February  2022, 16(1): 179-195. doi: 10.3934/ipi.2021045

Learning to scan: A deep reinforcement learning approach for personalized scanning in CT imaging

1. 

Academy for Advanced Interdisciplinary Studies, Peking University, China

2. 

Computer Science Department, Carnegie Mellon University, USA

3. 

Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School, USA

4. 

Department of Mathematics, University of California, Santa Barbara, USA

5. 

Beijing International Center for Mathematical Research, Center for Data Science, Institute for Artificial Intelligence, Peking University, China

Corresponding Author

* Equal Contribution

Received  October 2020 Revised  April 2021 Published  February 2022 Early access  July 2021

. Computed Tomography (CT) takes X-ray measurements on the subjects to reconstruct tomographic images. As X-ray is radioactive, it is desirable to control the total amount of dose of X-ray for safety concerns. Therefore, we can only select a limited number of measurement angles and assign each of them limited amount of dose. Traditional methods such as compressed sensing usually randomly select the angles and equally distribute the allowed dose on them. In most CT reconstruction models, the emphasize is on designing effective image representations, while much less emphasize is on improving the scanning strategy. The simple scanning strategy of random angle selection and equal dose distribution performs well in general, but they may not be ideal for each individual subject. It is more desirable to design a personalized scanning strategy for each subject to obtain better reconstruction result. In this paper, we propose to use Reinforcement Learning (RL) to learn a personalized scanning policy to select the angles and the dose at each chosen angle for each individual subject. We first formulate the CT scanning process as an Markov Decision Process (MDP), and then use modern deep RL methods to solve it. The learned personalized scanning strategy not only leads to better reconstruction results, but also shows strong generalization to be combined with different reconstruction algorithms.

Citation: Ziju Shen, Yufei Wang, Dufan Wu, Xu Yang, Bin Dong. Learning to scan: A deep reinforcement learning approach for personalized scanning in CT imaging. Inverse Problems and Imaging, 2022, 16 (1) : 179-195. doi: 10.3934/ipi.2021045
References:
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show all references

References:
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W. van AarleW. J. PalenstijnJ. CantE. JanssensF. BleichrodtA. DabravolskiJ. De BeenhouwerK. J. Batenburg and J. Sijbers, Fast and flexible x-ray tomography using the astra toolbox, Optics Express, 22 (2016), 25129-25147. 

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J. Adler and O. Oktem, Learned primal-dual reconstruction, IEEE Transactions on Medical Imaging, 37 (2018), 1322-1332. 

[4]

K. J. BatenburgW. J. PalenstijnP. Balázs and J. Sijbers, Dynamic angle selection in binary tomography, Computer Vision and Image Understanding, 117 (2013), 306-318. 

[5]

I. Bello, H. Pham, Q. V Le, M. Norouzi and S. Bengio, Neural combinatorial optimization with reinforcement learning, preprint, arXiv: 1611.09940, 2016.

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S. Boyd and N. Parikh, Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends in Machine Learning, 3 (2011), 1-122. 

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E. J. Candes, Y. C. Eldar, et al., Compressed Sensing With Coherent and Redundant Dictionaries, 2010.

[11]

E. J. CandesJ. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52 (2006), 489-509.  doi: 10.1109/TIT.2005.862083.

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H. ChenY. ZhangM. K. KalraF. LinY. ChenP. LiaoJ. Zhou and G. Wang, Low-dose CT with a residual encoder-decoder convolutional neural network, IEEE Transactions on Medical Imaging, 36 (2017), 2524-2535. 

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K. DabovA. FoiV. Katkovnik and K. Egiazarian, Image denoising by sparse 3-d transform-domain collaborative filtering, IEEE Transactions on Image Processing, 16 (2007), 2080-2095.  doi: 10.1109/TIP.2007.901238.

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[19]

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[20]

J. M. Ede, Adaptive partial scanning transmission electron microscopy with reinforcement learning, preprint, arXiv: 2004.02786.

[21]

M. Elad and M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries, IEEE Transactions on Image processing, 15 (2006), 3736-3745.  doi: 10.1109/TIP.2006.881969.

[22]

E. Esser and X. Zhang, A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science, SIAM Journal on Imaging Sciences, 3 (2010), 1015-1046.  doi: 10.1137/09076934X.

[23]

M. GiesW. A. KalenderH. Wolf and C. Suess, Dose reduction in CT by anatomically adapted tube current modulation. i. Simulation studies, Medical Physics, 26 (1999), 2235-2247. 

[24]

G. D. Godaliyadda, M. A. Uchic, D. H. Ye, M. A. Groeber, G. T. Buzzard and C. A. Bouman, A supervised learning approach for dynamic sampling, S & T Imaging. International Society for Optics and Photonics, 2016.

