## High throughput transmission optical projection tomography using low cost graphics processing unit

Optics Express, Vol. 17, Issue 25, pp. 22320-22332 (2009)

http://dx.doi.org/10.1364/OE.17.022320

Acrobat PDF (9098 KB)

### Abstract

We implement the use of a graphics processing unit (GPU) in order to achieve real time data processing for high-throughput transmission optical projection tomography imaging. By implementing the GPU we have obtained a 300 fold performance enhancement in comparison to a CPU workstation implementation. This enables to obtain on-the-fly reconstructions enabling for high throughput imaging.

© 2009 OSA

## 1. Introduction

1. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. **23**(3), 313–320 (
2005). [CrossRef] [PubMed]

2. D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics **3**(7), 412–417 (
2009). [CrossRef]

3. C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods **5**(1), 45–47 (
2007). [CrossRef] [PubMed]

4. J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science **296**(5567), 541–545 (
2002). [CrossRef] [PubMed]

5. H. S. Sakhalkar and M. Oldham, “Fast, high-resolution 3D dosimetry utilizing a novel optical-CT scanner incorporating tertiary telecentric collimation,” Med. Phys. **35**(1), 101–111 (
2008). [CrossRef] [PubMed]

*f*from an infinite set of its line integrals. Due to the finite number of acquisitions that can be usually acquired, the reconstruction transform (inverse Radon transform formula) is modified into the discrete case [7

7. R. M. Mersereau and A. V. Oppenheim, “Digital reconstruction of multidimensional signals from their projections,” Proc. IEEE **62**(10), 1319–1338 (
1974). [CrossRef]

8. R. M. Mersereau, “Direct Fourier transform techniques in 3-D image reconstruction,” Comput. Biol. Med. **6**(4), 247–258 (
1976). [CrossRef] [PubMed]

13. H. Schomberg and J. Timmer, “The gridding method for image reconstruction by Fourier transformation,” IEEE Trans. Med. Imaging **14**(3), 596–607 (
1995). [CrossRef] [PubMed]

14. A. Brandt, J. Mann, M. Brodski, and M. Galun, “A fast and accurate multilevel inversion of the radon transform,” SIAM J. Appl. Math. **60**(2), 437–462 (
2000). [CrossRef]

15. S. Basu and Y. Bresler, “O(N(2)log(2)N) filtered backprojection reconstruction algorithm for tomography,” IEEE Trans. Image Process. **9**(10), 1760–1773 (
2000). [CrossRef] [PubMed]

^{3}) computational complexity, but fast algorithms are able to reduce it to O(N

^{2}log

_{2}N). Unfortunately the use of fast algorithms for many real-time medical applications would be impossible without hardware acceleration.

16. G. C. Sharp, N. Kandasamy, H. Singh, and M. Folkert, “GPU-based streaming architectures for fast cone-beam CT image reconstruction and demons deformable registration,” Phys. Med. Biol. **52**(19), 5771–5783 (
2007). [CrossRef] [PubMed]

17. T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express **16**(16), 11776–11781 (
2008). [CrossRef] [PubMed]

^{3}and 1024

^{3}volumes we chose to use a standard FBP Algorithm. We avoided iterative methods because of their computational complexity and because the SNR and the number of projections of OPT data sets were so high that non-IR algorithms were required. Our data show that a 300 fold enhancement of reconstruction speed can be achieved using a < 1500 USD GPU.

## 2. Experimental section

## 3. Backprojection algorithm

*f(x,y)*be the image density distribution to be reconstructed. For OPT the image will correspond to the light absorption map of the sample under investigation. We then define the line integral of

*f*along the line

*L*at a distance

*s*from the origin and at angle

*θ*with the

*x*-axis, as the Radon transform

*θ*and

*s*fixed, the integral

*projection*which in parallel beam geometry, as is the case in first approximation for OPT due to the high telecentricity of the system and the lack of scattering present within the sample, consists of the sum of all parallel ray integrals. In OPT, the projections represent the optical transillumination CCD measurements. We can describe each ray emitted from an arbitrary source at position

*x*in a discretized one-dimensional fashion (Fig. 3 ) as it passes through the absorbing object and before being collected by the CCD’s pixel located at position

_{s}*x*as exponentially attenuated following a simple Beer-Lambert-type attenuation law given byHere

