Dual-energy CT imaging with limited-angular-range data

Abstract

In dual-energy computed tomography (DECT), low- and high-kVp data are collected often over a full-angular range (FAR) of 360°. While there exists strong interest in DECT with low- and high-kVp data acquired over limited-angular ranges (LARs), there remains little investigation of image reconstruction in DECT with LAR data.Objective: we investigate image reconstruction with minimized LAR artifacts from low- and high-kVp data over LARs of ≤180° by using a directional-total-variation (DTV) algorithm.Methods: image reconstruction from LAR data is formulated as a convex optimization problem in which data-ℓ₂is minimized with constraints on image's DTVs along orthogonal axes. We then achieve image reconstruction by applying the DTV algorithm to solve the optimization problem. We conduct numerical studies from data generated over arcs of LARs, ranging from 14° to 180°, and perform visual inspection and quantitative analysis of images reconstructed.Results: monochromatic images of interest obtained with the DTV algorithm from LAR data show substantially reduced artifacts that are observed often in images obtained with existing algorithms. The improved image quality also leads to accurate estimation of physical quantities of interest, such as effective atomic number and iodine contrast concentration.Conclusion: our study reveals that from LAR data of low- and high-kVp, monochromatic images can be obtained that are visually, and physical quantities can be estimated that are quantitatively, comparable to those obtained in FAR DECT.Significance: as LAR DECT is of high practical application interest, the results acquired in the work may engender insights into the design of DECT with LAR scanning configurations of practical application significance.

Keywords: atomic number; directional-total-variation; dual-energy CT; iodine cocentration; limited-angular-range reconstruction.

Figure A1.

Monochromatic images at 34 keV of the breast phantom obtained by use of the DTV algorithm from 60° data with $\left(t_x^L,t_y^L,t_x^H,t_y^H\right)=(123.5,224.0,80.8,156.0)$ (a), (169.0, 224.0, 102.0, 156.0) (b), (130.0, 224.0, 80.8, 165.8) (c), and (130.0, 238.0, 85.0, 175.5) (d), respectively. Display window: [0.2, 0.35] cm⁻¹.

Figure 1.

Scanning configuration with overlapping arcs of LAR (thin and thick curves) for collecting low- and high-kVp data. The coordinate system of the image array is set up such that the circular scanning arc is symmetric relative to the y-axis.

Figure 2.

Monochromatic images for the (a) suitcase phantom at 40 keV and (b) breast phantom at 34 keV. The numbers in each of the phantoms indicate ROIs of different materials. In the suitcase phantom, ROIs 0–6 contain C, Al, Ca, water, ANFO, teflon, and PVC, respectively. In the breast phantom, the darker and brighter background regions are adipose tissue and breast tissue (including skin), respectively; ROI 0 contains breast tissue, whereas ROIs 1–3 are filled with iodine contrast agent of concentration 5, 2, and 2.5 mg ml⁻¹, respectively. Display windows for the suitcase and breast phantoms are [0.1, 0.65] cm⁻¹ and [0.2, 0.35] cm⁻¹, respectively.

Figure 3.

Monochromatic images at 40 keV (top row) and their respective zoomed-in ROI views (bottom row) of the suitcase phantom obtained by use of the DTV (column 1) and FBP (column 2) algorithms from noiseless data generated over an arc of 60°, and the DTV-reference image (column 3) and FBP-reference image (column 4). The ROI is enclosed by the rectangular box depicted in the FBP-reference image. Display window: [0.1, 0.65] cm⁻¹.

Figure 4.

Monochromatic images (rows 1 and 3) of the suitcase phantom at 40 keV obtained from noiseless data generated over arcs of LARs 14°, 20°, 30°, 60°, 90°, 120°, 150°, and 360° by use of the DTV algorithm, along with their respective zoomed-in ROI views (rows 2 and 4). The zoomed-in ROI is enclosed by the rectangular box depicted in the FBP-reference image in figure 3. Display window: [0.1, 0.65] cm⁻¹.

Figure 5.

Metrics PCC and nMI, as functions of LAR α, of monochromatic images of the suitcase at 40 keV obtained by use of the DTV (solid) and FBP (dotted) algorithms from noiseless data.

Figure 6.

