Addressing CT metal artifacts using photon-counting detectors and one-step spectral CT image reconstruction

Abstract

Purpose: The constrained one-step spectral CT image reconstruction (cOSSCIR) algorithm with a nonconvex alternating direction method of multipliers optimizer is proposed for addressing computed tomography (CT) metal artifacts caused by beam hardening, noise, and photon starvation. The quantitative performance of cOSSCIR is investigated through a series of photon-counting CT simulations.

Methods: cOSSCIR directly estimates basis material maps from photon-counting data using a physics-based forward model that accounts for beam hardening. The cOSSCIR optimization framework places constraints on the basis maps, which we hypothesize will stabilize the decomposition and reduce streaks caused by noise and photon starvation. Another advantage of cOSSCIR is that the spectral data need not be registered, so that a ray can be used even if some energy window measurements are unavailable. Photon-counting CT acquisitions of a virtual pelvic phantom with low-contrast soft tissue texture and bilateral hip prostheses were simulated. Bone and water basis maps were estimated using the cOSSCIR algorithm and combined to form a virtual monoenergetic image for the evaluation of metal artifacts. The cOSSCIR images were compared to a "two-step" decomposition approach that first estimated basis sinograms using a maximum likelihood algorithm and then reconstructed basis maps using an iterative total variation constrained least-squares optimization (MLE+TV ${}_{\min }$ ). Images were also compared to a nonspectral TV ${}_{\min }$ reconstruction of the total number of counts detected for each ray with and without normalized metal artifact reduction (NMAR) applied. The simulated metal density was increased to investigate the effects of increasing photon starvation. The quantitative error and standard deviation in regions of the phantom were compared across the investigated algorithms. The ability of cOSSCIR to reproduce the soft-tissue texture, while reducing metal artifacts, was quantitatively evaluated.

Results: Noiseless simulations demonstrated the convergence of the cOSSCIR and MLE+TV ${}_{\min }$ algorithms to the correct basis maps in the presence of beam-hardening effects. When noise was simulated, cOSSCIR demonstrated a quantitative error of -1 HU, compared to 2 HU error for the MLE+TV ${}_{\min }$ algorithm and -154 HU error for the nonspectral TV ${}_{\min }$ +NMAR algorithm. For the cOSSCIR algorithm, the standard deviation in the central iodine region of interest was 20 HU, compared to 299 HU for the MLE+TV ${}_{\min }$ algorithm, 41 HU for the MLE+TV ${}_{\min }$ +Mask algorithm that excluded rays through metal, and 55 HU for the nonspectral TV ${}_{\min }$ +NMAR algorithm. Increasing levels of photon starvation did not impact the bias or standard deviation of the cOSSCIR images. cOSSCIR was able to reproduce the soft-tissue texture when an appropriate regularization constraint value was selected.

Conclusions: By directly inverting photon-counting CT data into basis maps using an accurate physics-based forward model and a constrained optimization algorithm, cOSSCIR avoids metal artifacts due to beam hardening, noise, and photon starvation. The cOSSCIR algorithm demonstrated improved stability and accuracy compared to a two-step method of decomposition followed by reconstruction.

Keywords: metal artifacts; photon-counting CT; reconstruction.

Figure 1:

(left) Pelvic phantom used for simulations depicting regions of water, adipose, bone, titanium of 11-mm diameter in each femur, and two 3 mg/ml iodine contrast elements marked with arrows. (center) Ground truth 55 keV monoenergetic image of the phantom displayed at a window of −250 HU to 250 HU to visualize the texture in the adipose and soft tissue regions. (right) ROIs in water and adipose tissue extracted to estimate NPS.

Figure 2:

Spectra of photons detected by each of the four simulated energy windows. These spectra take into account the flux-independent spectral response of the modeled CdTe detector.

Figure 3:

Convergence of the cOSSCIR algorithm in the absence of noise is demonstrated by: (top) The Poisson likelihood data error metric, normalized by mean total number of simulated photons, and the RMSE normalized by total number of photons plotted against iteration number; (bottom); RMSE between estimated basis maps and ground truth phantom plotted against iteration number.

Figure 4:

The ground truth 55 keV image of the pelvic phantom is displayed along with the 55 keV virtual monoenergetic image reconstructed by the cOSSCIR and two-step MLE+TV_min methods for the case of noiseless data. The image resulting from summing all counts in each ray and reconstructing with the nonspectral TV_min algorithm is also displayed to demonstrate beam hardening artifacts due to metal, which are reduced using the TV_min+NMAR method. All images are displayed at a window of −250 to 250 HU, therefore the metal is not visible. Instead, the metal regions are identified by the circle contours in the ground truth image.