_{d}*I*represents the intensity of the source,

_{0}*x*the thickness of the sample, and μ

_{s}, L_{a}the absorption coefficient (if we consider μ

*a function of the two coordinates*

_{a}*x,y*this is equivalent to an image function

*f(x,y) =*μ

*).*

_{a}(x,y)*given all the projections. The most commonly used algorithm for X-CT, and by extension to the OPT case, is the filtered backprojection method (FBP) which can be formulated as [21*

_{a}(x,y)21. J. B. T. M. Roerdink and M. A. Westenbrg, “Data-parallel tomographyc reconstruction: a comparison of filtered backprojection and direct fourier reconstruction,” Parallel Comput. **24**(14), 2129–2142 (
1998). [CrossRef]

*θ*and where the multiplication by

*π*] calculates the back-projections. Note that for practical use the ramp filter is substituted with a function

21. J. B. T. M. Roerdink and M. A. Westenbrg, “Data-parallel tomographyc reconstruction: a comparison of filtered backprojection and direct fourier reconstruction,” Parallel Comput. **24**(14), 2129–2142 (
1998). [CrossRef]

## 4. Implementation

*n*from the different scans are moved into a separate matrix. Each row of this matrix is shifted to adjust for the real center of rotation and padded with zeros to filter the length. Because the process is symmetric for scans corresponding to K and (180-K) degrees of rotation angle, an optimization is applied: values from scans corresponding to an angle of rotation of (180-K) degree are reversed around the center of rotation and summed with the values corresponding to a K degree scan. Note that such an optimization could be done only if we have corresponding pairs of scans. We then performed the calculations on each row of the matrix. First, we applied a 1D Discrete Fourier Transform, then the results are filtered using a Hamming filter for example, and finally a 1D Inverse Discrete Fourier Transform is applied. At the end the matrix is backprojected into the corresponding reconstruction slice number

*n*(see Fig. 5 ). The required computations are mapped to the CUDA kernel executions with the procedure repeated for all the projection rows depending on the number of reconstructed slices needed.

## 4. Results

^{2}or 1024

^{2}each to reconstruct a 512

^{3}or 1024

^{3}volume. Saggital, longitudinal, axial, and 3D reconstructions of the heart data utilized in this work are shown in Fig. 7 .

^{3}volumes typical times were around 3.8 s, while for 1024

^{3}volumes times of the order of 36 sec were obtained.

## Conclusion

27. C. Vinegoni, D. Razansky, J. L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. **34**(3), 319–321 (
2009). [CrossRef] [PubMed]

28. J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. **52**(10), 2775–2790 (
2007). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. |

2. | D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics |

3. | C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods |

4. | J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science |

5. | H. S. Sakhalkar and M. Oldham, “Fast, high-resolution 3D dosimetry utilizing a novel optical-CT scanner incorporating tertiary telecentric collimation,” Med. Phys. |

6. | J. Radon, “On the determination of function from their integrals along certain manifolds,” Ber. Saechs. Akad. Wiss, Leipzig Math. Phys. Kl. |

7. | R. M. Mersereau and A. V. Oppenheim, “Digital reconstruction of multidimensional signals from their projections,” Proc. IEEE |

8. | R. M. Mersereau, “Direct Fourier transform techniques in 3-D image reconstruction,” Comput. Biol. Med. |

9. | H. Stark, J. W. Woods, I. Paul, and R. Hingorani, “An investigation of computerized tomography by direct Fourier inversion and optimum interpolation,” IEEE Trans. Biomed. Eng. |

10. | R. M. Lewitt, “Reconstruction algorithms: Transform methods,” Proc. IEEE |

11. | J. D. O’Sullivan, “A fast sinc function gridding algorithm for fourier inversion in computer tomography,” IEEE Trans. Med. Imaging |

12. | S. Matej and I. Bajla, “A high-speed reconstruction from projections using direct Fourier method with optimized parameters-an experimental analysis,” IEEE Trans. Med. Imaging |

13. | H. Schomberg and J. Timmer, “The gridding method for image reconstruction by Fourier transformation,” IEEE Trans. Med. Imaging |

14. | A. Brandt, J. Mann, M. Brodski, and M. Galun, “A fast and accurate multilevel inversion of the radon transform,” SIAM J. Appl. Math. |

15. | S. Basu and Y. Bresler, “O(N(2)log(2)N) filtered backprojection reconstruction algorithm for tomography,” IEEE Trans. Image Process. |

