Recently, we proposed a scatter correction method for x-ray imaging using primary modulation. A primary
modulator with spatially variant attenuating materials is inserted between the x-ray source and the object to
make the scatter and part of the primary distributions strongly separate in the Fourier domain. Linear filtering
and demodulation techniques suffice to extract and correct the scatter for this modified system. The method has
been verified by computer simulations and preliminary experimental results on a simple object. In this work, we
improve performance by using a new primary modulator with a higher modulation frequency and by refining the
algorithm. The improved method is evaluated experimentally using a pelvis phantom. The imaging parameters
are chosen to match the Varian Acuity CT simulator, where scatter correction has been shown to be challenging
due to complicated artifact patterns. The results using our approach are compared with those without scatter
correction, and with scatter estimated and corrected using a slit measurement as a pre-scan. The comparison
shows that the primary modulation method greatly reduces the scatter artifacts and improves image contrast.
Using only one single scan, this method achieves CT HU accuracy comparable to that obtained using a slit measurement as a pre-scan.
The noise of low-dose computed tomography (CT) sinogram follows approximately a Gaussian distribution with nonlinear dependence between the sample mean and variance. The noise is statistically uncorrelated among detector bins at any view angle. However the correlation coefficient matrix of data signal indicates a strong signal correlation among neighboring views. Based on above observations, Karhunen-Loeve (KL) transform can be used to de-correlate the signal among the neighboring views. In each KL component, a penalized weighted least-squares (PWLS) objective function can be constructed and optimal sinogram can be estimated by minimizing the objective function, followed by filtered backprojection (FBP) for CT image reconstruction. In this work, we compared the KL-PWLS method with an iterative image reconstruction algorithm, which uses the Gauss-Seidel iterative calculation to minimize the PWLS objective function in image domain. We also compared the KL-PWLS with an iterative sinogram smoothing algorithm, which uses the iterated conditional mode calculation to minimize the PWLS objective function in sinogram space, followed by FBP for image reconstruction. Phantom experiments show a comparable performance of these three PWLS methods in suppressing the noise-induced artifacts and preserving resolution in reconstructed images. Computer simulation concurs with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS noise reduction may have the advantage in computation for low-dose CT imaging, especially for dynamic high-resolution studies.
Helical computed tomography (HCT) has several advantages over conventional step-and-shoot CT for imaging a relatively large object, especially for dynamic studies. However, HCT may increase X-ray exposure significantly to the patient. This work aims to reduce the radiation by lowering the X-ray tube current (mA) and filtering the low-mA (or dose) sinogram noise. Based on the noise properties of HCT sinogram, a three-dimensional (3D) penalized weighted least-squares (PWLS) objective function was constructed and an optimal sinogram was estimated by minimizing the objective function. To consider the difference of signal correlation among different direction of the HCT sinogram, an anisotropic Markov random filed (MRF) Gibbs function was designed as the penalty. The minimization of the objection function was performed by iterative Gauss-Seidel updating strategy. The effectiveness of the 3D-PWLS sinogram smoothing for low-dose HCT was demonstrated by a 3D Shepp-Logan head phantom study. Comparison studies with our previously developed KL domain PWLS sinogram smoothing algorithm indicate that the KL+2D-PWLS algorithm shows better performance on in-plane noise-resolution trade-off while the 3D-PLWS shows better performance on z-axis noise-resolution trade-off. Receiver operating characteristic (ROC) studies by using channelized Hotelling observer (CHO) shows that 3D-PWLS and KL+2DPWLS algorithms have similar performance on detectability in low-contrast environment.