Figure 5:

ROIs extracted from the soft tissue regions of the phantom for the ground truth 55 keV image and the 55 keV image reconstructed by cOSSCIR at a range of GTV constraint values. The GTV constraint values are labeled as the factor multiplying the true GTV value.

Figure 6:

ROIs extracted from the adipose regions of the phantom for the ground truth 55 keV image and the 55 keV image reconstructed by cOSSCIR at a range of GTV constraint values. The GTV constraint values are labeled as the factor multiplying the true GTV value.

Figure 7:

The radial NPS of the ground truth 55 keV image and the 55 keV images reconstructed by cOSSCIR at a range of GTV constraint values for (top) soft tissue regions and (bottom) adipose regions, where the NPS represents the anatomical texture in these noise free simulations.

Figure 8:

Images reconstructed from noisy data by cOSSCIR, MLE+TV_min, and nonspectral TV_min displayed for a range of constraint levels. The displayed constraint level is the factor by which the true TV parameter for each respective algorithm was multiplied to generate the constraint applied during reconstruction. Images are displayed at a window of −250 HU to 250 HU.

Figure 9:

Bias versus standard deviation in the peripheral iodine ROI plotted for the cOSSCIR, MLE+TV_min, and MLE+TV_min+Mask algorithms for the range of studied TV constraint levels (1 to 4 times the true TV level).

Figure 10:

Images reconstructed from data with noise but without photon starvation. The ground truth 55 keV image of the pelvic phantom is displayed along with the 55 keV virtual monoenergetic image reconstructed by the cOSSCIR, two-step MLE+TV_min, two-step with rays through metal excluded ( MLE+TV_min+Mask), nonspectral TV_min, and nonspectral TV_min+NMAR methods. All images are displayed at a window of −250 to 250 HU. The metal regions are identified by the circle contours in the ground truth image.

Figure 11:

Box plots comparing the CT numbers in the central and peripheral iodine ROIs of the images compared in Figure 10, for simulations with noise but without photon starvation. The solid horizontal line represents the ground truth value.

Figure 12:

The NPS due to anatomical texture in the (top) soft tissue and (bottom) adipose regions of the phantom for cOSSCIR images reconstructed from noisy data at a range of GTV constraint values. The NPS of the ground truth 55 keV images is also plotted for reference. The NPS due to texture was estimated by subtracting the estimated NPS due to noise from the NPS estimated from images reconstructed with texture and noise, as described in Section V..

Figure 13:

The 55 keV monoenergetic images resulting from the studied reconstruction algorithms for data with the titanium density increased by a factor of 1.5 causing photon starvation in the two lowest energy windows of some rays. All images are displayed at a window of −250 to 250 HU. The metal regions are identified by the circle contours in the ground truth image.

Figure 14:

Box plots comparing the CT numbers in the central and peripheral iodine ROIs of the images compared in Figure 13 for data with titanium density increased by a factor of 1.5. The solid horizontal line represents the ground truth value.

Figure 15:

The 55 keV monoenergetic images resulting from the studied reconstruction algorithms for data with the titanium density increased by a factor of 4 causing 0.6% of rays to detect zero counts in all energy windows, with higher percentages of photon starvation in the lower energy windows. The image reconstructed by MLE+TV_min excluded rays where all or all but one energy window detected zero counts, while the image reconstructed by nonspectral TV_min excluded all rays with zero detected counts, which is signified with the label ‘counts>0’ in the figure. Images reconstructed by MLE+TV_min+Mask excluded all rays through metal. Images reconstructed by nonspectral TV_min+NMAR replaced the rays corrupted by metal using the NMAR technique. All images are displayed at a window of −250 to 250 HU. The metal regions are identified by the circle contours in the ground truth image.

Figure 16:

Box plots comparing the CT numbers in the central and peripheral iodine ROIs of the images compared in Figure 15 for data with titanium density increased by a factor of 4.0. The MLE+TV_min algorithm excluded rays for which the lowest three energy windows detected zero counts, while the nonspectral TV_min algorithm excluded rays that detected zero counts across all energy windows. The MLE+TV_min+Mask excluded all rays through metal, while the nonspectral TV_min+NMAR algorithm replaced the sinogram measurements through metal using the NMAR technique. The solid horizontal line represents the ground truth value.