Atomic numbers (solid), as functions of LAR α, for (a) water, (b) ANFO, (c) teflon, and (d) PVC in the suitcase phantom estimated from images reconstructed by use of the DTV algorithm from noiseless data. The two horizontal lines, which are very close, indicate the atomic numbers estimated from the DTV-reference (dashed) and FBP-reference (dotted) images.

Figure 7.

Monochromatic images (rows 1 and 3) of the suitcase phantom at 40 keV obtained from noisy data generated over arcs of LARs 14°, 20°, 30°, 60°, 90°, 120°, 150°, and 360° by use of the DTV algorithm, along with their respective zoomed-in ROI views (rows 2 and 4). The zoomed-in ROI is enclosed by the rectangular box depicted in the FBP-reference image in figure 3. Display window: [0.1, 0.65] cm⁻¹.

Figure 8.

Metrics PCC and nMI, as functions of LAR α, of monochromatic images of the suitcase at 40 keV obtained by use of the DTV (solid) and FBP (dotted) algorithms from noisy data.

Figure 9.

Atomic numbers (solid), as functions of LAR α, for (a) water, (b) ANFO, (c) teflon, and (d) PVC in the suitcase phantom estimated from images reconstructed by use of the DTV algorithm from noisy data. The two horizontal lines, which are very close, indicate the atomic numbers estimated from the DTV-reference (dashed) and FBP-reference (dotted) images.

Figure 10.

Monochromatic images at 34 keV (top row) and their respective zoomed-in ROI views (bottom row) within the breast phantom obtained by use of the DTV (column 1) and FBP (column 2) algorithms from noiseless data generated over an arc of LAR 60°, and the DTV-reference image (column 3) and FBP-reference image (column 4). The zoomed-in ROI is enclosed by the rectangular box depicted in the FBP-reference image. Display window: [0.2, 0.35] cm⁻¹.

Figure 11.

Monochromatic images (rows 1 and 3) of the breast phantom at 34 keV obtained from noiseless data generated over arcs of LARs 14°, 20°, 30°, 60°, 90°, 120°, 150°, and 360° by use of the DTV algorithm, along with their respective zoomed-in ROI views (rows 2 and 4). The zoomed-in ROI is enclosed by the rectangular box depicted in the FBP-reference image in figure 10. Display window: [0.2, 0.35] cm⁻¹.

Figure 12.

Metrics PCC and nMI, as functions of LAR α, of monochromatic images at 34 keV obtained by use of the DTV (solid) and FBP (dotted) algorithms from noiseless data of the breast phantom.

Figure 13.

Estimated iodine concentrations (solid), as functions of LAR α, for ROIs 1–3 in the breast phantom from images reconstructed by use of the DTV algorithm from noiseless data. The two horizontal lines, which are very close, indicate the iodine concentrations estimated from the DTV-reference (dashed) and FBP-reference (dotted) images.

Figure 14.

Monochromatic images (rows 1 and 3) of the breast phantom at 34 keV obtained from noisy data generated over arcs of LARs 14°, 20°, 30°, 60°, 90°, 120°, 150°, and 360° by use of the DTV algorithm, along with their respective zoomed-in ROI views (rows 2 and 4). The zoomed-in ROI is enclosed by the rectangular box depicted in the FBP-reference image in figure 10. Display window: [0.2, 0.35] cm⁻¹.

Figure 15.

Metrics PCC and nMI, as functions of LAR α, of monochromatic images at 34 keV obtained by use of the DTV (solid) and FBP (dotted) algorithms from noisy data of the breast phantom.

Figure 16.

Estimated iodine concentrations (solid), as functions of LAR α, for ROIs 1–3 in the breast phantom from images reconstructed by use of the DTV algorithm from noisy data. The two horizontal lines, which are very close, indicate the atomic numbers estimated from the DTV-reference (dashed) and FBP-reference (dotted) images.

Figure 17.

Monochromatic images of the suitcase phantom at 40 keV (row 1) and of the breast phantom at 34 keV (row 2) obtained from noiseless data generated over arcs of LARs 14° (columns 1), 20° (columns 2), 30° (columns 3), and 60° (columns 4) by use of the ITV algorithm. Display windows: [0.1, 0.65] cm⁻¹ and [0.2, 0.35] cm⁻¹ for the suitcase and breast phantoms, respectively.