David A. Reimann

A method for measuring the presampled MTF of digital radiographic systems using an edge test device

The modulation transfer function (MTF) of radiographic systems is frequently evaluated by measuring the systems line spread function (LSF) using narrow slits. The slit method requires precise fabrication and alignment of a slit and high radiation exposure. An alternative method for determining the MTF uses a sharp, attenuating edge device. We have constructed an edge device from a 250-microm-thick lead foil laminated between two thin slabs of acrylic. The device is placed near the detector and aligned with the aid of a laser beam and a holder such that a polished edge is parallel to the x-ray beam. A digital image of the edge is processed to obtain the presampled MTF. The image processing includes automated determination of the edge angle, reprojection, sub-binning, smoothing of the edge spread function (ESF), and spectral estimation. This edge method has been compared to the slit method using measurements on standard and high-resolution imaging plates of a digital storage phosphor (DSP) radiography system. The experimental results for both methods agree with a mean MTF difference of 0.008. The edge method provides a convenient measurement of the presampled MTF for digital radiographic systems with good response at low frequencies.

Human vertebral body apparent and hard tissue stiffness

Cancellous bone apparent stiffness and strength are dependent upon material properties at the tissue level and trabecular architecture. Microstructurally accurate, large-scale finite element (LS-FE) models were used to predict the experimental apparent stiffness of human vertebral cancellous bone and to estimate the trabecular hard tissue stiffness. Twenty-eight LS-FE models of cylindrical human vertebral cancellous bone specimens (8 mm in diameter, 9.5 mm in height, one each from twenty-eight individuals) were generated directly from microcomputed tomography images and solved by a special purpose iterative finite element program. The experimental apparent stiffness and strength of the specimens were determined by mechanical testing to failure in the infero superior direction. Morphometric measurements including bone volume fraction (BV/TV), three eigenvalues of the fabric tensor and average P(L) were also calculated. The finite element estimate of apparent stiffness explained much of the variance in both experimental apparent stiffness (r2=0.89) and experimental apparent strength (r2=0.87). Stepwise linear regression analysis demonstrated that the LS-FE estimated apparent stiffness was the only significant predictor of experimental apparent stiffness and strength when it was included with all measured morphometric values. Hard tissue stiffness was quite variable between individuals (mean, 5.7 GPa; S.D. 1.6 GPa), but was not significantly related to age, sex, race, weight or morphometric measures for this sample.

Eigenimage filtering in MR imaging.

This article presents the technical aspects of a linear filter, referred to as eigenimage filtering, and its applications in magnetic resonance (MR) imaging. The technique is used to obtain a single composite image depicting a particular feature of interest while suppressing one or more interfering features. The appropriate weighting components to be used in the linear filter are determined on the criterion that the desired feature is enhanced while the interfering features are suppressed. The criterion is expressed mathematically as a ratio. By applying Rayleighs principle, the ratio is maximized by finding the eigenvector associated with the maximum eigenvalue of the corresponding generalized eigenvalue problem. The appropriate weighting factors for the linear filter are the elements of the eigenvector which maximize the ratio. The utilization of the technique is demonstrated in its application to a simulated MR image sequence as well as to acquired MR image sequences of a normal and an abnormal brain. Index Terms: Magnetic resonance imaging, physics and instrumentation—Magnetic resonance imaging, techniques—Eigenimage filtering.

Microfocus X-ray sources for 3D microtomography

Abstract An analytic model for the performance of cone beam microtomography is described. The maximum power of a microfocus X-ray source is assumed to be approximately proportional to the focal spot size. Radiation flux penetrating the specimen is predicted by a semi-empirical relation which is valid for X-ray energies less than 20 keV. Good signal to noise ratio is predicted for bone specimens of 0.1 to 10 mm when scanned at the optimal energy. A flux of about 1 × 10 10 photons/mm 2 /s is identified for 0.2 mm specimens. Cone beam volumetric microtomography is found to compare favorably with synchrotron based methods.