Low-dose CT (computed tomography) sinogram data have been shown to be signal-dependent with an analytical relationship between the sample mean and sample variance. Spatially-invariant low-pass linear filters, such as the Butterworth and Hanning filters, could not adequately handle the data noise and statistics-based nonlinear filters may be an alternative choice, in addition to other choices of minimizing cost functions on the noisy data. Anisotropic diffusion filter and nonlinear Gaussian filters chain (NLGC) are two well-known classes of nonlinear filters based on local statistics for the purpose of edge-preserving noise reduction. These two filters can utilize the noise properties of the low-dose CT sinogram for adaptive noise reduction, but can not incorporate signal correlative information for an optimal regularized solution. Our previously-developed Karhunen-Loeve (KL) domain PWLS (penalized weighted least square) minimization considers the signal correlation via the KL strategy and seeks the PWLS cost function minimization for an optimal regularized solution for each KL component, i.e., adaptive to the KL components. This work compared the nonlinear filters with the KL-PWLS framework for low-dose CT application. Furthermore, we investigated the nonlinear filters for post KL-PWLS noise treatment in the sinogram space, where the filters were applied after ramp operation on the KL-PWLS treated sinogram data prior to backprojection operation (for image reconstruction). By both computer simulation and experimental low-dose CT data, the nonlinear filters could not outperform the KL-PWLS framework. The gain of post KL-PWLS edge-preserving noise filtering in the sinogram space is not significant, even the noise has been modulated by the ramp operation.
Reinhard Schulte, Margio Klock, Vladimir Bashkirov, Ivan Evseev, Joaquim de Assis, Olga Yevseyeva, Ricardo Lopes, Tianfang Li, David Williams, Andrew Wroe, Hugo Schelin
Conformal proton radiation therapy requires accurate prediction of the Bragg peak position. This problem may be solved by using protons rather than conventional x-rays to determine the relative electron density distribution via proton computed tomography (proton CT). However, proton CT has its own limitations, which need to be carefully studied before this technique can be introduced into routine clinical practice. In this work, we have used analytical relationships as well as the Monte Carlo simulation tool GEANT4 to study the principal resolution limits of proton CT. The GEANT4 simulations were validated by comparing them to predictions of the Bethe Bloch theory and Tschalar's theory of energy loss straggling, and were found to be in good agreement. The relationship between phantom thickness, initial energy, and the relative electron density uncertainty was systematically investigated to estimate the number of protons and dose needed to obtain a given density resolution. The predictions of this study were verified by simulating the performance of a hypothetical proton CT scanner when imaging a cylindrical water phantom with embedded density inhomogeneities. We show that a reasonable density resolution can be achieved with a relatively small number of protons, thus providing a possible dose advantage over x-ray CT.
KEYWORDS: Signal to noise ratio, X-ray computed tomography, Data modeling, X-rays, Sensors, Smoothing, Calibration, Linear filtering, Image filtering, Scanners
To treat the noise in low-dose x-ray CT projection data more accurately, analysis of the noise properties of the data and development of a corresponding efficient noise treatment method are two major problems to be addressed. In order to obtain an accurate and realistic model to describe the x-ray CT system, we acquired thousands of repeated measurements on different phantoms at several fixed scan angles by a GE high-speed multi-slice spiral CT scanner. The collected data were calibrated and log-transformed by the sophisticated system software, which converts the detected photon energy into sinogram data that satisfies the Radon transform. From the analysis of these experimental data, a nonlinear relation between mean and variance for each datum of the sinogram was obtained. In this paper, we integrated this nonlinear relation into a penalized likelihood statistical framework for a SNR (signal-to-noise ratio) adaptive smoothing of noise in the sinogram. After the proposed preprocessing, the sinograms were reconstructed with unapodized FBP (filtered backprojection) method. The resulted images were evaluated quantitatively, in terms of noise uniformity and noise-resolution tradeoff, with comparison to other noise smoothing methods such as Hanning filter and Butterworth filter at different cutoff frequencies. Significant improvement on noise and resolution tradeoff and noise property was demonstrated.
