Citation: |
[1] |
L. Bregman, The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex optimization, USSR Computational Mathematics and Mathematical Physics, 7 (1967), 620-631. |
[2] |
M. Burger, Y. Landa, N. Tanushev and R. Tsai, Discovering point sources in unknown environments, in WAFR 2008: The Eighth International Workshop on the Algorithmic Foundations of Robotics, 57 2010, 663-678.doi: 10.1007/978-3-642-00312-7_41. |
[3] |
J. Cai, S. Osher and Z. Shen, Convergence of the linearized Bregman iteration for $l_1$-norm minimization, Math. Comp., 78 (2009), 2127-2136.doi: 10.1090/S0025-5718-09-02242-X. |
[4] |
E. J. Candès and T. Tao, Decoding by linear programming, IEEE Transactions on Information Theory, 51(12) (2005). |
[5] |
Y. Cheng and T. Singh, Source term estimation using convex optimization, The Eleventh International Conference on Information Fusion, Cologne, Germany, (2008). |
[6] |
D. Donoho, Compressed sensing, IEEE Transactions on Information Theory, 52 (2006), 1289-1306.doi: 10.1109/TIT.2006.871582. |
[7] |
A. El Badia, T. Ha Duong and A. Hamdi, Identification of a point source in a linear advection-dispersion-reaction equation: Application to a pollution source problem, Inverse Problems, 21 (2005), 1121-1136.doi: 10.1088/0266-5611/21/3/020. |
[8] |
B. Farmer, C. Hall and S. Esedoglu, Source identification from line integral measurements and simple atmospheric models, Inverse Probl. Imaging, 7 (2013), 471-–490.doi: 10.3934/ipi.2013.7.471. |
[9] |
E. Haber, Numerical methods for optimal experimental design of large-scale ill-posed problems, Inverse Problems, 24 (2008). |
[10] |
Y. Landa, N. Tanushev and R. Tsai, Discovery of point sources in the Helmholtz equation posed in unknown domains with obstacles, