42陈志强-55

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1 13 2 CT Vol (11~20) CT Theory and Applications May, ) Development of Accelerated CT Reconstruction Based on General Graphics Boards CHEN Zhi-qiang, WANG Xu, ZHANG Li, XIAO Yong-shun Department of Engineering Physics, Tsinghua University, Beijing , China Abstract: Objective: The technical application of general graphics boards in CT accelerated reconstruction is summarized. Methods: Introduce the current technique of graphics boards, and the principle of how their special structure operates in accelerating reconstruction. Results: Analyze the method and character in the use of graphics hardware to accelerate reconstruction. Conclusion: According to the latest technique of graphics boards, we introduce the way to improve the application of graphics boards in reconstruction Key words: CT accelerated reconstruction graphics board shader 1 together with the prospect in this research.. 3dfx [1] PC 3D CPU D CT 3D CT CT CT CT *

12 CT 1 GPU Graphic Processing Unit CPU 0.13 1.3 Intel Pentium4 5500 GPU API API DirectX PC API 8.

4] FPM Fast Page Mode DRAM SDRAM(Synchronous DRAM DDR Double Data Rate SDRAM GDDR-3 Graphics [5] DDR3 2 EISA(Extended

2 12 CT 1 GPU Graphic Processing Unit CPU Intel Pentium GPU API API DirectX PC API 8.0 Shader Vertex Shader, VS Pixel Shader, PS DirectX 9 VS 4 Shader Shader DirectX 10 Integrated Shader IS VS PS 1 GPU [2, 3, 4] FPM Fast Page Mode DRAM SDRAM(Synchronous DRAM DDR Double Data Rate SDRAM GDDR-3 Graphics [5] DDR3 2 EISA(Extended Industry Standard Architecture Equipment Standard Association Interconnect VESA Video PCI Peripheral Component AGP Accelerated Graphics Port PCI Express 3 2 3

3 2 CT K.Akeley [7] SGI RealityEngine 3D Cullip Neumann [8] SGI RealityEngine Onyx [9] 1994 Cabral [10] SGI RealityEngine Onyx 2D DFX VOODOO1 PC 3D 3D DFX VOODOO2 CT 1998 NVIDIA Riva TNT [1] CT 1998 Klaus Mueller Roni Yagel CT SGI Octane Algebraic Reconstruction methods ART Simultaneous ART SART [11, 12] 1 SART bits SGI Octane MIPS R MHz 640M 1999 Matthias Hopf Thomas Ertl 3D [13] 2000 GPU 2001 Markus Hadwiger CT [9] NVIDIA ATI Shader Geforce [14, 15, 16] Radeon CT 4 SIMD CT Single Instruction Multiple Data, SIMD SIMD 4 4 SIMD [17]

14 CT 1 [18] 4 4 SIMD SIMD CT 4.1.2 5 CT CT 6 [19] 6 CT 4.

4 14 CT 1 [18] 4 4 SIMD SIMD CT CT CT 6 [19] 6 CT 4.2 T Convolution Back Projection, CBP CT Markus Hadwiger [9] 7 7 CBP Markus Hadwiger [9]

5 2 CT 15 g ( x) = f [ x]* h( x) f(x) h(x) g(x) (1 [ x] + m = f[] ihx ( i) m (2) i= [ x] m+ 1 ( f [ j] h( xi j) ) 8 9 [9] [11, 12] Klaus Mueller [19] SART ˆP I ˆX J R I J Pˆˆ= RX (3) ˆP R ˆX SART k + 1 θ ˆp θ j x = x + λ ( k+ 1) ( k) j j pi pˆ θ p N ( k ) i rx il l l= 1 N r il l= 1 r ij pi ˆpθ r ij j = 1,2,..., N( N = n n) rij j i λ A N ( k ) i rx il l l = 1 (4) p = (5)

16 CT 1 p ˆp θ p ' i [19] i 60 10 Bezier Surface [19] SIMD 10 B ci (6) p c = i i N l = 1 SIMD C w (7)

6 16 CT 1 p ˆp θ p ' i [19] i Bezier Surface [19] SIMD 10 B ci (6) p c = i i N l = 1 SIMD C w (7) w = λ p r pi pˆ θ ' i il pi pˆ θ cr i ij r ij (6) (7) SIMD [19] 11 D x = x + w (8) ( k+ 1) ( k) j j 11

2 CT 17 4.3 CT 8bit 12bit SART CT 5.1 64 DirectX 9 64 RGBA 16 128 32 5.

7 2 CT CT 8bit 12bit SART CT DirectX 9 64 RGBA D 3D 11 SART GPU ATI Smartshader NVIDIA nfinitefx Engine CPU

18 CT 1 SIMD mov mul add mad dp3 dp4 dst min max slt sge expplog rsq rcp nop 12 ( Input) Output Constant ( Temp) [20, 21, 22, 23 ] 12 5.