[25]

G. M. D. P. GodaliyaddaD. H. YeM. D. UchicM. A. GroeberG. T. Buzzard and C. A. Bouman, A framework for dynamic image sampling based on supervised learning (slads), IEEE Trans. Comput. Imaging, 4 (2018), 1-16.  doi: 10.1109/TCI.2017.2777482.

[26]

T. Goldstein and S. Osher, The split bregman method for l1-regularized problems, SIAM Journal Imaging Sciences, 2 (2009), 323-343.  doi: 10.1137/080725891.

[27]

T. Goldstein and S. Osher, The split bregman method for $l_1$-regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), 323-343.  doi: 10.1137/080725891.

[28]

R. Gordon, R. Benderab and G. T. Herman, Algebraic Reconstruction Techniques (ART) for Three-Dimensional Electron Microscopy and X-ray Photography, Journal of Theoretical Biology, 1970.

[29]

S. Gu, L. Zhang, W. Zuo and X. Feng, Weighted nuclear norm minimization with application to image denoising, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, (2014), 2862–2869.

[30]

A. Halimi, P. Ciuciu, A. Mccarthy, S. Mclaughlin and G. Buller, Fast adaptive scene sampling for single-photon 3d lidar images, IEEE CAMSAP 2019 - International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2019.

[31]

S. JiY. Xue and L. Carin, Bayesian compressive sensing, IEEE Transactions on Signal Processing, 56 (2008), 2346-2356.  doi: 10.1109/TSP.2007.914345.

[32]

K. H. JinM. T. McCannE. Froustey and M. Unser, Deep convolutional neural network for inverse problems in imaging, IEEE Transactions on Image Processing, 26 (2017), 4509-4522.  doi: 10.1109/TIP.2017.2713099.

[33]

W. A. KalenderH. Wolf and C. Suess, Dose reduction in CT by anatomically adapted tube current modulation. ii. Phantom measurements, Medical Physics, 26 (1999), 2248-2253. 

[34]

E. Kang, J. Min and J. C. Ye, A deep conversational neural network using directional wavelets for low-dose x-ray ct reconstruction, Medical Physics, 44 (2017), e360–e375. doi: 10.1002/mp.12344.

[35]

A. Katsevich, Theoretically exact filtered backprojection-type inversion algorithm for spiral CT, SIAM Journal on Applied Mathematics, 62 (2002), 2012-2026.  doi: 10.1137/S0036139901387186.

[36]

D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv: 1412.6980, 2014.

[37]

W. Kool, H. V. Hoof and M. Welling, Attention, learn to solve routing problems!, preprint, arXiv: 1803.08475, 2018.

[38]

Y. Li, Deep Reinforcement Learning: An overview, arXiv: 1701.07274, 2017.

[39]

L. Ly and Y.-H. R. Tsai, Autonomous exploration, reconstruction, and surveillance of 3d environments aided by deep learning, arXiv: 1809.06025, 2018.

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M. T. McCannK. H. Jin and M. Unser, Convolutional neural networks for inverse problems in imaging: A review, IEEE Signal Processing Magazine, 34 (2017), 85-95. 

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C. McCollough, Tu-fg-207a-04: Overview of the low dose ct grand challenge, Medical Physics, 43 (2016), 3760-3760.  doi: 10.1118/1.4957556.

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A. Mittal, A. Dhawan, S. Manchanda, S. Medya, S. Ranu and A. Singh, Learning heuristics over large graphs via deep reinforcement learning, preprint, arXiv: 1903.03332, 2019.

