Jongduk Baek

Local and global 3D noise power spectrum in cone-beam CT system with FDK reconstruction

PURPOSE The authors examine the nonstationary noise behavior of a cone-beam CT system with FDK reconstruction. METHODS To investigate the nonstationary noise behavior, an analytical expression for the NPS of local volumes and an entire volume was derived and quantitatively compared to the NPS estimated from experimental air and water images. RESULTS The NPS of local volumes at different locations along the z-axis showed radial symmetry in the f(x)-f(y) plane and different missing cone regions in the f(z) direction depending on the tilt angle of rays through the local volumes. For local volumes away from the z-axis, the NPS of air and water images showed sharp transitions in the f(x)-f(y) and f(y)-f(z) planes and lack of radial symmetry in the f(x)-f(y) plane. These effects are mainly caused by varying magnification and different noise levels from view to view. In the NPS of the entire volume, the f(x)-f(y) plane showed radial symmetry because the nonstationary noise behaviors of local volumes were averaged out. The nonstationary sharp transitions were manifested as a high-frequency roll-off. CONCLUSIONS The results from noise power analysis for local volumes and an entire volume demonstrate the spatially varying noise behavior in the reconstructed cone-beam CT images.

The noise power spectrum in CT with direct fan beam reconstruction

The noise power spectrum (NPS) is a useful metric for understanding the noise content in images. To examine some unique properties of the NPS of fan beam CT, the authors derived an analytical expression for the NPS of fan beam CT and validated it with computer simulations. The nonstationary noise behavior of fan beam CT was examined by analyzing local regions and the entire field-of-view (FOV). This was performed for cases with uniform as well as nonuniform noise across the detector cells and across views. The simulated NPS from the entire FOV and local regions showed good agreement with the analytically derived NPS. The analysis shows that whereas the NPS of a large FOV in parallel beam CT (using a ramp filter) is proportional to frequency, the NPS with direct fan beam FBP reconstruction shows a high frequency roll off. Even in small regions, the fan beam NPS can show a sharp transition (discontinuity) at high frequencies. These effects are due to the variable magnification and therefore are more pronounced as the fan angle increases. For cases with nonuniform noise, the NPS can show the directional dependence and additional effects.

Enhanced optical coupling performance in an InGaAs photodiode integrated with wet-etched microlens

In this letter, we report over 50% enhancement in optical coupling tolerance between a single-mode fiber and a photodiode. The enhancement is made possible by integrating a microlens on the polished backside of an InGaAs photodiode device. The microlenses are fabricated by one step wet chemical etching in the mixed solution of bromic acid and hydrogen peroxide. Surface profiles of the microlenses are simulated using the finite-difference-method to solve a simplified diffusion model. The optical coupling tolerance is also theoretically calculated based on ray optics, of which results show an excellent agreement with the experimental data.

Ring artifact correction using detector line-ratios in computed tomography.

Ring artifacts in computed tomography (CT) images degrade image quality and obscure the true shapes of objects. While several correction methods have been developed, their performances are often task-dependent and not generally applicable. Here, we propose a novel method to reduce ring artifacts by calculating the ratio of adjacent detector elements in the projection data, termed the line-ratio. Our method estimates the sensitivity of each detector element and equalizes them in sinogram space. As a result, the stripe pattern can be effectively removed from sinogram data, thereby also removing ring artifacts from the reconstructed CT image. Numerical simulations were performed to evaluate and compare the performance of our method with that of conventional methods. We also tested our method experimentally and demonstrated that our method has superior performance to other methods.

To bin or not to bin? The effect of CT system limiting resolution on noise and detectability

We examine the noise advantages of having a computed tomography (CT) detector whose spatial resolution is significantly better (e.g. a factor of 2) than needed for a desired resolution in the reconstructed images. The effective resolution of detectors in x-ray CT is sometimes degraded by binning cells because the small cell size and fine sampling are not needed to achieve the desired resolution (e.g. with flat panel detectors). We studied the effect of the binning process on the noise in the reconstructed images and found that while the images in the absence of noise can be made identical for the native and the binned system, for the same system MTF in the presence of noise, the binned system always results in noisier reconstructed images. The effect of the increased noise in the reconstructed images on lesion detection is scale (frequency content) dependent with a larger difference between the high resolution and binned systems for imaging fine structure (small objects). We show simulated images reconstructed with both systems for representative objects and quantify the impact of the noise on the detection of the lesions based on mathematical observers. Through both subjective assessment of the reconstructed images and the quantification using mathematical observers, we show that for a CT system where the photon noise is dominant, higher resolution in the detectors leads to better noise performance in the reconstructed images at any resolution.

Use of sphere phantoms to measure the 3D MTF of FDK reconstructions

To assess the resolution performance of modern CT scanners, a method to measure the 3D MTF is needed. Computationally, a point object is an ideal test phantom but is difficult to apply experimentally. Recently, Thornton et al. described a method to measure the directional MTF using a sphere phantom. We tested this method for FDK reconstructions by simulating a sphere and a point object centered at (0.01 cm , 0.01 cm, 0.01 cm) and (0.01 cm, 0.01 cm, 10.01 cm) and compared the directional MTF estimated from the reconstructed sphere with that measured from an ideal point object. While the estimated MTF from the sphere centered at (0.01 cm , 0.01 cm, 0.01 cm) showed excellent agreement with that from the point object, the estimated MTF from a sphere centered at (0.01 cm , 0.01 cm, 10.01 cm) had significant errors, especially along the fz axis. We found that this is caused by the long tails of the impulse response of the FDK reconstruction far off the central plane. We developed and tested a new method to estimate the directional MTF using the sphere data. The new method showed excellent agreement with the MTF from an ideal point object. Caution should be used when applying the original method in cases where the impulse response may be wide.

