634 T. SICE Vol.50 No.9 September 2014 ML-EM Maximum Likelihood-Expectation Maximization Method 5) FBP CT Zhao 6) Zhang 2 7) 8), 9) X CT X CT CT CT CT

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1 Vol.50, No.9, 633/ Two Dimensional Metal Artifact Reduction Algorithm in CT and Its Application to Three Dimensional Data Toru Kano and Michihiko Koseki X-ray CT is one of the most important diagnostic techniques which can generate cross-sectional images of an object. However, X-ray CT is still facing some technical issues; in particular, metal artifacts are a significant problem in CT imaging. A metal artifact is a radial noise caused by a discrepancy of projection data, and makes it difficult to diagnose patients with metal implants in their body. Even though various studies to reduce metal artifacts were conducted, the problem is not resolved yet. Therefore, the purpose of this study is to propose a method to reduce metal artifact, so as to widely disseminate a superior diagnostic technology. First, we propose a method for two dimensional CT data in this paper. The proposed method is divided into three processes, metal extraction, non-metal interpolation, and synthesizing. The algorithm is highly effective in metal artifact reduction because it is not sensitive to the discrepancy of projection data. And then, we extend the method to three dimensional CT data, and evaluate the effectiveness. Key Words: X-ray CT, nondestructive inspection, image processing, metal artifact 1. X CT X X CT (Fig. 1) X CT Alvarez X X 2 X Interdisciplinary Graduate School of Science and Technology, Shinshu University, Tokida, Ueda Faculty of Textile Science and Technology, Shinshu University, Tokida, Ueda Received January 29, 2014 Revised April 28, 2014 Fig. 1 Metal artifact generation examples are shown here. (a) is a CT image of a human head with metallic tooth implants, (b) is an image of an electronic circuit 1) DE Dual-Energy DE 2), 3) DE CT DE CT 2 CT 2 Man 4) CT FBP Filtered Back Projection ART Algebraic Reconstruction Technique TR 0009/14/ c 2014 SICE

2 634 T. SICE Vol.50 No.9 September 2014 ML-EM Maximum Likelihood-Expectation Maximization Method 5) FBP CT Zhao 6) Zhang 2 7) 8), 9) X CT X CT CT CT CT CT 2. X X t X I 0 X I I = I 0 exp( μt) 1 μ X X p (1) p = ln I = μt 2 I 0 p X X X μ X X X I I = I 0(E)exp(μ(E)t)dE 3 E p p= ln I I 0(E)exp(μ(E)t)dE = ln E I 0 4 I 0(E)dE X X CT X X (2) X X X X 10) X (Table 1) (4) AMPTEX Inc. XR-100T-CdTe 130 kv X 3. CT 3. 1 X CT 360 X X Fig. 2(a) X Fig. 2(b) CT X X E

50 9 2014 9 635 Table 1 Composition of discrete X-ray and Physical properties used for forward projection simulation Energy Relative X-ray attenuation coefficients [/mm] [KeV] intensity Resin Soft

02797 0.02432 0.03242 0.04053 0.09983 2.858 50 17 0.02468 0.02048 0.02730 0.03413 0.06363 1.542 60 12 0.02290 0.01852 0.02470 0.03087 0.04722 0.9488 80 3 0.01953 0.01648 0.02197 0.02747 0.03344 0.

3 Table 1 Composition of discrete X-ray and Physical properties used for forward projection simulation Energy Relative X-ray attenuation coefficients [/mm] [KeV] intensity Resin Soft tissue Midium tissue Hard tissue Bone Iron Fig. 3 Conceptual diagram of the proposed algorithm Fig. 2 An X-ray CT simulation example. (a) is the numerical phantom composed of resin and metals, (b) is the sinogram generated from (a), (c) is the FBP result ( ) 1 FBP Filtered Back Projection Fig. 2(c) Fig (x, y) (r, φ) x = r cos φ, y = r sin φ f(θ) f(θ)=r sin(θ + φ)= x 2 + y 2 sin (atan y ) x + θ 5 θ X p θ =2πi/p (i =0,..., p 1) (x, y) f(θ) v (f(θ)) cont(θ) ( ) d 1 cont(θ) = dθ v (f(θ)) DIFF 6 0 otherwise p 1 cont(θ)dθ p RATIO 7 DIFF RATIO 1 1

636 T. SICE Vol.50 No.9 September 2014 Fig. 5 An experimental resin sample in which metal poles are embedded Fig. 4 Comparison of the shape extraction.

continuity information, (d) is the reconstruction result using sine curves with continuity information Fig. 4 Fig. 4(a) 2 Fig. 4(b) FBP Fig. 4(c) Fig.

4 636 T. SICE Vol.50 No.9 September 2014 Fig. 5 An experimental resin sample in which metal poles are embedded Fig. 4 Comparison of the shape extraction. (a) is the numerical phantom of cross shaped metal, (b) is the threshold processing result after FBP, (c) is the reconstruction result using sine curves without continuity information, (d) is the reconstruction result using sine curves with continuity information Fig. 4 Fig. 4(a) 2 Fig. 4(b) FBP Fig. 4(c) Fig. 4(d) p = 800, DIFF = 1000, RATIO = 0.95 v (f(θ)) DIFF [0, 65535] FBP Fig X CT ScanXmate- A130SS940 Fig. 5 Fig. 6 Fig. 6(a) Fig. 6(b) Fig. 6(a) 3. 6 Fig. 7 Table 1 X X CT Fig. 8(a)

processes for sinograms Fig. 6 The result of application to actual CT data.