8 18 CT 1 SIMD mov mul add mad dp3 dp4 dst min max slt sge expplog rsq rcp nop 12 ( Input) Output Constant ( Temp) [20, 21, 22, 23 ] F-Buffer F-Buffer Fragment-stream FIFO Buffer 2003 ATI Radeon 9800 Pro [24] F_Buffer F_Buffer F_Buffer 14 [24] 13 -Buffer F 14 F-Buffer

9 2 CT F-Buffer Shader F_Buffer CT GPU CT CT [1]. 3dfx VOODOO1 VOODOO5[OL] [2] llfirin. DirectX Next Early Preview[OL]. Dec 4, [3] Craig Peeper, Jason L. Mitchell. Introduction to DirectX 9 High Level Shading Language[OL].July 2003 msdn.microsoft.com [4] Jacek Artymiak. Introduction to Programming with Managed DirectX 9.0[OL] [5] Jim. GDDR-3 [OL] [6]. PCI Expres s I/O [OL] Itdoor.net [7] K.Akeley. RealityEngine graphics[c]. In Proceedings of SIGGRAPH s 1993 pages 109~116. [8] T.J. Cullip and U.Neumann. Accelerating Volume reconstruction with 3D texture mapping hardware[r]. Technical Report TR93-027, Department of Computer Science, University of North Carolina, Chapel Hill [9] Markus Hadwiger, Thomas Theußl, Helwig Hauser, Eduard Gröller. Hardware-Accelerated High-Quality Reconstruction of Volumetric Data on PC Graphics Hardware[C]. VMV 2001(Vision, Modeling, and Visualization 2001): pages ~112 [10] Brian Cabral, Nancy Cam, and Jim Foran. Accelerated volume rendering and tomographic reconstruction using texture mapping hardware[c]. In Proceedings of IEEE Symposium on Volume Visualization 1994 pages 91~98. [11] Klaul. Mueller and Roni. Yagel. On the use of graphics hardware to accelerate algebraic reconstruction methods[c]. SPIE Medical Imaging Conference 1999 No ~62. [12] Klaus Mueller and Roni Yagel. Rapid 3-D Cone-Beam Reconstruction with the Simultaneous Algebraic Reconstruction Technique (SART) Using 2-D Texture Mapping Hardware[J]. IEEE Transactions on Medical Imaging, 2000 VOL. 19 NO.12 [13] Matthias Hopf and Thomas Ertl, Accelerating 3D Convolution using Graphics Hardware[C]. In Proceedings of IEEE Visualization 1999 pages 471~474. [14] Chris Trendall and A. James Stewart. General Calculations using Graphics Hardware, With Application to Interactive Caustics[C]. Rendering Techniques th Eurographics Workshop on Rendering, pages 287~298. [15] Andrew A.Murdoch. Potential of Commodity Graphics Hardware for Scientific Computation[OL]. Nov 5, Available at:

10 20 CT 1 [16] E.Scott Larsen and David McAllister, Fast Matrix Multiplies using Graphics Hardware[C].Proceedings of the 2001 ACM/IEEE conference on Supercomputing,2001 pages 55 ~ 55. [17] Mason Woo, Jackie Neider. The Official Guide to Learning OpenGL Version 1.2[M] [18] Wolfgang Engel. vertex Shader [OL] Available at: [19]. CT [D].: [20] Wolfgang Engel. Shader Programming[OL], , Available at: [21] Konstantin Marty nenko. Introduction to Shaders[OL] , Available at: [22] Cover. Ati SmartShader [OL] , 2001 Available at: tech.163.com [23]. ATi Radeon R350 [OL]. -18, [24]. ATI R350 F_Buffer [OL] , * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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2002/06/25 ... 1 GPU... 1 1.... 1 2.... 1 3.... 2 4.... 2 5.... 2 6. MX460... 3 6.1... 3 6.2... 4 7. MX440... 5 7.1... 5 7.2... 6 8. MX420... 7 8.1... 7 8.2... 8 9. MX420D... 9 9.1... 9 9.2... 10 10....11