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Efficient image reconstruction for fluorescence molecular tomography via linear regression approximation scheme with dual augmented Lagrangian method

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Abstract

With the development of non-contact fluorescence molecular tomography (FMT) imaging system, multi-fluorescence projections data can be obtained to improve the quality of reconstruction images. However, it remains a challenging issue to obtain fast and accurate reconstruction of the fluorescent probe distribution due to the large computational burden and the ill-posed nature of the inverse problem. In this work, we present an innovative method associating dual augmented lagrangian method (DALM) with a linear regression approximation (LRA) strategy to locate the fluorescence probe, which guarantees the accuracy, efficiency, and robustness for FMT reconstruction. Numerical experiments based on a heterogeneous phantom are performed to validate the feasibility of the proposed method. The results demonstrate that the proposed method can achieve accurate target localization, and satisfactory computational efficiency. Furthermore, this approach is robust even under quite ill-posed condition.

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References

  1. Cherry, S.R.: In vivo molecular and genomic imaging: new challenges for imaging physics. Phys. Med. Biol. 49(3), R13 (2004)

    Article  Google Scholar 

  2. Ntziachristos, V., et al.: Looking and listening to light: the evolution of whole-body photonic imaging. Nat. Biotechnol. 23(3), 313–320 (2005)

    Article  Google Scholar 

  3. Fan-Minogue, H., Cao, Z., Paulmurugan, R., Chan, C.T., Massoud, T.F., Felsher, D.W., Gambhir, S.S.: Noninvasive molecular imaging of c-Myc activation in living mice. Proc. Natl. Acad. Sci. USA 107(36), 15892–15897 (2010)

    Article  Google Scholar 

  4. Ntziachristos, V.: Fluorescence molecular imaging. Annu. Rev. Biomed. Eng. 8(1), 1–33 (2006)

    Article  Google Scholar 

  5. Ale, A., Ermolayev, V., Herzog, E., Cohrs, C., de Angelis M.H., Ntziachristos, V.: FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography. Nat. Methods. 9(6), 615–620 (2012)

    Article  Google Scholar 

  6. Song, X., et al.: Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm. Opt. Exp. 15, 18300–18317 (2007)

    Article  Google Scholar 

  7. Shi, J., et al.: Efficient L1 regularization-based reconstruction for fluorescent molecular tomography using restarted nonlinear conjugate gradient. Opt. Lett. 38, 3696–3699 (2013)

    Article  Google Scholar 

  8. Han, D., et al.: A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization. Opt. Exp. 18, 8630–8646 (2010)

    Article  Google Scholar 

  9. Ripoll, J.: Hybrid Fourier-real space method for diffuse optical tomography. Opt. Lett. 35(5), 688–690 (2010)

    Article  Google Scholar 

  10. Rudge, T.J., Soloviev, V.Y., Arridge, S.R.: Fast image reconstruction in fluoresence optical tomography using data compression. Opt. Lett. 35(5), 763–765 (2010)

    Article  Google Scholar 

  11. Ducros, N., Andrea, C.D., Valentini, G., Rudge, T., Arridge, S., Bassi, A.: Full-wavelet approach for fluorescence diffuse optical tomography with structured illumination. Opt. Lett. 35(21), 3676–3678 (2010)

    Article  Google Scholar 

  12. Ducros, N., Bassi, A., Valentini, G., Schweiger, M., Arridge, S., DAndrea, C.: Multiple-view fluorescence optical tomography reconstruction using compression of experimental data. Opt. Lett. 36(8), 1377–1379 (2011)

    Article  Google Scholar 

  13. Shi, J., et al.: Fluorescence molecular tomography reconstruction via discrete cosine transform-based regularization. J. Biomed. Opt. 20(5), 055004 (2015)

    Article  Google Scholar 

  14. Cao, X., Wang, X., Zhang, B., et al.: Accelerated image reconstruction in fluorescence molecular tomography using dimension reduction. Biomed. Opt. Express. 4(1), 1–14 (2013)

    Article  Google Scholar 

  15. Zhu, D., Li, C.: Accelerated image reconstruction in fluorescence molecular tomography using a nonuniform updating scheme with momentum and ordered subsets methods. J. Biomed. Opt. 21(1), 16004 (2016)

    Article  Google Scholar 

  16. Markel, V.A., Mital, V., Schotland, J.C.: Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition. J. Opt. Soc. Am. A. 20(5), 890–902 (2003)

    Article  Google Scholar 

  17. Zacharopoulos, A.D., Svenmarker, P., Axelsson, J., et al.: A matrix-free algorithm for multiple wavelength fluorescence tomography. Opt. Express. 17(5), 3025–3035 (2010)

    Google Scholar 

  18. Lasser, T., Ntziachristos, V.: Optimization of 360o projection fluorescence molecular tomography. Med. Image Anal. 11(4), 389–399 (2007)