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Figure 1.  Policy network architecture. Each MLP contains two hidden layers with 512 neurons. We use a multi-layer GRU which contains 3 recurrent layers and each layer has 256 neurons. The Angle MLP has one hidden layer of 512 neurons, and the Dose MLP has 2 hidden layers with 512 neurons
Figure 2.  Histograms of PSNR and SSIM from all the 350 test images as shown in Table 1. Figures in (a), (b) and (c) correspond to the three different noise levels. For each (a), (b) and (c), the first row is PSNR and the second is SSIM. Figures from left to right are results from reconstruction methods SART, TV, WF and PD-net respectively. Every sub-figure contains histograms of three scanning strategies, i.e., RL-AD, DS-ED and UF-AEC
Figure 3.  Two examples of the reconstructed images. The top row contains the ground truth images and their zoom-in views. The second through the fourth row contain results from UF-AEC, DS-ED and RL-AD respectively, and combined with PD-net's reconstruction. Note that RL-AD selects 65 measurement angles for the subject in (a) and 54 measurement angles for the subject in (b)
Figure 4.  (a) Distribution of number of measurements of the learned policy (RL-AD) on all the 350 testing CT images. (b) Dose usage distribution of 8 images that use around 54 measurements. (c) Dose usage distribution of 8 images that use around 65 measurements
Figure 5.  (a): an example image that takes 54 measurements. (b): an example image that takes 64 measurements. We can see that the images for which RL selects more measurement angles contains more structures
Figure 6.  The angle selection of the CT image in Figure 5. Top row: RL-AD, bottom row: DS-ED. The lines show the selected angles
Table 1.  This table presents comparisons of different scanning strategies (1-3rd column for RL-AD, DS-ED and UF-AEC respectively) combined with different image reconstruction methods (1-4th row for SART, TV, WF and PD-net respectively). Last row presents the inference times of angle selection (in seconds) of the three compared scanning strategies. The mean (std) of the PSNR and SSIM of the reconstructed images and the inference times are computed among all 350 testing CT images. The best results among the compared algorithms are shown in bold numbers
Reconstruction Method RL-AD DS-ED UF-AEC
Noise 1
SART PSNR 23.48(0.47) 23.30(0.64) 23.01(0.64)
SSIM 0.424(0.020) 0.403(0.023) 0.391(0.022)
TV PSNR 23.85(0.42) 23.75(0.41) 23.63(0.38)
SSIM 0.582(0.030) 0.579(0.030) 0.578(0.028)
WF PSNR 25.14(0.40) 25.05(0.42) 24.91(0.39)
SSIM 0.659(0.027) 0.652(0.027) 0.649(0.026)
PD-net PSNR 30.87(0.64) 30.44(0.51) 30.23(0.46)
SSIM 0.776(0.036) 0.771(0.029) 0.773(0.028)
Noise 2
SART PSNR 23.15(0.48) 22.91(0.53) 22.60(0.64)
SSIM 0.413(0.020) 0.390(0.024) 0.378(0.024)
TV PSNR 23.74(0.40) 23.50(0.36) 23.27(0.40)
SSIM 0.580(0.030) 0.576(0.030) 0.573(0.028)
WF PSNR 24.98(0.29) 24.84(0.41) 24.68(0.39)
SSIM 0.657(0.027) 0.649(0.026) 0.646(0.026)
PD-net PSNR 30.78(0.64) 30.35(0.51) 30.15(0.77)
SSIM 0.774(0.037) 0.769(0.030) 0.771(0.029)
Noise 3
SART PSNR 20.71(0.55) 20.26(0.72) 19.83(0.66)
SSIM 0.334(0.026) 0.304(0.030) 0.291(0.029)
TV PSNR 21.73(0.57) 21.43(0.48) 21.08(0.47)
SSIM 0.568(0.027) 0.555(0.026) 0.545(0.026)
WF PSNR 23.35(0.48) 23.05(0.51) 22.72(0.55)
SSIM 0.636(0.0326) 0.616(0.027) 0.605(0.028)
PD-net PSNR 29.97(0.66) 29.56(0.51) 29.36(0.47)
SSIM 0.753(0.038) 0.746(0.032) 0.747(0.031)
Inference Time (s) 0.46(0.02) 0.21(0.008) 0.20(0.001)
Reconstruction Method RL-AD DS-ED UF-AEC
Noise 1
SART PSNR 23.48(0.47) 23.30(0.64) 23.01(0.64)
SSIM 0.424(0.020) 0.403(0.023) 0.391(0.022)
TV PSNR 23.85(0.42) 23.75(0.41) 23.63(0.38)
SSIM 0.582(0.030) 0.579(0.030) 0.578(0.028)
WF PSNR 25.14(0.40) 25.05(0.42) 24.91(0.39)
SSIM 0.659(0.027) 0.652(0.027) 0.649(0.026)
PD-net PSNR 30.87(0.64) 30.44(0.51) 30.23(0.46)
SSIM 0.776(0.036) 0.771(0.029) 0.773(0.028)
Noise 2
SART PSNR 23.15(0.48) 22.91(0.53) 22.60(0.64)
SSIM 0.413(0.020) 0.390(0.024) 0.378(0.024)
TV PSNR 23.74(0.40) 23.50(0.36) 23.27(0.40)
SSIM 0.580(0.030) 0.576(0.030) 0.573(0.028)
WF PSNR 24.98(0.29) 24.84(0.41) 24.68(0.39)
SSIM 0.657(0.027) 0.649(0.026) 0.646(0.026)
PD-net PSNR 30.78(0.64) 30.35(0.51) 30.15(0.77)
SSIM 0.774(0.037) 0.769(0.030) 0.771(0.029)
Noise 3
SART PSNR 20.71(0.55) 20.26(0.72) 19.83(0.66)
SSIM 0.334(0.026) 0.304(0.030) 0.291(0.029)
TV PSNR 21.73(0.57) 21.43(0.48) 21.08(0.47)
SSIM 0.568(0.027) 0.555(0.026) 0.545(0.026)
WF PSNR 23.35(0.48) 23.05(0.51) 22.72(0.55)
SSIM 0.636(0.0326) 0.616(0.027) 0.605(0.028)
PD-net PSNR 29.97(0.66) 29.56(0.51) 29.36(0.47)
SSIM 0.753(0.038) 0.746(0.032) 0.747(0.031)
Inference Time (s) 0.46(0.02) 0.21(0.008) 0.20(0.001)
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