Reconstruction method for optical tomography based on the linearized Bregman iteration with sparse regularization. (English) Zbl 1335.92051
Summary: Optical molecular imaging is a promising technique and has been widely used in physiology, and pathology at cellular and molecular levels, which includes different modalities such as bioluminescence tomography, fluorescence molecular tomography and Cerenkov luminescence tomography. The inverse problem is ill-posed for the above modalities, which cause a nonunique solution. In this paper, we propose an effective reconstruction method based on the linearized Bregman iterative algorithm with sparse regularization (LBSR) for reconstruction. Considering the sparsity characteristics of the reconstructed sources, the sparsity can be regarded as a kind of a priori information and sparse regularization is incorporated, which can accurately locate the position of the source. The linearized Bregman iteration method is exploited to minimize the sparse regularization problem so as to further achieve fast and accurate reconstruction results. Experimental results in a numerical simulation and in vivo mouse
demonstrate the effectiveness and potential of the proposed method.
MSC:
| 92C55 | Biomedical imaging and signal processing |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
References:
| [1] | Ntziachristos, V.; Ripoll, J.; Wang, L. V.; Weissleder, R., Looking and listening to light: the evolution of whole-body photonic imaging, Nature Biotechnology, 23, 3, 313-320 (2005) · doi:10.1038/nbt1074 |
| [2] | Wang, L. V.; Wu, H. I., Biomedical Optics: Principles and Imaging (2007), Wiley-Interscience, John Wiley & Sons |
| [3] | Weissleder, R.; Pittet, M. J., Imaging in the era of molecular oncology, Nature, 452, 7187, 580-589 (2008) · doi:10.1038/nature06917 |
| [4] | Willmann, J. K.; van Bruggen, N.; Dinkelborg, L. M.; Gambhir, S. S., Molecular imaging in drug development, Nature Reviews Drug Discovery, 7, 7, 591-607 (2008) · doi:10.1038/nrd2290 |
| [5] | Gong, R.; Wang, G.; Cheng, X.; Han, W., A novel approach for studies of multispectral bioluminescence tomography, Numerische Mathematik, 115, 4, 553-583 (2010) · Zbl 1190.92021 · doi:10.1007/s00211-010-0293-8 |
| [6] | Ye, J. Z.; Chi, C. W.; Xue, Z. W.; Wu, P.; An, Y.; Xu, H.; Zhang, S.; Tian, J., Fast and robust reconstruction for fluorescence molecular tomography via a sparsity adaptive subspace pursuit method, Biomedical Optics Express, 5, 2, 387-406 (2014) · doi:10.1364/boe.5.000387 |
| [7] | Ding, X. T.; Wang, K.; Jie, B.; Luo, Y. L.; Hu, Z. H.; Tian, J., Probability method for Cerenkov luminescence tomography based on conformance error minimization, Biomedical Optics Express, 5, 7, 2091-2112 (2014) · doi:10.1364/boe.5.002091 |
| [8] | Cong, W.; Wang, G.; Kumar, D.; Liu, Y.; Jiang, M.; Wang, L. V.; Hoffman, E. A.; McLennan, G.; McCray, P. B.; Zabner, J.; Cong, A., Practical reconstruction method for bioluminescence tomography, Optics Express, 13, 18, 6756-6771 (2005) · doi:10.1364/opex.13.006756 |
| [9] | Wang, G.; Li, Y.; Jiang, M., Uniqueness theorems in bioluminescence tomography, Medical Physics, 31, 8, 2289-2299 (2004) · doi:10.1118/1.1766420 |
