Roger H. Johnson

An Iterative Approach to the Beam Hardening Correction in Cone Beam CT

In computed tomography (CT), the beam hardening effect has been known to be one of the major sources of deterministic error that leads to inaccuracy and artifact in the reconstructed images. Because of the polychromatic nature of the x-ray source used in CT and the energy-dependent attenuation of most materials, Beers law no longer holds. As a result, errors are present in the acquired line integrals or measurements of the attenuation coefficients of the scanned object. In the past, many studies have been conducted to combat image artifacts induced by beam hardening. In this paper, we present an iterative beam hardening correction approach for cone beam CT. An algorithm that utilizes a tilted parallel beam geometry is developed and subsequently employed to estimate the projection error and obtain an error estimation image, which is then subtracted from the initial reconstruction. A theoretical analysis is performed to investigate the accuracy of our methods. Phantom and animal experiments are conducted to demonstrate the effectiveness of our approach.

Feldkamp and circle-and-line cone-beam reconstruction for 3D micro-CT of vascular networks

Detailed morphometric knowledge of the microvascular network is needed for studies relating structure to haemodynamic function in organs like the lung. Clinical volumetric CT is limited to millimetre-order spatial resolution. Since evidence suggests that small arterioles (50 to 300 micrometres) dominate pulmonary haemodynamics, we built a micro-CT scanner, capable of imaging excised lungs in 3D with 100 microm resolution, for basic physiology research. The scanner incorporates a micro-focal (3 microm) x-ray source, an xyz theta stage and a CCD-coupled image intensifier detector. We imaged phantoms and contrast-enhanced rat lungs, reconstructing the data with either the Feldkamp or the circle-and-line cone-beam reconstruction algorithm. We present reconstructions using 180 views over 360 degrees for the circular trajectory, augmented with views from a linear scan for the circle-and-line algorithm. Especially for platelike features perpendicular to the rotation axis and remote from the midplane, the circle-and-line algorithm produces superior reconstructions compared with Feldkamps algorithm. We conclude that the use of nonplanar source trajectories to perform micro-CT on contrast-enhanced, excised lungs can provide data useful for morphometric analysis of vascular trees, currently down to the 130 microm level.

Improved iterative algorithm for sparse object reconstruction and its performance evaluation with micro-CT data

This paper proposes a new row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The main idea is to use the L/sub 1/ norm to pick up a sparse solution from a set of feasible solutions to the measurement equation. By perturbing the linear program to a quadratic program, we use the duality of nonlinear programming to construct a row-action type iterative algorithm to find the solution. We also prove that the algorithm converges to the solution under mild assumptions. We show that this method works well in the 3-D blood-vessel reconstruction and its computation time is shorter than those of our previous method and MART method. Furthermore, we apply the method to real data measured with the Micro-CT device developed at Marquette University.

Automated detection of BB pixel clusters in digital fluoroscopic images

Small ball bearings (BBs) are often used to characterize and correct for geometric distortion of x-ray image intensifiers. For quantitative applications the number of BBs required for accurate distortion correction is prohibitively large for manual detection. A method to automatically determine the BB coordinates is described. The technique consists of image segmentation, pixel coalescing and centroid calculation. The dependence of calculated BB coordinates on segmentation threshold was also evaluated and found to be within the uncertainty of measurement.

Exploiting self-similarity of arterial trees to reduce the complexity of analysis

Vascular structures such as the pulmonary arterial tree contain hundreds of thousands of vessel segments, making structural and functional analysis of an entire 3D image volume very difficult. Currently-available methods for segmentation and morphometry of 3D vascular tree images require user interaction making the task very tedious and sometimes impossible. Our aim is to exploit the self-similar nature of arterial trees to simplify morphometric analysis. The structure of pulmonary arterial trees exhibits self- similarity in the sense that the segment length and diameter data from different pathways are statistically indistinguishable for subtrees distal to a given segment diameter. We analyze 3D micro-CT images of mouse and rat pulmonary arterial trees by measuring the lengths and diameters of the vessel segments of the several longest arterial pathways and their immediate branches interactively. Since measurements made on the longest pathways are representative of the tree as a whole, and there are less than 30 branches off the main trunk, the morphometry of the complex tree can be characterized by less than 100 length and diameter measurements.

