1. Evaluation of mA Switching Method with Penalized Weighted Least-Square Noise Reduction for Low-dose CT
Yunjeong Lee, Hyekyun Chung, and Seungryong Cho
Department of Nuclear and Quantum Engineering, KAIST
Results
Computed Tomography (CT) has been increasingly used in clinics for many purposes including diagnosis, intervention, and prognosis.
Its image quality should be guaranteed for successful completion of such medical tasks, but at minimal cost of radiation dose to patients.
In this work, we investigated whether mAs switching during a scan improves image quality after the penalized-weighted least-square (PWLS) noise reduction under a constraint of constant total exposure.
Introduction
Reconstructed images of the phantom
(a)
(b)
(c)
Methods
Fig. 2 (a) : from projection images acquired with 9 mAs scan
(b) : from PWLS noise reduction for 9 mAs projection images
(c) : from PWLS noise reduction for the shuffled 4 mAs and 14 mAs projection images
Acquire the data sample
The XCAT phantom was used to simulate a human torso and we focused our study on the reconstruction of 2 dimensional slice of the abdominal region.
We numerically simulated an mA switching in CT and acquired projections: one at higher tube current time product setting (e.g. 14 mAs) and the other at lower tube current time product setting (e.g. 4 mAs) in an alternating fashion. For comparison, we also acquired projections at a constant tube current setting (e.g. 9 mAs).
1 D line profile of the reconstructed image and noise-resolution trade-off.
Penalized Weighted Least-Squares (PWLS) noise reduction
PWLS algorithm was adapted to study whether the mAs switching method can produce better images than the constant mAs method. The PWLS criterion can be used to estimate the corresponding ideal sinogram by minimizing the following cost function.
Fig. 3. 2D line profile along the horizontal midline of the reconstructed image in Fig. 2.,
and noise-resolution trade-off curve for 9 mAs CT scan and modulated CT scan with PWLS
The root mean square error and relative standard deviation in every region of interest
ŷ: system-calibrated and log-transformed projection measurements
q: vector of ideal projection data
∑: diagonal variance matrix
R: roughness penalty
β : smoothing parameter
TABLE 1. RMSE for regions of interest
ROI 1
ROI 2
ROI 3
ROI 4
9 mAs
10.695
8.551
10.246
8.644
9 mAs, PWLS
6.501
5.426
7.133
4.697
mixed, PWLS
6.666
5.203
8.289
4.841
TABLE 2. RSD for regions of interest ( x 102 )
The iterative Gauss-Seidal (GS) update algorithm was adapted and the update rule follows the below equation.
ROI 1
ROI 2
ROI 3
ROI 4
9 mAs
1.357
1.123
1.305
1.078
9 mAs, PWLS
0.825
0.712
0.909
0.586
mixed, PWLS
0.845
0.684
1.068
0.604
n: iterative number
Ni1: upper and left pixels of qi
Ni2: right and lower pixels of qi
σi: variance
Wim: weight parameter
Comparing the line profiles of the reconstructed images, we observed that the image reconstructed from the mAs switching method has different noise patterns from the one with the constant mAs method.
The relative standard deviation and root mean square error at the selected ROIs did not show practical advantage of the mAs switching method in terms of denoising.
The resolution-noise tradeoff curves implied that the PWLS denoising method does not selectively work better for the data acquired by mAs switching.
Root mean square error & Relative standard deviation
For a quantitative analysis of image quality, the reconstructed image noise was characterized by the root mean square error (RMSE) and the relative standard deviation (RSD) of uniform regions of the phantom as shown in the Fig. 1.
Denoised images were obtained from both the contrast and alternating mAs scanned data after the PWLS algorithm were applied. However, alternating scanning dose not seem to show better performance compared to the constant scanning method.
Conclusions
f: reconstructed image
fr: reference image
N: number of pixels
References
σ: variance of pixel values
μ: mean of pixel values
Patrick J. La Rivière, “Penalized-likelihood sinogram smoothing for low-dose CT,” Med. Phys. vol. 32, no. 6, pp , June
Jing Wang, Tianfang Li, Hongbing Lu, and Zhengrong Liang, “Penalized weighted least-square approach to sinogram noise reduction and image reconstruction for low-dose x-ray computed tomography,” IEEE Trans. Medical Imaging, vol. 25, no. 10, pp , Oct
Trlet Le, Rick Chartrand, and Thomas J. Asaki, “A variational approach to reconstructing images corrupted by poisson noise,” J Math Imaging Vis 27, pp , 2007.
Fig. 1 Four regions of interest of the reconstructed image.