| [10] | Leng, C. C.; Tian, J., Mathematical method in optical molecular imaging, Science China: Information Sciences, 58, 3, 1-13 (2015) · Zbl 1335.92050 · doi:10.1007/s11432-014-5222-5 |
| [11] | Cong, A. X.; Wang, G., Multispectral bioluminescence tomography: methodology and simulation, International Journal of Biomedical Imaging, 2006 (2006) · doi:10.1155/ijbi/2006/57614 |
| [12] | Dehghani, H.; Davis, S. C.; Pogue, B. W., Spectrally resolved bioluminescence tomography using the reciprocity approach, Medical Physics, 35, 11, 4863-4871 (2008) · doi:10.1118/1.2982138 |
| [13] | Feng, J.; Jia, K.; Yan, G.; Zhu, S.; Qin, C.; Lv, Y.; Tian, J., An optimal permissible source region strategy for multispectral bioluminescence tomography, Optics Express, 16, 20, 15640-15654 (2008) · doi:10.1364/oe.16.015640 |
| [14] | Naser, M. A.; Patterson, M. S., Algorithms for bioluminescence tomography incorporating anatomical information and reconstruction of tissue optical properties, Biomedical Optics Express, 1, 2, 512-526 (2010) · doi:10.1364/boe.1.000512 |
| [15] | Lu, Y.; Machado, H. B.; Douraghy, A.; Stout, D.; Herschman, H.; Chatziioannou, A. F., Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework, Optics Express, 17, 19, 16681-16695 (2009) · doi:10.1364/oe.17.016681 |
| [16] | Guo, W.; Jia, K. B.; Zhang, Q.; Liu, X. Y.; Feng, J. C.; Qin, C. H.; Ma, X. B.; Yang, X.; Tian, J., Sparse reconstruction for bioluminescence tomography based on the semigreedy method, Computational and Mathematical Methods in Medicine, 2012 (2012) · Zbl 1401.92125 · doi:10.1155/2012/494808 |
| [17] | Tikhonov, A. N.; Aresenin, V. Y., Solutions of Ill-Posed Problems (1977), Washington, DC, USA: V.H. Winston and Sons, Washington, DC, USA · Zbl 0354.65028 |
| [18] | Gao, H.; Zhao, H., Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization, Optics Express, 18, 3, 1854-1871 (2010) · doi:10.1364/oe.18.001854 |
| [19] | Li, S.-L.; Kun, L.; Feng, Z.; Li, Z.; Xiao, L.-L.; Han, D.-P., Innovative remote sensing imaging method based on compressed sensing, Optics and Laser Technology, 63, 83-89 (2014) · doi:10.1016/j.optlastec.2014.03.019 |
| [20] | Kavuri, V. C.; Lin, Z.-J.; Tian, F. H.; Liu, H. L., Sparsity enhanced spatial resolution and depth localization in diffuse optical tomography, Biomedical Optics Express, 3, 5, 943-957 (2012) · doi:10.1364/boe.3.000943 |
| [21] | Rudin, L. I.; Osher, S.; Fatemi, E., Nonlinear total variation based noise removal algorithms, Physica D, 60, 1-4, 259-268 (1992) · Zbl 0780.49028 · doi:10.1016/0167-2789(92)90242-f |
| [22] | Yao, L.; Jiang, H., Enhancing finite element-based photoacoustic tomography using total variation minimization, Applied Optics, 50, 25, 5031-5041 (2011) · doi:10.1364/ao.50.005031 |
| [23] | Zhu, Y. G.; Shi, Y. Y., A fast method for reconstruction of total-variation MR images with a periodic boundary condition, IEEE Signal Processing Letters, 20, 4, 291-294 (2013) · doi:10.1109/lsp.2013.2245502 |
| [24] | Feng, J. C.; Qin, C. H.; Jia, K. B.; Zhu, S. P.; Liu, K.; Han, D.; Yang, X.; Gao, Q. S.; Tian, J., Total variation regularization for bioluminescence tomography with the split Bregman method, Applied Optics, 51, 19, 4501-4512 (2012) · doi:10.1364/ao.51.004501 |