16. | G. C. Sharp, N. Kandasamy, H. Singh, and M. Folkert, “GPU-based streaming architectures for fast cone-beam CT image reconstruction and demons deformable registration,” Phys. Med. Biol. |

17. | T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express |

18. | K. Mueller, F. Xu, and N. Neophytou, “Why do GPUs work so well for acceleration of CT? SPIE Electronic Imaging '07,” Keynote, Computational Imaging V, San Jose, (2007). |

19. | H. Scherl, B. Keck, M. Kowarschik, and J. Hornegger, “Fast GPU-Based CT Reconstruction using the Common Unified Device Architecture (CUDA),” Nuclear Science Symposium Conference Record |

20. | P. B. Noël, A. Walczak, K. R. Hoffmann, J. Xu, J. J. Corso, and S. Schafer, “Clinical Evaluation of GPU-Based Cone Beam Computed Tomography,” Proc. of High-Performance Medical Image Computing and Computer-Aided Intervention (HP-MICCAI), (2008). |

21. | J. B. T. M. Roerdink and M. A. Westenbrg, “Data-parallel tomographyc reconstruction: a comparison of filtered backprojection and direct fourier reconstruction,” Parallel Comput. |

22. | NVIDIA Corporation. CUDA Programming Guide (manual), February (2007). |

23. | J. Nickolls, I. Buck, M. Garland, and K. Skadron, “Scalable parallel programming with CUDA,” Queueing Syst. |

24. | J. Nickolls and I. Buck, “NVIDIA CUDA software and GPU parallel computing architecture,” Microprocessor Forum, May (2007). |

25. | S. Ryoo, C. I. Rodrigues, S. S. Stone, S. S. Baghsorkhi, S. Z.Ueng, J. A. Stratton, and W. W. Hwu “Program Optimization Space Pruning for a Multithreaded GPU,” Proc. of the sixth annual IEEE/ACM int. symp. on Code gen. and opt, (2008). |

26. | C. Vinegoni, D. Razansky, L. Fexon, J. L. Figueiredo, M. Pivovarov, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Born normalization for fluorescence optical projection tomography for whole heart imaging,” J Vis Exp. |

27. | C. Vinegoni, D. Razansky, J. L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. |

28. | J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. |

**OCIS Codes**

(170.0110) Medical optics and biotechnology : Imaging systems

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

(170.3880) Medical optics and biotechnology : Medical and biological imaging

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: August 25, 2009

Revised Manuscript: October 21, 2009

Manuscript Accepted: October 25, 2009

Published: November 23, 2009

**Virtual Issues**

Vol. 5, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Claudio Vinegoni, Lyuba Fexon, Paolo Fumene Feruglio, Misha Pivovarov, Jose-Luiz Figueiredo, Matthias Nahrendorf, Antonio Pozzo, Andrea Sbarbati, and Ralph Weissleder, "High throughput transmission optical projection tomography using low cost graphics processing unit," Opt. Express **17**, 22320-22332 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22320

