Source reconstruction for bioluminescence tomography via L1/2 regularization

Jingjing Yu; Qiyue Li; Haiyu Wang

doi:10.1142/s1793545817500146

[1] C. Darne, Y. Lu, E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: A review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1 (2014).

[2] C. Qin, J. Feng, S. Zhu, X. Ma, J. Zhong, P. Wu, Z. Jin, J. Tian, “Recent advances in bioluminescence tomography: Methodology and system as well as application,” Laser Photon. Rev. 8, 94–114 (2014).

[3] W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13, 6756–6771 (2005).

[4] X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).

[5] H. Gao, H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18, 1854–1871 (2010).

[6] J. Yu, B. Zhang, I. Iordachita, J. Reyes, Z. Lu, M. Brock, M. Patterson, J. Wong, K. Wong, “Systematic study of target localization for bioluminescence tomography guided radiation therapy,” Med. Phys. 43, 2619–2629 (2016).

[7] X. Ma, J. Tian, C. Qin, X. Yang, B. Zhang, Z. Xue, X. Zhang, D. Han, D. Dong, X. Liu. “Early detection of liver cancer based on bioluminescence tomography,” Appl. Opt. 50, 1389–1395 (2011).

[8] S. Mollard, R. Fanciullino, S. Giacometti, C. Serdjebi, S. Benzekry, J. Ciccolini, “In vivo bioluminescence tomography for monitoring breast tumor growth and metastatic spreading: Comparative study and mathematical modeling,” Sci. Rep. 6, 36173 (2016).

[9] W. Guo, K. Jia, D. Han, Q. Zhang, X. Liu, J. Feng, C. Qin, X. Ma, J. Tian, “E±cient sparse reconstruction algorithm for bioluminescence tomography based on duality and variable splitting,” Appl. Opt. 51, 5676–5685 (2012).

[10] J. Yu, F. Liu, J. Wu, L. Jiao, X. He, “Fast source reconstruction for bioluminescence tomography based on sparse regularization,” IEEE Trans. Biomed. Eng. 57, 2583–2586 (2010).

[11] M. Yukawa, S. Amari, “Lp-regularized least squares (0 < p < 1) and critical path,” IEEE Trans. Inf. Theory. 62, 488–502 (2016).

[12] M. Lai, J. Wang, “An unconstrained ‘q minimization with 0 < q < 1 for sparse solution of under-determined linear systems,” SIAM 21, 82–101 (2011).

[13] Z. Xu, X. Chang, F. Xu, H. Zhang, “L1/2 regularization: A thresholding representation theory and a fast solver,” IEEE Trans. Neural Netw. 23, 1013–1027 (2012).

[14] S. Okawa, Y. Hoshi, Y. Yamada, “Improvement of image quality of time-domain diffuse optical tomography with lp sparsity regularization,” Biomed. Opt. Express 2, 3334–3348 (2011).

[15] W. Xie, Y. Deng, K. Wang, X. Yang, Q. Luo, “Reweighted L1 regularization for restraining artifacts in FMT reconstruction images with limited measurements,” Opt. Lett. 39, 4148–4151 (2014).

[16] D. Zhu, C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59, 2901–2912 (2014).

[17] H. Guo, J. Yu, X. He, Y. Hou, F. Dong, S. Zhang, “Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization,” Biomed. Opt. Express 6, 1648–1664 (2015).

[18] J. Shi, F. Liu, H. Pu, S. Zuo, J. Luo, J. Bai, “An adaptive support driven reweighted L1-regularization algorithm for fluorescence molecular tomography,” Biomed. Opt. Express 5, 4039–4052 (2014).

[19] L. Lian, Y. Deng, W. Xie, G. Xu, X. Yang, Z. Zhang, Q. Luo, “High-dynamic-range fluorescence molecular tomography for imaging of fluorescent targets with large concentration differences,” Opt. Express 24, 19920–19933 (2016).

[20] J. Shi, F. Liu, J. Zhang, J. Luo, J. Bai, “Fluorescence molecular tomography reconstruction via discrete cosine transform-based regularization,” J. Biomed. Opt. 20, 055004 (2015).

[21] H. Zhang, G. Geng, X. Wang, X. Qu, Y. Hou, X. He, “Fast and robust reconstruction for fluorescence molecular tomography via L1-2 regularization,” Biomed. Res. Int. 2016, 5065217 (2016).

[22] X. Chen, D. Yang, Q. Zhang, J. Liang, “L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography,” Appl. Phys. 115, 184702 (2014).

[23] M. R. Osborne, B. A. Turlach, “A homotopy algorithm for the quantile regression lasso and related piecewise linear problems,” J. Comput. Graph. Statist. 20, 972–987 (2011).

[24] D. L. Donoho, Y. Tsaig, I. Drori, J. L. Starck, “Sparsesolution of underdetermined linear equations by stagewise orthogonal matching pursuit,” IEEE Trans. Inf. Theory. 58, 1094–1121 (2012).

[25] R. Chartrand, V. Staneva, “Restricted isometry properties and nonconvex compressive sensing,” Inverse Probl. 24, 1–14 (2008).

[26] E. J. Candes, M. B. Wakin, S. P. Boyd, “Enhancing sparsity by reweighted L1 minimization,” J. Fourier Anal. Appl. 14, 877–905 (2008).

[27] M. Asif, J. Romberg, “Fast and accurate algorithms for re-weighted L1-norm minimization,” IEEE Trans. Signal Process. 61, 5905–5916 (2013).

[28] J. Fuchs, “On sparse representations in arbitrary redundant bases,” IEEE Trans. Inf. Theory 50, 1341–1344 (2004).

[29] B. Dogdas, D. Stout, A. F. Chatziioannou, R. M. Leahy, “Digimouse: A 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587 (2007).

[30] G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. McLennan, M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[31] X. Song, B. Pogue, S. Jiang, M. Doyley, H. Dehghani, T. Tosteson, K. Paulsen, “Automated region detection based on the contrast-to-noise ratio in near-infrared tomography,” Appl. Opt. 43, 1053–1062 (2004).