9 (x, y, z) D D 0 D = D 0 D 0 D D 0 (x 0,y 0,z 0) (D, 0, 0) x D x 0 D = y y0 = z z0 8 y 0 z 0 Fig.

5 Fig. 7 X-ray CT simulation software which can input/output CT data, perform forward projection, filtered back projection and various processes for sinograms Fig. 6 The result of application to actual CT data. (a) is the CT image by FBP, (b) is the result of applying the proposed algorithm Fig. 8(b) 4. CT 1 CT 1 CT 4. 1 Fig. 9 (x, y, z) D D 0 D = D 0 D 0 D D 0 (x 0,y 0,z 0) (D, 0, 0) x D x 0 D = y y0 = z z0 8 y 0 z 0 Fig. 8 The result of application to simulation data. (a) is the chest numerical phantom with three metal poles, (b) is the result of applying the proposed algorithm YZ (Y 0,Z 0) (8) ( ) ( ) Y0 = y0 1 D x 0 D ( ) 9 z 0 1 D Z 0 x 0 D (x 0,y 0,z 0) θ (x θ,y θ,z θ ) z x θ x 0 cos θ sin θ 0 y θ = y 0 sin θ cos θ 0 z θ z x 0 cos θ y 0 sin θ = x 0 sin θ + y 0 cos θ 10 z 0 (10) (9)

638 T. SICE Vol.50 No.9 September 2014 Fig.

cos θ) 1+ z 0 (1+ D D x 0 cos θ+y 0 sin θ D D x 0 cos θ+y 0 sin θ ) ) 11 (x 0,y 0,z

6 638 T. SICE Vol.50 No.9 September 2014 Fig. 9 Dimensions definition of cone beam CT imaging Fig. 11 A 3D sinogram generated from Fig. 10 Fig. 10 An experimental sample composed of 9 iron poles ( Yθ Z θ ) ( = (x0 sin θ + y0 cos θ) 1+ z 0 (1+ D D x 0 cos θ+y 0 sin θ D D x 0 cos θ+y 0 sin θ ) ) 11 (x 0,y 0,z 0) θ v(θ, x 0,y 0,z 0) 2 CT 4. 2 Fig. 10 X Fig. 11 (z ) 1 1 (11) 4. 3 Fig Fig. 12 The FBP result of the cone beam data of the experimental sample shown in Fig. 10 Fig. 12 (11) Fig X CT

50 9 2014 9 639 Fig. 13 The result of applying the proposed algorithm for cone beam data CT CT 1 R.E. Alvarez and A.

Nikolaou, M.F. Reiser, C.R. Becker and T.R. Johnson: Metal artifact reduction by dual energy computed tomography using monoenergetic extrapolation, Eur. Radiol., 21-7, 1424/1429 (2011) 4 B. De Man, J.

ng, T. Frei and M.W. Vannier: Fast iterative algorithm for metal artifact reduction in X-ray CT, Acad. Radiol., 7-8, 607/614 (2000) 6 S. Zhao, K.T. Bae, B. Whiting and G.

7 Fig. 13 The result of applying the proposed algorithm for cone beam data CT CT 1 R.E. Alvarez and A. Macovski: Energy-selective Reconstructions in X-ray Computerized Tomography, Physics in Medicine and Biology, 21-5, 733/744 (1976) 2 X CT J99-D-3, 956/966 (2007) 3 F. Bamberg, A. Dierks, K. Nikolaou, M.F. Reiser, C.R. Becker and T.R. Johnson: Metal artifact reduction by dual energy computed tomography using monoenergetic extrapolation, Eur. Radiol., 21-7, 1424/1429 (2011) 4 B. De Man, J. Nuyts, P. Dupont, G. Marchal and P. Suetens: An iterative maximum-likelihood polychromatic algorithm for CT, IEEE Transactions on Medical Imaging, 20-10, 999/1008 (2001) 5 G. Wang, T. Frei and M.W. Vannier: Fast iterative algorithm for metal artifact reduction in X-ray CT, Acad. Radiol., 7-8, 607/614 (2000) 6 S. Zhao, K.T. Bae, B. Whiting and G. Wang: A wavelet method for metal artifact reduction with multiple metallic objects in the field of view, Journal of X-ray Science and Technology, , 67/76 (2002) 7 Y. Zhang, L. Zhang, X.R. Zhu, A.K. Lee, M. Chambers and L. Dong: Reducing metal artifacts in cone-beam CT images by preprocessing projection data, International Journal of Radiation Oncology Biology Physics, 67-3, 924/932 (2007) 8 W.A. Kalender, R. Hebel and J. Ebersberger: Reduction of CT artifacts Caused by Metallic Implants, Radiology, 164, 576/577 (1987) 9 X CT A , 1888/1894 (2006) 10 J.H. Hubbell and S.M. Seltzer: Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 kev to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest, NISTIR 5632, (2011)

X CT - - ( ) ( ) CT Image Reconstruction Algorithm to Reduce Metal Artifact - Metal Extraction and Non-Metal Interpolation of Sinogram - Toru KANO, Mi

X CT - - ( ) ( ) CT Image Reconstruction Algorithm to Reduce Metal Artifact - Metal Extraction and Non-Metal Interpolation of Sinogram - Toru KANO, Michihiko KOSEKI, Hirohisa MORIKAWA Shinshu University,