Andy Ziegler

Noise and resolution in images reconstructed with FBP and OSC algorithms for CT

This paper presents a comparison between an analytical and a statistical iterative reconstruction algorithm for computed transmission tomography concerning their noise and resolution performance. The reconstruction of two-dimensional images from simulated fan-beam transmission data is performed with a filtered back-projection (FBP) type reconstruction and an iterative ordered subsets convex (OSC) maximum-likelihood method. A special software phantom, which allows measuring the resolution and noise in a nonambiguous way, is used to simulate transmission tomography scans with different signal-to-noise ratios (SNR). The noise and modulation transfer function is calculated for FBP and OSC reconstruction at several positions, distributed over the field-of-view (FOV). The reconstruction with OSC using different numbers of subsets shows an inverse linear relation to the number of iterations that are necessary to reach a certain resolution and SNR, i.e., increasing the number of subsets by a factor x reduces the number of required iterations by the same factor. The OSC algorithm is able to achieve a nearly homogeneous high resolution over the whole FOV, which is not achieved with FBP. The OSC method achieves a lower level of noise compared with FBP at the same resolution. The reconstruction with OSC can save a factor of up to nine of x-ray dose compared with FBP in the investigated range of noise levels.

Iterative reconstruction of a region of interest for transmission tomography

It was shown that imagesreconstructed for transmission tomography with iterative maximum likelihood (ML) algorithms exhibit a higher signal-to-noise ratio than imagesreconstructed with filtered back-projection type algorithms. However, a drawback of ML reconstruction in particular and iterative reconstruction in general is the requirement that the reconstructed field of view (FOV) has to cover the whole volume that contributes to the absorption. In the case of a high resolution reconstruction, this demands a huge number of voxels. This article shows how an iterative ML reconstruction can be limited to a region of interest (ROI) without losing the advantages of a ML reconstruction. Compared with a full FOV ML reconstruction, the reconstruction speed is mainly increased by reducing the number of voxels which are necessary for a ROI reconstruction. In addition, the speed of convergence is increased.

Efficient projection and backprojection scheme for spherically symmetric basis functions in divergent beam geometry

In cone-beam transmission tomography the measurements are performed with a divergent beam of x-rays. The reconstruction with iterative methods is an approach that offers the possibility to reconstruct the corresponding images directly from these measurements. Another approach based on spherically symmetric basis functions (blobs) has been reported with results demonstrating a better image quality for iterative reconstruction algorithms. When combining the two approaches (i.e., using blobs in iterative cone-beam reconstruction of divergent rays) the problem of blob sampling without introducing aliasing must be addressed. One solution to this problem is to select a blob size large enough to ensure a sufficient sampling, but this prevents a high resolution reconstruction, which is not desired. Another solution is a heuristic low-pass filtering, which removes this aliasing, but neglects the different contributions of blobs to the absorption depending on the spatial position in the volume and, therefore, cannot achieve the best image quality. This article presents a model of sampling the blobs which is motivated by the beam geometry. It can be used for high resolution reconstruction and can be implementedefficiently.

On the influence of noise correlations in measurement data on basis image noise in dual‐energylike x‐ray imaging

In conventional dual-energy systems, two transmission measurements with distinct spectral characteristics are performed. These measurements are used to obtain the line integrals of two basis material densities. Usually, the measurement process is such that the two measured signals can be treated as independent and therefore uncorrelated. Recently, however, a readout system for x-ray detectors has been introduced for which this is no longer the case. The readout electronics is designed to obtain simultaneous measurements of the total number of photons N and the total energy E they deposit in the sensor material. Practically, this is realized by a signal replication and separate counting and integrating processing units. Since the quantities N and E are (electronically) derived from one and the same physical sensor signal, they are statistically correlated. Nevertheless, the pair N and E can be used to perform a dual-energy processing following the well-known approach by Alvarez and Macovski. Formally, this means that N is to be identified with the first dual-energy measurement M1 and E with the second measurement M2. In the presence of input correlations between M1 = N and M2 = E, however, the corresponding analytic expressions for the basis image noise have to be modified. The main observation made in this paper is that for positively correlated data, as is the case for the simultaneous counting and integrating device mentioned above, the basis image noise is suppressed through the influence of the covariance between the two signals. We extend the previously published relations for the basis image noise to the case where the original measurements are not independent and illustrate the importance of the input correlations by comparing dual-energy basis image noise resulting from the device mentioned above and a device measuring the photon numbers and the deposited energies consecutively.

Image reconstruction and evaluation of system performance for optical fluorescence tomography

Diffuse optical tomography is a non-invasive method aiming at the detection of breast cancer. The sensitivity and specificity of the method can be increased if a fluorescent contrast agent is used that accumulates in malignant lesions. Recently, Philips developed an optical scanner, where the patient is lying on a bed, with one breast hanging freely in a cup containing an optical matching fluid. 507 optical fibers are mounted in the surface of the measurement cup. The breast is illuminated sequentially by half of these fibers while the other half is used to collect the light that is emanating from the breast. The system uses near-infrared light of continuous wave solid-state lasers to illuminate the breast at four different wavelengths. A complete measurement takes less than ten minutes and involves five breast scans: transmission data are collected for four wavelengths, and fluorescence data for excitation at one wavelength. Here, we present the image reconstruction scheme and a novel method to assess the system performance in terms of lesion detectability. This method uses a statistical significance test on simulated data with and without a lesion. It allows the quantification of the detectability of lesions for different size, position, or contrast of the lesion. It also allows to analyze the potential impact of system improvements or to judge the performance of an image reconstruction algorithm.

Motion compensated iterative reconstruction of a cardiac region of interest for CT

A method for motion compensated iterative CT reconstruction of a cardiac region of interest is presented. The 4D motion field used during reconstruction is obtained from a three-dimensional thin-plate spline warping of a limited number of anatomical point landmarks of the right coronary artery. Results on a clinical case are compared with standard gated iterative reconstruction. The motion compensated iterative reconstruction provides sharp images of the right coronary artery with significantly better image quality compared to traditional gated reconstruction.

Efficient projection model for blobs in motion-compensated iterative cone-beam CT

We present a three-dimensional method to reconstruct moving objects from cone-beam X-ray projections using an iterative reconstruction algorithm and a given motion vector field. For the image representation, adapted blobs are used which can be implemented efficiently as basis functions. In the case of a divergent motion vector field, blob volume change has to be taken into account in the forward-projections. An efficient method to calculate the line integral through the adapted blobs is proposed, and in two simulated data sets it is shown that this method prevents blurring and streak artifacts.

Maximum likelihood reconstruction of circular cone-beam CT data

The behavior of a Maximum Likelihood reconstruction algorithm applied to circular cone-beam CT data is examined. In a simulation study, it is shown that unacceptable artifacts appear, if a constant initial image is used. A start image that incorporates the borders of the reconstructed object correctly improves the situation, but artifacts remain that degrade the image quality. If the initial image is generated from a low-dose helical pre-scan, a cone-beam artifact free image is achieved.

Advanced convergence of iterative reconstruction of circular cone-beam short-scans

The iterative reconstruction of a circular cone-beam short-scan (180/spl deg/ plus fan angle) measurement with algebraic reconstruction technique (ART) is investigated. Simulated projections of a transmission tomography scan of the Forbild head phantom are reconstructed. The reconstruction of the short-scan sinogram with ART is compared with the reconstruction of a Parker weighted iterative update, which compensates for the redundancy of the measured rays. The results show that a Parker weighting improves the image quality of the reconstruction with ART during the first few iterations compared with the standard ART, but that this difference vanishes with increasing number of iterations.