method developed is a robust, user-friendly tool for comparing heterogeneity in similar volume preclinical tumor tissues

Task-Driven Trajectory Design for Endovascular Embolization

Computed Tomography (CT) is one of the most useful and widely applied imaging modalities, employed in both diagnostic and treatment planning purposes in the medical field. Circular and spiral acquisition trajectories are traditionally employed and work well in many cases. The advent of technologies such as robotic C-arms in interventional imaging allow for more complex data acquisitions, which enables potential improvements in image quality, increased field of view, and sampling. This capability has particular potential crucial in interventional cases where images may be compromised by complex anatomy or surgical tools. In this work, we present a paradigm that uses custom non-circular orbits and prior patient information along with segmentation and registration techniques to account for surgical tools and/or implants, to improve image quality. The framework leverages the anatomical model to optimize a parameterized source-detector trajectory for a variety of specific imaging tasks. We propose an overall workflow for orbit customization with investigations of the various workflow stages as well as the overall performance of the framework