Glenn R. Myers

High-resolution helical cone-beam micro-CT with theoretically-exact reconstruction from experimental data

PURPOSE In this paper we show that optimization-based autofocus may be used to overcome the instabilities that have, until now, made high-resolution theoretically-exact tomographic reconstruction impractical. To our knowledge, this represents the first successful use of theoretically-exact reconstruction in helical micro computed tomography (micro-CT) imaging. We show that autofocus-corrected, theoretically-exact helical CT is a viable option for high-resolution micro-CT imaging at high cone-angles (∼50°). The elevated cone-angle enables better utilization of the available X-ray flux and therefore shorter image acquisition time than conventional micro-CT systems. METHODS By using the theoretically-exact Katsevich 1PI inversion formula, we are not restricted to a low-cone-angle regime; we can in theory obtain artefact-free reconstructions from projection data acquired at arbitrary high cone-angles. However, this reconstruction method is sensitive to misalignments in the tomographic data, which result in geometric distortion and streaking artefacts. We use a parametric model to quantify the deviation between the actual acquisition trajectory and an ideal helix, and use an autofocus method to estimate the relevant parameters. We define optimal units for each parameter, and use these to ensure consistent alignment accuracy across different cone-angles and different magnification factors. The tomographic image is obtained from a set of virtual projections in which software correction for hardware misalignment has been applied. RESULTS We make significant modifications to the autofocus method that allow this method to be used in helical micro-CT reconstruction, and show that these developments enable theoretically-exact reconstruction from experimental data using the Katsevich 1PI (K1PI) inversion formula. We further demonstrate how autofocus-corrected, theoretically-exact helical CT reduces the image acquisition time by an order of magnitude compared to conventional circular scan micro-CT. CONCLUSIONS Autofocus-corrected, theoretically-exact cone-beam reconstruction is a viable option for reducing acquisition time in high-resolution micro-CT imaging. It also opens up the possibility of efficiently imaging long objects.

Reliable automatic alignment of tomographic projection data by passive auto-focus.

PURPOSE The authors present a robust algorithm that removes the blurring and double-edge artifacts in high-resolution computed tomography (CT) images that are caused by misaligned scanner components. This alleviates the time-consuming process of physically aligning hardware, which is of particular benefit if components are moved or swapped frequently. METHODS The proposed method uses the experimental data itself for calibration. A parameterized model of the scanner geometry is constructed and the parameters are varied until the sharpest 3D reconstruction is found. The concept is similar to passive auto-focus algorithms of digital optical instruments. The parameters are used to remap the projection data from the physical detector to a virtual aligned detector. This is followed by a standard reconstruction algorithm, namely the Feldkamp algorithm. Feldkamp et al. [J. Opt. Soc. Am. A 1, 612-619 (1984)]. RESULTS An example implementation is given for a rabbit liver specimen that was collected with a circular trajectory. The optimal parameters were determined in less computation time than that for a full reconstruction. The example serves to demonstrate that (a) sharpness is an appropriate measure for projection alignment, (b) our parameterization is sufficient to characterize misalignments for cone-beam CT, and (c) the procedure determines parameter values with sufficient precision to remove the associated artifacts. CONCLUSIONS The algorithm is fully tested and implemented for regular use at The Australian National University micro-CT facility for both circular and helical trajectories. It can in principle be applied to more general imaging geometries and modalities. It is as robust as manual alignment but more precise since we have quantified the effect of misalignment.

Phase-contrast tomography of single-material objects from few projections

A method is presented for quantitative polychromatic cone-beam phase-contrast tomographic imaging of a single-material object from few projections. This algorithm exploits the natural combination of binary tomography with a phase-retrieval method that makes explicit use of the single-material nature of the sample. Such consistent use of a priori knowledge reduces the number of required projections, implying significantly reduced dose and scanning time when compared to existing phase-contrast tomography methods. Reconstructions from simulated data sets are used to investigate the effects of noise and establish a minimum required number of projections. An experimental demonstration is then given, using data from a point-projection X-ray microscope. Here, the complex distribution of refractive index in a sample containing several nylon fibers with diameters between 100 microm and 420 microm is reconstructed at a spatial resolution of approximately 4 microm from 20 polychromatic phase-contrast projection images with a mean photon energy of 8.4 keV.

Extending reference scan drift correction to high-magnification high-cone-angle tomography.

The reference scan method is a simple yet powerful method for measuring spatial drift of the x-ray spot during a low-cone-angle μ-CT experiment. As long as the drift is smooth, and occurring on a time scale that is long compared to the acquisition time of each projection, this method provides a way to compensate for the drift by applying 2D in-plane translations to the radiographs. Here we show that this compensation may be extended to the regime of high-magnification, high-cone-angle CT experiments where source drift perpendicular to the detector plane can cause significant magnification changes throughout the acquisition.

Stability of phase-contrast tomography

Phase-contrast tomography (PCT) allows three-dimensional imaging of objects that display insufficient contrast for conventional absorption-based tomography. We prove that PCT is stable with respect to high-frequency noise in experimental phase-contrast data, unlike conventional tomography, which is known to be mildly unstable. We use known properties of the three-dimensional x-ray transform and transport-of-intensity equation to construct a matrix representation of the forward PCT operator. We then invert this formula to show that, under natural boundary conditions, the PCT reconstruction operator exists and leads to a unique solution. We show that the singular values s(n) of the reconstruction operator have asymptotic behavior s(n)=O(n(-3/2)), guaranteeing the mathematical stability of the reconstruction process.

