Cone-beam image reconstruction using spherical harmonics

Three-dimensional iterative reconstruction of pulsed radiation sources using spherical harmonic decomposition

Neutron and x-ray imaging are essential ways to diagnose a pulsed radiation source. The three-dimensional (3D) intensity distribution reconstructed from two-dimensional (2D) radiation images can significantly promote research regarding the generation and variation mechanisms of pulsed radiation sources. Only a few (≤5) projected images at one moment are available due to the difficulty in building imaging systems for high-radiation-intensity and short-pulsed sources. The reconstruction of a 3D source with a minimal number of 2D images is an ill-posed problem that leads to severe structural distortions and artifacts of the image reconstructed by conventional algorithms. In this paper, we present an iterative method to reconstruct a 3D source using spherical harmonic decomposition. Our algorithm improves the representation ability of spherical harmonic decomposition for 3D sources by enlarging the order of the expansion, which is limited in current analytical reconstruction algorithms. Prior knowledge of the source can be included to obtain a reasonable solution. Numerical simulations demonstrate that the reconstructed image quality of the iterative algorithm is better than that of the analytical algorithm. The iterative method can suppress the effect of noise in the integral projection image and has better robustness and adaptability than the analytical method.

Computed tomography image representation using the Legendre polynomial and spherical harmonics functions

The representation of computed tomography (CT) images using the Legendre polynomial (LPF) and spherical harmonics (SHF) functions was investigated. We selected 100 two-dimensional (2D) CT images of 10 lung cancer patients and 33 three-dimensional (3D) CT images of head and neck cancer patients. The reproducibility of these special functions was evaluated in terms of the normalized cross-correlation (NCC). For the 2D images, the NCC was 0.990 ± 0.002 (1sd) with an LPF of order 70, whereas for the 3D images, the NCC was 0.971 ± 0.004 (1sd) with an SHF of degree 70. The results showed that the LPF was more efficient than the Fourier series. As the thoracic and head areas are cylindrical and spherical, respectively, expansions with the LPF and SHF achieved an efficient representation of the human body. CT image representation with analytical functions can be potentially beneficial, such as in X-ray scattering estimation.

Multislice CT: technical principles and future trends

Multislice scanning has substantially improved the performance of CT scanners, and thus the relation between scan duration, available scan length, and spatial resolution along the patient axis (z-axis). Near-isotropic imaging of whole organ systems is already possible with 4-slice scanners, but only with 8- to 16-slice scanners can the scan duration be shortened as well. Reconstructing overlapping thin-section data ("secondary raw data set") provides the basis for image reconstruction in any desired plane. By using thick multiplanar reformation (MPR) techniques, image quality can be improved while keeping patient dose low. Using unfavorable scanning parameters, exposure dose can be substantially increased compared with single-slice scanning, but thick MPR and individual-dose modulation techniques can provide the basis for dose reduction. Low-kVp scanning, in particular, is useful in children and slim adults and is an excellent technique to improve image contrast in CT angiographic studies. Short spiral scans should be avoided with multislice CT since overranging (extra rotations at the beginning and end of the scan, used for data interpolation) can substantially increase patient dose. Future trends include the introduction of thinner detector rows, wider detector arrays, faster tube rotation, and area detectors than can also be used for fluoroscopy. Noise-reduction techniques and individual dose modulation will gain importance with higher isotropic resolution. Functional and perfusion imaging, as well as advanced image processing and computer-aided diagnosis programs, will add to the possibilities of the next generation of multislice CT scanners.

Cone-beam and fan-beam image reconstruction algorithms based on spherical and circular harmonics

A cone-beam image reconstruction algorithm using spherical harmonic expansions is proposed. The reconstruction algorithm is in the form of a summation of inner products of two discrete arrays of spherical harmonic expansion coefficients at each cone-beam point of acquisition. This form is different from the common filtered backprojection algorithm and the direct Fourier reconstruction algorithm. There is no re-sampling of the data, and spherical harmonic expansions are used instead of Fourier expansions. As a special case, a new fan-beam image reconstruction algorithm is also derived in terms of a circular harmonic expansion. Computer simulation results for both cone-beam and fan-beam algorithms are presented for circular planar orbit acquisitions. The algorithms give accurate reconstructions; however, the implementation of the cone-beam reconstruction algorithm is computationally intensive. A relatively efficient algorithm is proposed for reconstructing the central slice of the image when a circular scanning orbit is used.

Temporal resolution and the evaluation of candidate algorithms for four-dimensional CT

The four-dimensional computed tomography ("4D-CT") with area detector has been developed for dynamic volumetric imaging with large longitudinal coverage. In this paper one of the key technologies for 4D-CT development is discussed: Image reconstruction algorithm with high temporal resolution. All of the cone-beam algorithms investigated previously assume that the object is stationary. In this paper a new class of cone-beam problem is addressed: a dynamic volumetric (4-D) imaging. A continuously rotating circular (stationary couch) scanning is employed, and then, a generalized version of the well-known Feldkamp algorithm with the following three steps is performed: (1) applying a weighting function (along the time axis) to projection data, (2) filtering the weighted data along the detector row direction, (3) cone-beam backprojecting of the filtered data along the corresponding x-ray path. The weighting function controls the time center, the temporal resolution, and the image quality. Four weighting functions developed for fan-beam reconstruction were applied to the first step: (a) a constant weight fixed at 0.5 (FS-FDK), (b) feathering both edges of the (time) window (OS-FDK), (c) Parker's weight for a half-scan (HF-FDK), and (d) an extended Parker's weight, which allows us to use a larger range of projection data up to one rotation (NHS-FDK). We evaluated them in terms of temporal resolution, image noise, and image quality. Also, the cause of the artifact has been investigated. The temporal resolution of NHF-FDK equals that of HS-FDK, which is half of the one rotation period. For the moving object, NHS-FDK offers the best image quality. The images with FS-FDK are degraded by streak artifacts; HS-FDK provides poor image quality with good temporal resolution; and images by OS-FDK are blurred due to insufficient temporal resolution. The cause of the artifact was found as an inconsistency of projection data due to object motion (in FS-FDK) and lost 3-D-Radon data caused by applying Parker's weight (in HS-FDK). A hand toy was employed for the preliminary evaluation of dynamic volumetric imaging with the real 256-slice scanner. In an overall evaluation, NHS-FDK provides the stable and the sufficient image quality both with moving and stationary objects.

General principles of MDCT

Multidetector CT (MDCT, multislice CT, multidetector-row CT, multisection CT) represents a breakthrough in CT technology. It has transformed CT from an transaxial cross-sectional technique into a true 3D imaging modality that allows for arbitrary cut planes as well as excellent 3D displays of the data volume. Multislice CT scanners provide a huge gain in performance that can be used to reduce scan time, to reduce section collimation, or to increase scan length substantially. The following article will provide an overview of the principles of multislice CT scanning. It describes the various detector systems and gives an introduction to the most important acquisition and reconstruction parameters. The article describes how reconstruction of thick multiplanar reformations can be used to take advantage of the 3D capabilities of multislice CT while keep radiation exposure to a minimum.