Advantages of proton computed tomography (pCT) have been recognized in the past decades. However, the quality of
pCT images is limited due to the stochastic nature of the proton path inside the object. Numerous small angle scatters
by the nuclei Coulomb field cause the exact proton path impossible to trace. The reconstruction from measurements of
the proton energy-loss has a spatial resolution limit due to these deflections. However, it has been shown that the proton
path inside a uniform medium follows certain probability distribution so that a most likely trajectory (MLT) can be
derived analytically for each proton. For real scan of a regular non-uniform object in pCT, the internal trajectory is
better approximated by the MLT rather than a straight-line estimation. In this report, we presented preliminary studies
on how the curved trajectories would affect the quality of the reconstructed images, and how much improvement we can
achieve in reconstruction with the exact trajectory information. Analytical simulations with three phantoms, including a
uniform disk phantom, multi-hole Aluminum phantom and Shepp-Logan phantom, were performed using artificial
internal trajectories calculated based on the entrance and exit proton information. Reconstructions with the exact paths
were compared to those with the straight-line path estimation. Significant improvement in density uniformity and
spatial resolution were observed in the reconstructions with the path information.
In the past decades, analytical (non-iterative) methods have been extensively investigated and developed for the reconstruction of three-dimensional (3D) single-photon emission computed tomography (SPECT). However, it becomes possible only recently when the exact analytic non-uniform attenuation reconstruction algorithm was derived. Based on the explicit inversion formula for the attenuated Radon transform discovered by Novikov (2000), we extended the previous researches of inverting the attenuated Radon transform of parallel-beam collimation geometry to fan-beam and variable focal-length fan-beam (VFF) collimators and proposed an efficient, analytical solution to 3D SPECT reconstruction with VFF collimators, which compensates simultaneously for non-uniform attenuation, scatter, and spatially-variant or distance-dependent resolution variation (DDRV), as well as suppression of signal-dependent non-stationary Poisson noise. In this procedure, to avoid the reconstructed images being corrupted by the presence of severe noise, we apply a Karhune-Loève (K-L) domain adaptive Wiener filter, which accurately treats the non-stationary Poisson noise. The scatter is then removed by our scatter estimation method, which is based on the energy spectrum and modified from the triple-energy-window acquisition protocol. For the correction of DDRV, a distance-dependent deconvolution is adapted to provide a solution that realistically characterizes the resolution kernel in a real SPECT system. Finally image is reconstructed using our VFF non-uniform attenuation inversion formula.
In this work, we have developed a new method for SPECT (single photon emission computed tomography) image reconstruction, which has shown the potential to provide higher resolution results than any other conventional methods using the same projection data. Unlike the conventional FBP- (filtered backprojection) and EM- (expectation maximization) type algorithms, we utilize as much system response information as we can during the reconstruction process. This information can be pre-measured during the calibration process and stored in the computer. By selecting different sampling schemes for the point response measurement, different system kernel matrices are obtained. Reconstruction utilizing these kernels generates a set of reconstructed images of the same source. Based on these reconstructed images and their corresponding sampling schemes, we are able to achieve a high resolution final image that best represents the object. Because a uniform attenuation, resolution variation and some other effects are included during the formation of the system kernel matrices, the reconstruction from the acquired projection data also compensates for all these effects correctly.
Based on Kunyansky's and our previous work, an efficient, analytical solution to the reconstruction problem of myocardial perfusion SPECT has been developed that allows simultaneous compensation for non-uniform attenuation, scatter, and system-dependent resolution variation, as well as suppression of signal-dependent Poisson noise. To avoid reconstructed images being corrupted by the presence of Poisson noise, a Karhunen-Loeve (K-L) domain adaptive Wiener filter is applied first to suppress the noise in the primary- and scatter-window measurements. The scatter contribution to the primary-energy-window measurements is then removed by our scatter estimation method, which is energy spectrum based, modified from the triple-energy-window acquisition protocol. The resolution variation is corrected by the depth-dependent deconvolution, which, being based on the central-ray approximation and the distance-frequency relation, deconvolves the scatter-free data with the accurate detector-response kernel in frequency domain. Finally, the deblurred projection data are analytically reconstructed with non-uniform attenuation by an algorithm based on Novikov's explicit inversion formula. The preliminary Monte Carlo simulation results using a realistic human thoracic phantom demonstrate that, for parallel-beam geometry, the proposed analytical reconstruction scheme is computationally comparable to filtered backprojection and quantitatively equivalent to iterative maximum a posteriori expectation-maximization reconstruction. Extension to other geometries is under progress.
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