A multi-source inverse-geometry CT system: initial results with an 8 spot x-ray source array

We present initial experimental results of a rotating-gantry multi-source inverse-geometry CT (MS-IGCT) system. The MS-IGCT system was built with a single module of 2 × 4 x-ray sources and a 2D detector array. It produced a 75 mm in-plane field-of-view (FOV) with 160 mm axial coverage in a single gantry rotation. To evaluate system performance, a 2.5 inch diameter uniform PMMA cylinder phantom, a 200 µm diameter tungsten wire, and a euthanized rat were scanned. Each scan acquired 125 views per source and the gantry rotation time was 1 s per revolution. Geometric calibration was performed using a bead phantom. The scanning parameters were 80 kVp, 125 mA, and 5.4 µs pulse per source location per view. A data normalization technique was applied to the acquired projection data, and beam hardening and spectral nonlinearities of each detector channel were corrected. For image reconstruction, the projection data of each source row were rebinned into a full cone beam data set, and the FDK algorithm was used. The reconstructed volumes from upper and lower source rows shared an overlap volume which was combined in image space. The images of the uniform PMMA cylinder phantom showed good uniformity and no apparent artifacts. The measured in-plane MTF showed 13 lp cm(-1) at 10% cutoff, in good agreement with expectations. The rat data were also reconstructed reliably. The initial experimental results from this rotating-gantry MS-IGCT system demonstrated its ability to image a complex anatomical object without any significant image artifacts and to achieve high image resolution and large axial coverage in a single gantry rotation.

Effect of detector lag on CT noise power spectra.

PURPOSE The authors examined the effect of detector lag on the noise power spectrum (NPS) of CT images reconstructed with filtered backprojection (FBP). METHODS The authors derived an analytical expression of the NPS with detector lag, and then verified it using computer simulations with parallel beam and fan beam geometries. The dependence of the NPS on the amount of lag, location within the scanned field of view (FOV), and the number of views used in the reconstruction (samples per rotation) was investigated using constant and view dependent noise in the raw data. RESULTS Detector lag introduces noise correlation in the azimuthal direction. The effect on the NPS is a frequency dependent reduction in amplitude. In small regions of the image, the effect is primarily in the frequencies corresponding to the azimuthal direction. The noise blurring and NPS filtering increases with increasing radial distance, and therefore regions at larger radial distances have lower noise power. With the same detector lag response function, the amount of noise correlation and NPS filtering decreases with increasing number of views. CONCLUSIONS The shape of the NPS depends on the detector lag coefficients, location of the region, and the number of views used in the reconstruction. In general, the noise correlation caused by detector lag decreased the amplitude of the NPS.

A new method to combine 3D reconstruction volumes for multiple parallel circular cone beam orbits

PURPOSE This article presents a new reconstruction method for 3D imaging using a multiple 360 degrees circular orbit cone beam CT system, specifically a way to combine 3D volumes reconstructed with each orbit. The main goal is to improve the noise performance in the combined image while avoiding cone beam artifacts. METHODS The cone beam projection data of each orbit are reconstructed using the FDK algorithm. When at least a portion of the total volume can be reconstructed by more than one source, the proposed combination method combines these overlap regions using weighted averaging in frequency space. The local exactness and the noise performance of the combination method were tested with computer simulations of a Defrise phantom, a FORBILD head phantom, and uniform noise in the raw data. RESULTS A noiseless simulation showed that the local exactness of the reconstructed volume from the source with the smallest tilt angle was preserved in the combined image. A noise simulation demonstrated that the combination method improved the noise performance compared to a single orbit reconstruction. CONCLUSIONS In CT systems which have overlap volumes that can be reconstructed with data from more than one orbit and in which the spatial frequency content of each reconstruction can be calculated, the proposed method offers improved noise performance while keeping the local exactness of data from the source with the smallest tilt angle.

Multi-source inverse-geometry CT: From system concept to research prototype

Third-generation CT architectures are approaching fundamental limits. Dose-efficiency is limited by finite detector efficiency and by limited control over the X-ray flux spatial profile. Increasing the volumetric coverage comes with increased scattered radiation, cone-beam artifacts, Heel effect, wasted dose and cost. Spatial resolution is limited by focal spot size and detector cell size. Temporal resolution is limited by mechanical constraints, and alternative geometries such as electron-beam CT and dual-source CT come with severe tradeoffs in terms of image quality, dose-efficiency and complexity. The concept of multi-source inverse-geometry CT (IGCT) breaks through several of the above limitations [1-3], promising a low-dose high image quality volumetric CT architecture. In this paper, we present recent progress with the design and integration efforts of the first gantry-based multi-source CT scanner.