    Article  Google Scholar 

  19. Wang, D., Liu, X., Bai, J.: Analysis of fast full angle fluorescence diffuse optical tomography with beamforming illumination. Opt. Exp. 17(24), 21376–21395 (2009)

    Article  Google Scholar 

  20. Zhu, D., Li, C.: Accelerated image reconstruction in fluorescence molecular tomography using a nonuniform updating scheme with momentum and ordered subsets methods. J. Biomed. Opt. 21(1), 016004 (2016)

    Article  Google Scholar 

  21. Ye, J., Chi, C., Xue, Z., et al.: Fast and robust reconstruction for fluorescence molecular tomography via a sparsity adaptive subspace pursuit method.[J]. Biomed. Opt. Express. 5(2), 387–406 (2014)

    Article  Google Scholar 

  22. He, X., Dong, F., Yu, J., et al.: Reconstruction algorithm for fluorescence molecular tomography using sorted L-one penalized estimation. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 32(11), 1928–1935 (2015)

    Article  Google Scholar 

  23. Kim, S., Koh, K., Lustig, M., Boyd, S., Gorinvesky, D.: An interior-point method for large-scale l-regularized least squares. IEEE J Sel Top Signal Process. 1, 606–617 (2007)

    Article  Google Scholar 

  24. Klose, A.D., Larsen, E.W.: Light transport in biological tissue based on the simplified spherical harmonics equations. J. Comput. Phys. 220(1), 441–470 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. Tan, Y., Jiang, H.: DOT guided fluorescence molecular tomography of arbitrarily shaped objects. Med. Phys. 35, 5703–5707 (2008)

    Article  Google Scholar 

  26. Panasyuk, G.Y., Wang, Z.M., Schotland, J.C., Markel, V.A.: Fluorescent optical tomography with large data sets. Opt. Lett. 33, 1744–1746 (2008)

    Article  Google Scholar 

  27. Qiao, Y., Hong, Q., Qin, C., et al.: Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation. Opt. Commun. 351, 75–84 (2015)

    Article  Google Scholar 

  28. Wang, X., Cao, X., Zhang, B., Liu, F., Luo, J., Bai, J.: A hybrid reconstruction algorithm for fluorescence tomography using Kirchhoff approximation and finite element method. Med. Biol. Eng. Comput. 51, 7–17 (2013)

    Article  Google Scholar 

  29. Bertsekas, D.P.: Nonlinear programming, 2nd edn. Athena Scientific, Belmont (1999)

  30. Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward–backward splitting. Multiscale Model Simul. 4(4), 1168–1200 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  31. Hanke, M., Groetsch, C.W.: Nonstationary iterated Tikhonov regularization. J. Optim. Theor. Appl. 98(1), 37–53 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  32. Faber, V., Manteuffel, A., White, A.B. Jr., Wing, G.M.: Asymptotic behavior of singular values and functions of certain convolution operators. Comput. Math. Appl. 12, 37–52 (1989)

    Google Scholar 

  33. Han, D., Tian, J., Qin, C., et al.: A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage. Proc. SPIE Int. Soc. Opt. Eng. 7965(1):19–23 (2011)

    Google Scholar 

  34. Zhang, G., He, W., Pu, H., et al.: Acceleration of dynamic fluorescence molecular tomography with principal component analysis. Biomed. Opt. Express. 6(6), 2036–2055 (2015)

    Article  Google Scholar 

  35. Shang, M., Nie, C.: A shrinkage-thresholding projection method for sparsest solutions of LCPs. J. Inequal. Appl. 2014(1), 51 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  36. Fang, E., Wang, J., Hu, D., et al.: Adaptive monotone fast iterative shrinkage thresholding algorithm for fluorescence molecular tomography. IET Sci. Meas. Technol. 9(5), 587–595 (2015)

    Article  Google Scholar 

  37. Dice, L.R.: Measures of the amount of ecologic association between species. Ecology. 26(3), 297–302 (1945)

    Article  Google Scholar 

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Author notes

  1. Bin Wang and Xu Zhang contributed equally to this work.

Authors and Affiliations

  1. School of Information Sciences and Technology, Northwest University, Xi’an, 710127, China

    Bin Wang, Xu Zhang, Yuqing Hou, Xuelei He, Huangjian Yi & Xiaowei He

Authors
  1. Bin Wang
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  2. Xu Zhang
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  3. Yuqing Hou
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  4. Xuelei He
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  5. Huangjian Yi
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  6. Xiaowei He
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Correspondence to Huangjian Yi or Xiaowei He.

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Wang, B., Zhang, X., Hou, Y. et al. Efficient image reconstruction for fluorescence molecular tomography via linear regression approximation scheme with dual augmented Lagrangian method. Multimedia Systems 25, 135–145 (2019). https://doi.org/10.1007/s00530-017-0575-4

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