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Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern
1. | Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland |
2. | Institute for Biomedical Engineering, University of Zurich and ETH Zurich, 8093 Zurich, Switzerland |
3. | Biomedical Optics Research Laboratory, University Hospital Zurich, 8091 Zurich, Switzerland |
Fluorescence molecular tomography (FMT) is an emerging tool for biomedical research. There are two factors that influence FMT reconstruction most effectively. The first one is regularization techniques. Traditional methods such as Tikhonov regularization suffer from low resolution and poor signal to noise ratio. Therefore, sparse regularization techniques have been introduced to improve the reconstruction quality. The second factor is the illumination pattern. A better illumination pattern ensures the quantity and quality of the information content of the data set, thus leading to better reconstructions. In this work, we take advantage of the discrete formulation of the forward problem to give a rigorous definition of an illumination pattern as well as the admissible set of patterns. We add restrictions in the admissible set as different types of regularizers to a discrepancy functional, generating another inverse problem with the illumination pattern as unknown. Both inverse problems of reconstructing the fluorescence distribution and finding the optimal illumination pattern are solved by efficient iterative algorithms. Numerical experiments have shown that with a suitable choice of regularization parameters, the two-step approach converges to an optimal illumination pattern quickly and the reconstruction result is improved significantly regardless of the initial illumination setting.
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V. Ntziachristos, C. H. Tung, C. Bremer and R. Weissleder,
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[24] |
W. Ren, A. Elmer, D. Buehlmann, M.-A. Augath, D. Vats, J. Ripoll and M. Rudin,
Dynamic measurement of tumor vascular permeability and perfusion using a hybrid system for simultaneous magnetic resonance and fluorescence imaging, Mol. Imaging Biol., 18 (2016), 191-200.
doi: 10.1007/s11307-015-0884-y. |
[25] |
W. Ren, H. Isler, M. Wolf, J. Ripoll and M. Rudin,
Smart toolkit for fluorescence tomography: Simulation, reconstruction, and validation, IEEE Trans. on Biomedical Engineering, 67 (2020), 16-26.
doi: 10.1109/TBME.2019.2907460. |
[26] |
J. Ripoll, R. B. Schulz and V. Ntziachristos, Free-space propagation of diffuse light: Theory and experiments, Phys. Rev. Lett., 91 (2003), 103901.
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![]() |
[28] |
M. Schweiger and S. R. Arridge,
The finite-element method for the propagation of light in scattering media: Frequency domain case, Medical Physics, 24 (1997), 895-902.
doi: 10.1118/1.598008. |
[29] |
M. Schweiger and S. R. Arridge, The toast++ software suite for forward and inverse modeling in optical tomography, J. Biomed. Opt., 19 (2014), 040801.
doi: 10.1117/1.JBO.19.4.040801. |
[30] |
D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan and C. Li,
Comparison of regularization methods in fluorescence molecular tomography, Photonics, 1 (2014), 95-109.
doi: 10.3390/photonics1020095. |
[31] |
Y. Zhu, A. K. Jha, D. F. Wong and A. Rahmim,
Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization, Biomed. Opt. Express, 9 (2018), 3106-3121.
doi: 10.1364/BOE.9.003106. |
show all references
References:
[1] |
G. S. Alberti, H. Ammari, F. Romero and T. Wintz,
Dynamic spike superresolution and applications to ultrafast ultrasound imaging, SIAM J. Imaging Sci., 12 (2019), 1501-1527.
doi: 10.1137/18M1174775. |
[2] |
H. Ammari, J. Garnier, H. Kang, L. H. Nguyen and L. Seppecher, Multi-wave medical imaging: Mathematical modelling & imaging reconstruction, Modelling and Simulation in Medical Imaging, 2 (2017), 688.
doi: 10.1142/q0067. |
[3] |
S. R. Arridge, M. Schweiger, M. Hiraoka and D. T. Delpy,
A finite element approach for modeling photon transport in tissue, Medical Physics, 20 (1993), 299-309.
doi: 10.1118/1.597069. |
[4] |
S. R. Arridge and J. C. Schotland, Optical tomography: Forward and inverse problems, Inverse Problems, 25 (2009), 123010, 59pp.
doi: 10.1088/0266-5611/25/12/123010. |
[5] |
A. Beck and M. Teboulle,
A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2 (2009), 183-202.
doi: 10.1137/080716542. |
[6] |
M. Bergounioux, E. Bretin and Y. Privat, How to position sensors in thermo-acoustic tomography, Inverse Problems, 35 (2019), 074003, 25pp.
doi: 10.1088/1361-6420/ab0e4d. |
[7] |
E. Candes, N. Braun and M. Wakin, Sparse signal and image recovery from compressive samples, 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2007, 976–979.
doi: 10.1109/ISBI.2007.357017. |
[8] |
T. Correia, M. Koch, A. Ale, V. Ntziachristos and S. Arridge,
Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography–part 2: Image reconstruction, Phys. Med. Biol., 61 (2016), 1452-1475.
doi: 10.1088/0031-9155/61/4/1452. |
[9] |
S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue and K. D. Paulsen,
Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization, Optics Express, 15 (2007), 4066-4082.
doi: 10.1364/OE.15.004066. |
[10] |
E. Demidenko, A. Hartov, N. Soni and K. D. Paulsen,
On optimal current patterns for electrical impedance tomography, IEEE Trans. on Biomedical Engineering, 52 (2005), 238-248.
doi: 10.1109/TBME.2004.840506. |
[11] |
N. Ducros, C. D'Andrea, A. Bassi, G. Valentini and S. Arridge,
A virtual source pattern method for fluorescence tomography with structured light, Phys. Med. Biol., 57 (2012), 3811-3832.
