Iterative reconstruction for sparse-view X-ray CT using alpha-divergence constrained total generalized variation minimization

Abstract

BCKGROUND:

Accurate statistical model of the measured projection data is essential for computed tomography (CT) image reconstruction. The transmission data can be described by a compound Poisson distribution upon an electronic noise background. However, such a statistical distribution is numerically intractable for image reconstruction.

OBJECTIVE:

Although the sinogram data is easily manipulated, it lacks a statistical description for image reconstruction. To address this problem, we present an alpha-divergence constrained total generalized variation (AD-TGV) method for sparse-view x-ray CT image reconstruction.

METHODS:

The AD-TGV method is formulated as an optimization problem, which balances the alpha-divergence (AD) fidelity and total generalized variation (TGV) regularization in one framework. The alpha-divergence is used to measure the discrepancy between the measured and estimated projection data. The TGV regularization can effectively eliminate the staircase and patchy artifacts which is often observed in total variation (TV) regularization. A modified proximal forward-backward splitting algorithm was proposed to minimize the associated objective function.

RESULTS:

Qualitative and quantitative evaluations were carried out on both phantom and patient data. Compared with the original TV-based method, the evaluations clearly demonstrate that the AD-TGV method achieves higher accuracy and lower noise, while preserving structural details.

CONCLUSIONS:

The experimental results show that the presented AD-TGV method can achieve more gains over the AD-TV method in preserving structural details and suppressing image noise and undesired patchy artifacts. The authors can draw the conclusion that the presented AD-TGV method is potential for radiation dose reduction by lowering the milliampere-seconds (mAs) and/or reducing the number of projection views.

Keywords

Sparse-view X-ray CT iterative reconstruction alpha-divergence total generalized variation

Get full access to this article

View all access options for this article.

References

Brenner

D.J.

and Hall

E.J.

, Computed tomography–an increasing source of radiation exposure, N Engl J Med 357 (2007), 2277–2284.

Hall

E.J.

and Brenner

D.J.

, Cancer risks from diagnostic radiology, Br J Radiol 81 (2008), 362–378.

Bian

, et al., SR-NLM: A sinogram restoration induced non-local means image filtering for low-dose computed tomography, Comput Med Imaging Graph 37 (2013), 293–303.

, et al., An efficient augmented lagrangian method for statistical X-ray CT image reconstruction, PloS One 10 (2015), e0140579.

La Rivière

P.J.

and Billmire

D.M.

, Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing. IEEE Transactions on Medical Imaging 24 (2005), 105–111.

, et al., Low-dose computed tomography image restoration using previous normal-dose scan, Med Phys 38 (2011), 5713–5731.

, et al., Low-dose computed tomography image reconstruction by α-divergence constrained total variation minimization, Fully three-dimensional image reconstruction in radiology and nuclear medicine Proceedings Germany, 2011.

, et al., Iterative image reconstruction for cerebral perfusion CT using a pre-contrast scan induced edge-preserving prior, Phys Med Biol 57 (2012), 7519–7542.

Niu

, et al., Low-dose cerebral perfusion computed tomography image restoration via low-rank and total variation regularizations, Neurocomputing 197 (2016), 143–160.

10.

Wang

, et al., Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography, IEEE Trans Med Imaging 25 (2006), 1272–1283.

11.

Chen

G.H.

, Tang

and Leng

, Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets, Med Phys 35 (2008), 660–663.

12.

Huang

, et al., Sparse angular CT reconstruction using non-local means based iterative-correction POCS. Comput Biol Med 41 (2011), 195–205.

13.

Liu

, et al., Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction, Phys Med Biol 57 (2012), 7923–7956.

14.

Bendory

and Feuer

, Sparse sampling in helical cone-beam CT perfect reconstruction algorithms, Journal of X-ray Science and Technology 24 (2016), 389–405.

15.

Niu

, et al., Sparse-view x-ray CT reconstruction via total generalized variation regularization, Phys Med Biol 59 (2014), 2997–3017.

16.

Sidky

E.Y.

, Kao

C.M.

and Pan

X.H.

, Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT, Journal of X-Ray Science and Technology 14 (2006), 119–139.

17.

Sidky

E.Y.

and Pan

, Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization, Phys Med Biol 53 (2008), 4777–4807.

18.

Tian

, et al., Low-dose CT reconstruction via edge-preserving total variation regularization, Phys Med Biol 56 (2011), 5949–5967.

19.

Lasio

G.M.

, Whiting

B.R.

and Williamson

J.F.

, Statistical reconstruction for x-ray computed tomography using energy-integrating detectors, Physics in Medicine and Biology 52 (2007), 2247–2266.

20.

Macovski

, Medical imaging systems, Prentice Hall 1983.

21.

Teng

and Zhang

, Iterative reconstruction algorithms with alpha-divergence for PET imaging, Comput Med Imaging Graph 35 (2011), 294–301.

22.

Teng

and Zhang

, Generalized EM-type reconstruction algorithms for emission tomography, IEEE Trans Med Imaging 31 (2012), 1724–1733.

23.

Bredies

, Kunisch

and Pock

, Total Generalized Variation, Siam Journal on Imaging Sciences 3 (2010), 492–526.

24.

Combettes

P.L.

and Pesquet

J.C.

, A proximal decomposition method for solving convex variational inverse problems, Inverse Problems 24 (2008), 065014.

25.

Knoll

, et al., Second order total generalized variation (TGV) for MRI, Magn Reson Med 65 (2011), 480–491.

26.

Anderson

J.M.

, et al., Weighted least-squares reconstruction methods for positron emission tomography, IEEE Trans Med Imaging 16 (1997), 159–165.

27.

Fessler

J.A.

, Penalized weighted least-squares image reconstruction for positron emission tomography, IEEE Trans Med Imaging 13 (1994), 290–300.

28.

Minka

, Divergence measures and message passin, Technical report, Microsoft Research, 2005.

29.

Segars

W.P.

, et al., 4D XCAT phantom for multimodality imaging research, Med Phys 37 (2010), 4902–4915.

30.

Wang

and Bovik

A.C.

, A universal image quality index, IEEE Signal Processing Letters 9 (2002), 81–84.

31.

Shun-ichi

, Differential-geometrical methods in statistics. Springer Science & Business Media, 2012.

32.

Tang

, Nett

B.E.

and Chen

G.H.

, Performance comparison between total variation (TV)-based compressed sensing and statistical iterative reconstruction algorithms, Phys Med Biol 54 (2009), 5781–5804.

33.

and Mueller

, Accelerating popular tomographic reconstruction algorithms on commodity PC graphics hardware, IEEE Transactions on Nuclear Science 52 (2005), 654–663.