| [25] | Shi, J. W.; Liu, F.; Zhang, G. L.; Luo, J. W.; Bai, J., Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm, Journal of Biomedical Optics, 19, 4 (2014) · doi:10.1117/1.jbo.19.4.046018 |
| [26] | Goldstein, T.; Osher, S., The split Bregman method for \(\text{L1} \) -regularized problems, SIAM Journal on Imaging Sciences, 2, 2, 323-343 (2009) · Zbl 1177.65088 · doi:10.1137/080725891 |
| [27] | Liu, Y.; Yu, J.; Qin, X.; Guo, J., The Split Bregman iteration algorithm for bioluminescence tomography, Scientia Sinica Informationis, 44, 2, 284-294 (2014) · doi:10.1360/112013-51 |
| [28] | Gu, X. J.; Zhang, Q. Z.; Larcom, L.; Jiang, H. B., Three-dimensional bioluminescence tomography with model-based reconstruction, Optics Express, 12, 17, 3996-4000 (2004) · doi:10.1364/opex.12.003996 |
| [29] | Han, D.; Yang, X.; Liu, K.; Qin, C. H.; Zhang, B.; Ma, X. B.; Tian, J., Efficient reconstruction method for L1 regularization in fluorescence molecular tomography, Applied Optics, 49, 36, 6930-6937 (2010) · doi:10.1364/ao.49.006930 |
| [30] | Schweiger, M.; Arridge, S. R.; Hiraoka, M.; Delpy, D. T., The finite element method for the propagation of light in scattering media: boundary and source conditions, Medical Physics, 22, 11, 1779-1792 (1995) · doi:10.1118/1.597634 |
| [31] | Yin, W.; Osher, S.; Goldfarb, D.; Darbon, J., Bregman iterative algorithm for \(l_1\)-minimization with applications to compressed sensing, SIAM Journal on Imaging Sciences, 1, 1, 143-168 (2008) · Zbl 1203.90153 · doi:10.1137/070703983 |
| [32] | Bush, J., Bregman algorithms [Senior thesis] (2011), Santa Barbara, Calif, USA: University of California, Santa Barbara, Calif, USA |
| [33] | Chen, C.; Tian, F.; Liu, H.; Huang, J., Diffuse optical tomography enhanced by clustered sparsity for functional brain imaging, IEEE Transactions on Medical Imaging, 33, 12, 2323-2331 (2014) · doi:10.1109/tmi.2014.2338214 |
| [34] | An, Y.; Liu, J.; Zhang, G. L.; Ye, J. Z.; Du, Y.; Mao, Y. M.; Chi, C. W.; Tian, J., A novel region reconstruction method for fluorescence molecular tomography, IEEE Transactions on Biomedical Engineering, 62, 7, 1818-1826 (2015) |
| [35] | Yan, G. R.; Tian, J.; Zhu, S. P.; Dai, Y. K.; Qin, C. H., Fast cone-beam CT image reconstruction using GPU hardware, Journal of X-Ray Science and Technology, 16, 4, 225-234 (2008) |
| [36] | Zhu, S. P.; Tian, J.; Yan, G. R.; Qin, C. H.; Feng, J. C., Cone beam micro-CT system for small animal imaging and performance evaluation, International Journal of Biomedical Imaging, 2009 (2009) · doi:10.1155/2009/960573 |
| [37] | Wu, P.; Hu, Y. F.; Wang, K.; Tian, J., Bioluminescence tomography by an iterative reweighted \(l_2\) norm optimization, IEEE Transaction on Biomedical Engineering, 61, 1, 189-196 (2014) |
| [38] | Hu, Z. H.; Ma, X. W.; Qu, X. C.; Yang, W. D.; Liang, J. M.; Wang, J.; Tian, J., Three-dimensional noninvasive monitoring iodine-131 uptake in the thyroid using a modified Cerenkov luminescence tomography approach, PLoS ONE, 7, 5 (2012) · doi:10.1371/journal.pone.0037623 |
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