doi: 10.1088/0031-9155/57/12/3811. |
[12] |
J. Dutta, S. Ahn, A. Joshi and R. M. Leahy,
Illumination pattern optimization for fluorescence tomography: Theory and simulation studies, Phys. Med. Biol., 55 (2010), 2961-2982.
doi: 10.1088/0031-9155/55/10/011. |
[13] |
J. Dutta, S. Ahn, C. Li, S. R. Cherry and R. M. Leahy,
Joint L1 and total variation regularization for fluorescence molecular tomography, Phys. Med. Biol., 57 (2012), 1459-1476.
doi: 10.1088/0031-9155/57/6/1459. |
[14] |
R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3$^rd$ edition, Prentice-Hall, Upper Saddle River, New Jersey, 2006. |
[15] |
R. A. J. Groenhuis, H. A. Ferwerda and J. J. T. Bosch,
Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory, Appl. Opt., 22 (1983), 2456-2462.
doi: 10.1364/AO.22.002456. |
[16] |
T. Hastie, R. Tibshirani and M. Wainwright, Statistical Learning with Sparsity: The Lasso and Generalizations, CRC Press, Boca Raton, FL, 2015.
![]() ![]() |
[17] |
N. Hyvönen, A. Seppänen and S. Staboulis,
Optimizing electrode positions in electrical impedance tomography, SIAM J. Appl. Math., 74 (2014), 1831-1851.
doi: 10.1137/140966174. |
[18] |
J. Kaipio, A. Seppänen, A. Voutilainen and H. Haario,
Optimal current patterns in dynamical electrical impedance tomography imaging, Inverse Problems, 23 (2007), 1201-1214.
doi: 10.1088/0266-5611/23/3/021. |
[19] |
J. R. Lorenzo, Principles of Diffuse Light Propagation: Light Propagation in Tissues with Applications in Biology and Medicine, World Scientific, 2012.
doi: 10.1142/7609. |
[20] |
A. Lyons, F. Tonolini, A. Boccolini, A. Repetti, R. Henderson, Y. Wiaux and D. Faccio,
Computational time-of-flight diffuse optical tomography, Nature Photonics, 13 (2019), 575-579.
doi: 10.1038/s41566-019-0439-x. |
[21] |
V. Ntziachristos, C. H. Tung, C. Bremer and R. Weissleder,
Fluorescence molecular tomography resolves protease activity in vivo, Nature Medicine, 8 (2002), 757-761.
doi: 10.1038/nm729. |
[22] |
V. Ntziachristos,
Going deeper than microscopy: The optical imaging frontier in biology, Nature Methods, 7 (2010), 603-614.
doi: 10.1038/nmeth.1483. |
[23] |
V. Ntziachristos and R. Weissleder,
Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation, Optics Letters, 26 (2001), 893-895.
doi: 10.1364/OL.26.000893. |
[24] |
W. Ren, A. Elmer, D. Buehlmann, M.-A. Augath, D. Vats, J. Ripoll and M. Rudin,
Dynamic measurement of tumor vascular permeability and perfusion using a hybrid system for simultaneous magnetic resonance and fluorescence imaging, Mol. Imaging Biol., 18 (2016), 191-200.
doi: 10.1007/s11307-015-0884-y. |
[25] |
W. Ren, H. Isler, M. Wolf, J. Ripoll and M. Rudin,
Smart toolkit for fluorescence tomography: Simulation, reconstruction, and validation, IEEE Trans. on Biomedical Engineering, 67 (2020), 16-26.
doi: 10.1109/TBME.2019.2907460. |
[26] |
J. Ripoll, R. B. Schulz and V. Ntziachristos, Free-space propagation of diffuse light: Theory and experiments, Phys. Rev. Lett., 91 (2003), 103901.
doi: 10.1103/PhysRevLett.91.103901. |
[27] |
M. Rudin, Molecular Imaging: Basic Principles and Applications in Biomedical Research, Imperial College Press, London, 2013.
![]() |
[28] |
M. Schweiger and S. R. Arridge,
The finite-element method for the propagation of light in scattering media: Frequency domain case, Medical Physics, 24 (1997), 895-902.
doi: 10.1118/1.598008. |
[29] |
M. Schweiger and S. R. Arridge, The toast++ software suite for forward and inverse modeling in optical tomography, J. Biomed. Opt., 19 (2014), 040801.
doi: 10.1117/1.JBO.19.4.040801. |
[30] |
D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan and C. Li,
Comparison of regularization methods in fluorescence molecular tomography, Photonics, 1 (2014), 95-109.
doi: 10.3390/photonics1020095. |
[31] |
Y. Zhu, A. K. Jha, D. F. Wong and A. Rahmim,
Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization, Biomed. Opt. Express, 9 (2018), 3106-3121.
doi: 10.1364/BOE.9.003106. |














experiment | round | MSE | Dice | VR | SNR |
initial | 0.018436 | 0.47761 | 0.52273 | 1.5303 | |
0.01489 | 0.53631 | 1.0341 | 3.6664 | ||
initial | 0.020026 | 0.35200 | 0.42045 | 0.70309 | |
0.015951 | 0.53125 | 1.1818 | 2.9783 |
experiment | round | MSE | Dice | VR | SNR |
initial | 0.018436 | 0.47761 | 0.52273 | 1.5303 | |
0.01489 | 0.53631 | 1.0341 | 3.6664 | ||
initial | 0.020026 | 0.35200 | 0.42045 | 0.70309 | |
0.015951 | 0.53125 | 1.1818 | 2.9783 |
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