SPECT imaging of pulmonary blood flow in a rat

Small animal imaging is experiencing rapid development due to its importance in providing high-throughput phenotypic data for functional genomics studies. We have developed a single photon emission computed tomography (SPECT) system to image the pulmonary perfusion distribution in the rat. A standard gamma camera, equipped with a pinhole collimator, was used to acquire SPECT projection images at 40 sec/view of the rat thorax following injection of Tc99m labeled albumin that accumulated in the rats lungs. A voxel-driven, ordered-subset expectation maximization reconstruction was implemented. Following SPECT imaging, the rat was imaged using micro-CT with Feldkamp conebeam reconstruction. The two reconstructed image volumes were fused to provide a structure/function image of the rat thorax. Reconstruction accuracy and performance were evaluated using numerical simulations and actual imaging of an experimental phantom consisting of Tc99m filled chambers with known diameters and count rates. Full-width half-maximum diameter measurement errors decreased with increasing chamber diameter, ranging from < 6% down to 0.1%. Errors in the ratio of count rate estimates between tubes were also diameter dependent but still relatively small. This preliminary study suggests that SPECT will be useful for imaging and quantifying the pulmonary blood flow distribution and the distribution of Tc99m labeled ligands in the lungs of small laboratory animals.

Sparse object reconstruction from a limited number of projections using the linear programming

This paper proposes a simple row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The main idea is to use the L/sub 1/ norm to pick up a sparse solution from a set of feasible solutions to the measurement equation. By perturbing the linear program to a quadratic program, we use the duality of the nonlinear programming to construct a row-action type iterative algorithm to find a solution, we also prove that the algorithm converges for any initial image. We show that this method works well in the 3D blood-vessel reconstruction and its computation time is shorter compared to our previous method.

Quantification of pulmonary arterial wall distensibility using parameters extracted from volumetric micro-CT images

Stiffening, or loss of distensibility, of arterial vessel walls is among the manifestations of a number of vascular diseases including pulmonary arterial hypertension. We are attempting to quantify the mechanical properties of vessel walls of the pulmonary arterial tree using parameters derived from high-resolution volumetric x-ray CT images of rat lungs. The pulmonary arterial trees of the excised lungs are filled with a contrast agent. The lungs are imaged with arterial pressures spanning the physiological range. Vessel segment diameters are measured from the inlet to the periphery, and distensibilities calculated from diameters as a function of pressure. The method shows promise as an adjunct to other morphometric techniques such as histology and corrosion casting. It possesses the advantages of being nondestructive, characterizing the vascular structures while the lungs are imaged rapidly and in a near-physiological state, and providing the ability to associate mechanical properties with vessel location in the intact tree hierarchy.

A simple derivation and analysis of a helical cone beam tomographic algorithm for long object imaging via a novel definition of region of interest.

We derive and analyse a simple algorithm first proposed by Kudo et al (2001 Proc. 2001 Meeting on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine (Pacific Grove, CA) pp 7-10) for long object imaging from truncated helical cone beam data via a novel definition of region of interest (ROI). Our approach is based on the theory of short object imaging by Kudo et al (1998 Phys. Med. Biol. 43 2885-909). One of the key findings in their work is that filtering of the truncated projection can be divided into two parts: one, finite in the axial direction, results from ramp filtering the data within the Tam window. The other, infinite in the z direction, results from unbounded filtering of ray sums over PI lines only. We show that for an ROI defined by PI lines emanating from the initial and final source positions on a helical segment, the boundary data which would otherwise contaminate the reconstruction of the ROI can be completely excluded. This novel definition of the ROI leads to a simple algorithm for long object imaging. The overscan of the algorithm is analytically calculated and it is the same as that of the zero boundary method. The reconstructed ROI can be divided into two regions: one is minimally contaminated by the portion outside the ROI, while the other is reconstructed free of contamination. We validate the algorithm with a 3D Shepp-Logan phantom and a disc phantom.

A helical cone beam algorithm for large cone angles with minimal overscan

Three-dimensional image reconstruction from axially truncated helical cone beam projections has been under active investigation. It is known that exact helical cone beam reconstruction can be achieved using only the data in the Tam window. Based on a property of filtering truncated cone beam projections discovered by Kudo et al. (2000), we proposed a simple helical cone beam algorithm for the long object problem by invoking virtual infinite detectors at both ends of the helix. However, Tam (2002) has suggested that the derivation using virtual infinite detectors were imprecise as well as the calculated overscan and complexity analysis. In this paper, we provide a new derivation to validate the simple algorithm based on a novel definition of a short object within the long object. We show that the proposed algorithm is essentially a simplified version of Defrises ZB method (2000). The minimal overscan we derive for the simple algorithm is the same as that of ZB method. Although simulation results indicate that a smaller overscan is required for the proposed algorithm relative to the ZB method, we lack an analytical verification. A modified 3D Shepp-Logan phantom and a disc phantom are used to validate the algorithm.