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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 |
. 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.
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show all references
References:
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W. van Aarle, W. J. Palenstijn, J. Cant, E. Janssens, F. Bleichrodt, A. Dabravolski, J. De Beenhouwer, K. J. Batenburg and J. Sijbers,
Fast and flexible x-ray tomography using the astra toolbox, Optics Express, 22 (2016), 25129-25147.
|
[2] |
W. van Aarle, W. J. Palenstijn, J. D. Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg and J. Sijbers,
The astra toolbox: A platform for advanced algorithm development in electron tomography, Ultramicroscopy, 24 (2015), 35-47.
|
[3] |
J. Adler and O. Oktem,
Learned primal-dual reconstruction, IEEE Transactions on Medical Imaging, 37 (2018), 1322-1332.
|
[4] |
K. J. Batenburg, W. J. Palenstijn, P. 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. |
[6] |
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.
|
[7] |
A. Buades, B. Coll and J. M. Morel,
A review of image denoising algorithms, with a new one, Multiscale Model. Simul., 2 (2005), 490-530.
doi: 10.1137/040616024. |
[8] |
J.-F. Cai, S. Osher and Z. Shen,
Split bregman methods and frame based image restoration, Multiscale Modeling and Simulation, 8 (2009), 337-369.
doi: 10.1137/090753504. |
[9] |
J.-F. Cai, H. Ji, Z. Shen and G. B. Ye,
Data-driven tight frame construction and image denoising, Applied and Computational Harmonic Analysis, 37 (2014), 89-105.
doi: 10.1016/j.acha.2013.10.001. |
[10] |
E. J. Candes, Y. C. Eldar, et al., Compressed Sensing With Coherent and Redundant Dictionaries, 2010. |
[11] |
E. J. Candes, J. 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. |
[12] |
A. Chambolle and T. Pock,
A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40 (2011), 120-145.
doi: 10.1007/s10851-010-0251-1. |
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H. Chen, Y. Zhang, M. K. Kalra, F. Lin, Y. Chen, P. Liao, J. Zhou and G. Wang,
Low-dose CT with a residual encoder-decoder convolutional neural network, IEEE Transactions on Medical Imaging, 36 (2017), 2524-2535.
|
[14] |
K. Dabov, A. Foi, V. 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. |
[15] |
A. Dabravolski, K. J. Batenburg and J. Sijbers,
Dynamic angle selection in x-ray computed tomography, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 324 (2014), 17-24.
|
[16] |
I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.
doi: 10.1137/1.9781611970104. |
[17] |
B. Dong, J. Li and Z. Shen,
X-ray CT image reconstruction via wavelet frame based regularization and radon domain inpainting, Journal of Scientific Computing, 54 (2013), 333-349.
doi: 10.1007/s10915-012-9579-6. |
[18] |
B. Dong and Z. Shen,
Mra based wavelet frames and applications, IAS Lecture Notes Series, Summer Program on "The Mathematics of Image Processing", Park City Mathematics Institute, 19 (2010), 9-158.
doi: 10.1090/pcms/019/02. |
[19] |
D. Donoho,
Compressed sensing, IEEE Transactions on Information Theory, 52 (2006), 1289-1306.
|
[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. Gies, W. A. Kalender, H. 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. Godaliyadda, D. H. Ye, M. D. Uchic, M. A. Groeber, G. 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. Ji, Y. 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. Jin, M. T. McCann, E. 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. Kalender, H. 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. |
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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. |
[40] |
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, Inc., San Diego, CA, 1998.
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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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