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### References

- V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005). [CrossRef] [PubMed]
- D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009). [CrossRef]
- C. Vinegoni, C. Pitsouli, D. Razansky, N. Perrimon, and V. Ntziachristos, “In vivo imaging of Drosophila melanogaster pupae with mesoscopic fluorescence tomography,” Nat. Methods 5(1), 45–47 (2007). [CrossRef] [PubMed]
- J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, “Optical projection tomography as a tool for 3D microscopy and gene expression studies,” Science 296(5567), 541–545 (2002). [CrossRef] [PubMed]
- H. S. Sakhalkar and M. Oldham, “Fast, high-resolution 3D dosimetry utilizing a novel optical-CT scanner incorporating tertiary telecentric collimation,” Med. Phys. 35(1), 101–111 (2008). [CrossRef] [PubMed]
- J. Radon, “On the determination of function from their integrals along certain manifolds,” Ber. Saechs. Akad. Wiss, Leipzig Math. Phys. Kl. 69, 262–277 (1917).
- R. M. Mersereau and A. V. Oppenheim, “Digital reconstruction of multidimensional signals from their projections,” Proc. IEEE 62(10), 1319–1338 (1974). [CrossRef]
- R. M. Mersereau, “Direct Fourier transform techniques in 3-D image reconstruction,” Comput. Biol. Med. 6(4), 247–258 (1976). [CrossRef] [PubMed]
- H. Stark, J. W. Woods, I. Paul, and R. Hingorani, “An investigation of computerized tomography by direct Fourier inversion and optimum interpolation,” IEEE Trans. Biomed. Eng. 28(7), 496–505 (1981). [CrossRef] [PubMed]
- R. M. Lewitt, “Reconstruction algorithms: Transform methods,” Proc. IEEE 71(3), 390–408 (1983). [CrossRef]
- J. D. O’Sullivan, “A fast sinc function gridding algorithm for fourier inversion in computer tomography,” IEEE Trans. Med. Imaging 4(4), 200–207 (1985). [CrossRef] [PubMed]
- S. Matej and I. Bajla, “A high-speed reconstruction from projections using direct Fourier method with optimized parameters-an experimental analysis,” IEEE Trans. Med. Imaging 9(4), 421–429 (1990). [CrossRef] [PubMed]
- H. Schomberg and J. Timmer, “The gridding method for image reconstruction by Fourier transformation,” IEEE Trans. Med. Imaging 14(3), 596–607 (1995). [CrossRef] [PubMed]
- A. Brandt, J. Mann, M. Brodski, and M. Galun, “A fast and accurate multilevel inversion of the radon transform,” SIAM J. Appl. Math. 60(2), 437–462 (2000). [CrossRef]
- S. Basu and Y. Bresler, “O(N(2)log(2)N) filtered backprojection reconstruction algorithm for tomography,” IEEE Trans. Image Process. 9(10), 1760–1773 (2000). [CrossRef] [PubMed]
- G. C. Sharp, N. Kandasamy, H. Singh, and M. Folkert, “GPU-based streaming architectures for fast cone-beam CT image reconstruction and demons deformable registration,” Phys. Med. Biol. 52(19), 5771–5783 (2007). [CrossRef] [PubMed]
- T. Shimobaba, Y. Sato, J. Miura, M. Takenouchi, and T. Ito, “Real-time digital holographic microscopy using the graphic processing unit,” Opt. Express 16(16), 11776–11781 (2008). [CrossRef] [PubMed]
- K. Mueller, F. Xu, and N. Neophytou, “Why do GPUs work so well for acceleration of CT? SPIE Electronic Imaging '07,” Keynote, Computational Imaging V, San Jose, (2007).
- H. Scherl, B. Keck, M. Kowarschik, and J. Hornegger, “Fast GPU-Based CT Reconstruction using the Common Unified Device Architecture (CUDA),” Nuclear Science Symposium Conference Record 6, 4464–4466 (2007).
- P. B. Noël, A. Walczak, K. R. Hoffmann, J. Xu, J. J. Corso, and S. Schafer, “Clinical Evaluation of GPU-Based Cone Beam Computed Tomography,” Proc. of High-Performance Medical Image Computing and Computer-Aided Intervention (HP-MICCAI), (2008).
- J. B. T. M. Roerdink and M. A. Westenbrg, “Data-parallel tomographyc reconstruction: a comparison of filtered backprojection and direct fourier reconstruction,” Parallel Comput. 24(14), 2129–2142 (1998). [CrossRef]
- NVIDIA Corporation. CUDA Programming Guide (manual), February (2007).
- J. Nickolls, I. Buck, M. Garland, and K. Skadron, “Scalable parallel programming with CUDA,” Queueing Syst. 6, 40–53 (2008).
- J. Nickolls and I. Buck, “NVIDIA CUDA software and GPU parallel computing architecture,” Microprocessor Forum, May (2007).
- S. Ryoo, C. I. Rodrigues, S. S. Stone, S. S. Baghsorkhi, S. Z.Ueng, J. A. Stratton, and W. W. Hwu “Program Optimization Space Pruning for a Multithreaded GPU,” Proc. of the sixth annual IEEE/ACM int. symp. on Code gen. and opt, (2008).
- C. Vinegoni, D. Razansky, L. Fexon, J. L. Figueiredo, M. Pivovarov, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Born normalization for fluorescence optical projection tomography for whole heart imaging,” J Vis Exp. 28, 1389 (2009).
- C. Vinegoni, D. Razansky, J. L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. 34(3), 319–321 (2009). [CrossRef] [PubMed]
- J. R. Walls, J. G. Sled, J. Sharpe, and R. M. Henkelman, “Resolution improvement in emission optical projection tomography,” Phys. Med. Biol. 52(10), 2775–2790 (2007). [CrossRef] [PubMed]

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