A cone beam computed tomography system for true 3D imaging of specimens

A system for 3D cone beam computed tomography has been developed, consisting of a microfocus x-ray source and x-ray image intensifier coupled to a CCD camera. Full width at half maximum resolving power has been experimentally measured to be 70 microns when imaging 10 mm diameter objects. The 3D nature of the resulting image data can be used to visualize internal structure and compute parameters such as volume, surface area, and surface/volume orientation.

Automated distortion correction of X-ray image intensifier images

An automated procedure for accurately correcting the distortion present in X-ray image intensifiers is described. An image of a rectilinear grid of wires is acquired. The wire crossing point positions are determined to sub-pixel accuracy without operator intervention. The points are then associated with their true coordinates. Following this association procedure, a piecewise affine transformation is found. Each output pixel point needed is mapped to the corresponding location in the distorted image. If it is not at a true acquired pixel location, bilinear interpolation is done to estimate the gray level at that point. After calibration data are analyzed, all subsequent images are corrected using a fast and simple table lookup algorithm. High accuracy is achieved for applications requiring sub-pixel registration.<<ETX>>

Parallel implementation of cone beam tomography

Three dimensional computed tomography is a computationally intensive procedure, requiring large amounts of RAM and processing power. Parallel methods for two dimensional computed tomography have been studied, but not extended or applied to 3D cone beam tomography. A discussion on how the 3D cone beam tomography problem can be implemented in parallel using MPI is given. We show an improvement in performance from 58.2% to 81.8% processor utilization in a heterogeneous cluster of workstations by load balancing. A 96.8% efficiency was seen using a 2 processor SMP.

Cone beam tomography using MPI on heterogeneous workstation clusters

With cone beam CT long computation and a large amount of memory is required. The majority of the computation is in the backprojection step. We have investigated the use of parallel methods on workstation clusters using MPI to overcome both the long processing time and lessen memory requirements on individual workstations. We used the asynchronous MPI implementation to reconstruct a 256/sup 3/ volume from 256/sup 2/ projection views with 6 workstations. Our previous efforts in load balancing resulted in processor utilization of 81.8%. Use of asynchronous communication in the cone beam CT problem has improved processor utilization to 91.9%.

Use of Wiener filtering in the measurement of the two-dimensional modulation transfer function

This paper presents a new method for the measurement of modulation transfer function (MTF) using Wiener filtering. The method, unlike conventional methods using slit or edge devices, allows the direct determination of the MTF in all directions at one step. An image containing a precise circular region is acquired and its Fourier transform is calculated. In the absence of any blurring, the Fourier transform yields a simple Bessel function. Because of the symmetry in the convolution theorem, the roles of the blurring function and object can be interchanged, allowing the blurring function to be recovered using a Wiener filter. We simulated this process to understand the effects of attenuation, signal-to-noise ratio, and circle size. Images were simulated containing a circular region and degraded by spatial domain blurring with a Gaussian convolution kernel and by additive Poisson noise. The determined MTF matches the expected MTF except for a slight high frequency overestimate due to noise aliasing, which can be compensated. This method allows one to easily measure the two-dimensional MTF, particularly in systems which have an asymmetrical point spread function such as computed radiography. The method can be used as a tool for quality assurance and for comparing the resolution characteristics of various digital radiography systems.

Direct measurement of resolution in volumetric imaging systems

The resolution of 2D imaging systems is frequently described by experimental estimates of the point, line, or edge spread function. It is shown that a response function across the normal to a boundary between two homogeneous volumes can provide a measure of resolution. The set of surface boundary voxels is determined by applying a simple threshold. The normal distance of every voxel to the surface is computed and an accumulator bin is incremented by the voxels gray level. This results in an aggregate surface response function, which is related to 3D point, line, and plane spread functions. This method can be applied to general boundary interfaces where precise surface normals are known, such as those on a sphere or plane. Results of applying this method to volumetric cone beam X-ray CT data are shown.<<ETX>>