The effects of misregistration of the projections on spatial resolution of CT scanners

Experimental correlation-based identification of X-ray CT point spread function. Part 2: Simulation and design of input signal

The preferred signals for non-parametric correlation-based point spread function identification are white noise or pseudo-random binary sequences (PRBSs). Given the difficulty of building a phantom based on either of these signals, a new input is devised that corresponds to pseudo-randomly located holes. The positions of the holes correspond to zeros in a 2-D PRBS. To optimise the design of the phantom and to ensure proper imaging procedure, a number of simulations are conducted. The effects of the following parameters on identification quality are investigated: the size of the holes and their minimum separation, the period of the PRBS, input-output translational and rotational mis-registration, pixel size and the presence of cupping. The factors affecting identification quality the most are rotational alignment, hole size and separation, as well as sequence length. During simulations, a point spread function offering characteristics similar to the Philips Tomoscan CX is identified. Optimal results are obtained when the signal consists of 0.6 mm holes, separated by 0.9 mm, whose position is based on a 32 x 32 PRBS generated with a ten-stage shift-register. When adequate rotational alignment is provided, it is shown that the pseudo-randomly located holes signal is a good substitute for a purely white signal when identifying the PSF of a CT scanner.

CT fan beam reconstruction with a nonstationary axis of rotation

To reconstruct an image using computed tomography (CT), the axis of rotation must pivot at the same point on the reconstruction plane that the X-ray source and the CT detector assembly rotate about around the imaged object. This pivot point is used as a reference point for backprojecting pixel values to their proper coordinates. Reconstructing an image with a nonstationary axis of rotation would backproject pixel values to incorrect coordinate points. A convolution filtered backprojection algorithm has been derived for correcting images that were acquired with a nonstationary axis of rotation using the fan beam geometry with a collinear (flat) detector. The correction method accounts for the vertical displacements of the axis of rotation as the CT scanner rotates around the imaged object, as may be the case when sagging occurs. Software simulations are performed to show how the algorithm corrects for the shift in the axis of rotation.

Diffusion imaging with paired CPMG sequences

We report a method for mapping apparent diffusion coefficients using two interleaved CPMG sequences. Image slice selection is performed prior to each sequence, allowing the use of non-selective "hard" refocussing pulses. Phase cycling of the slice-selection process for each projection minimizes out-of-slice contributions to echo amplitudes. This permits an accurate evaluation of both T2 and apparent proton self-diffusion coefficients.

The noise power spectrum of CT images

An expression for the noise power spectrum of images reconstructed by the discrete filtered backprojection algorithm has been derived. The formulation explicitly includes sampling within the projections, angular sampling, and the two-dimensional sampling implicit in the discrete representation of the image. The effects of interpolation are also considered. Noise power spectra predicted by this analysis differ from those predicted using continuous theory in two respects: they are rotationally asymmetric, and they do not approach zero at zero frequency. Both of these properties can be attributed to two-dimensional aliasing due to pixel sampling. The predictions were confirmed by measurement of noise power spectra of both simulated images and images from a commercial x-ray transmission CT scanner.

Reconstruction Algorithm for Fan Beam with a Displaced Center-of-Rotation

A convolutional backprojection algorithm is derived for a fan beam geometry that has its center-of-rotation displaced from the midline of the fan beam. In single photon emission computed tomography (SPECT), where a transaxial converging collimator is used with a rotating gamma camera, it is difficult to precisely align the collimator so that the mechanical center-of-rotation is colinear with the midline of the fan beam. A displacement of the center-of-rotation can also occur in X-ray CT when the X-ray source is mispositioned. Standard reconstruction algorithms which directly filter and backproject the fan beam data without rebinning into parallel beam geometry have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of a misalignment of the center-of-rotation, if these conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. We illustrate these artifacts with simulations and demonstrate how the news algorithm corrects for this misalignment. We also show a method to estimate the parameters of the fan beam geometry including the shift in the center-of-rotation.