A general few-projection method for tomographic reconstruction of samples consisting of several distinct materials

We present a method for tomographic reconstruction of objects containing several distinct materials, which is capable of accurately reconstructing a sample from vastly fewer angular projections than required by conventional algorithms. The algorithm is more general than many previous discrete tomography methods, as: (i) a priori knowledge of the exact number of materials is not required; (ii) the linear attenuation coefficient of each constituent material may assume a small range of a priori unknown values. We present reconstructions from an experimental x-ray computed tomography scan of cortical bone acquired at the SPring-8 synchrotron.

Considerations for high-magnification high-cone-angle helical micro-CT

This paper is motivated by our groups recent move from a conventional micro-CT system with a circular source-trajectory, to that with with a helical source-trajectory. By using a helix we can now image well beyond the limiting cone-angle of 10 degrees for a circle. We routinely perform micro-CT with cone-angles greater than 50° by using the Katsevich theoretically-exact reconstruction algorithm. Imaging with such large cone-angles enables high-signal-to-noise-ratio imaging but requires the specimen to be in a very close proximity to the source. This brings about its own challenges. Here we present experimental considerations and data post-processing techniques that allow us to obtain high-fidelity high-resolution micro-CT images at extreme cone-angles.

Multi-resolution radiograph alignment for motion correction in x-ray micro-tomography

Achieving sub-micron resolution in lab-based micro-tomography is challenging due to the geometric instability of the imaging hardware (spot drift, stage precision, sample motion). These instabilities manifest themselves as a distortion or motion of the radiographs relative to the expected system geometry. When the hardware instabilities are small (several microns of absolute motion), the radiograph distortions are well approximated by shift and magnification of the image. In this paper we examine the use of re-projection alignment (RA) to estimate per-radiograph motions. Our simulation results evaluate how the convergence properties of RA vary with: motion-type (smooth versus random), trajectory (helical versus space-filling) and resolution. We demonstrate that RA convergence rate and accuracy, for the space-filling trajectory, is invariant with regard to the motion-type. In addition, for the space-filling trajectory, the per-projection motions can be estimated to less than 0.25 pixel mean absolute error by performing a single quarter-resolution RA iteration followed by a single half-resolution RA iteration. The direct impact is that, for the space-filling trajectory, we need only perform one RA iteration per resolution in our iterative multi-grid reconstruction (IMGR).We also give examples of the effectiveness of RA motion correction method applied to real double-helix and space-filling trajectory micro-CT data. For double-helix Katsevich filtered-back-projection reconstruction (≈2500x2500x5000 voxels), we use a multi-resolution RA method as a pre-processing step. For the space-filling iterative reconstruction (≈2000x2000x5400 voxels), RA is applied during the IMGR iterations.

Bayesian approach to time-resolved tomography.

Conventional X-ray micro-computed tomography (μCT) is unable to meet the need for real-time, high-resolution, time-resolved imaging of multi-phase fluid flow. High signal-to-noise-ratio (SNR) data acquisition is too slow and results in motion artefacts in the images, while fast acquisition is too noisy and results in poor image contrast. We present a Bayesian framework for time-resolved tomography that uses priors to drastically reduce the required amount of experiment data. This enables high-quality time-resolved imaging through a data acquisition protocol that is both rapid and high SNR. Here we show that the framework: (i) encompasses our previous, algorithms for imaging two-phase flow as limiting cases; (ii) produces more accurate results from imperfect (i.e. real) data, where it can be compared to our previous work; and (iii) is generalisable to previously intractable systems, such as three-phase flow.

3D X-Ray Source Deblurring in High Cone-Angle Micro-CT

High geometric magnification X-ray micro-computed tomography (μCT) is used to study many high-resolution features in insects, cellular, bones, composite and mineral materials. The resolution of lab-based μCT in a fine-focus geometry is limited by blurring that occurs below the spatial coherence length of the illuminating radiation: resolution can be no smaller than the size of the X-ray source spot. In cases where the source spot size cannot be reduced (e.g. due to signal-to-noise, time or cost considerations) there is a need to model and correct for this blurring. In ANU CT-lab, we use a high cone angle and high geometric magnification with transmission x-ray source spot size up to three voxels, this creates blurring in the projection. This work takes a simulation approach mimicking such source spot size, and compares systems with horizontal cone-angles (often referred to as the fan angle) of 0.06, 14.36 and 60 degrees. We aim to eliminate this blurring in the reconstruction process. Furthermore, in a high cone-angle geometry, using a reconstruction method that only deconvolves each projection image leads to non-uniform resolution in the reconstruction volume. Alternatively, iterative methods that fully model the non-point source and avoid such artefacts are computationally expensive. We propose a hybrid method that corrects the effect of the non-point source by better modelling the physics rather than just deconvolving each projection image, therefore obtains results closer to the iterative full modelling method, and while being computationally much cheaper.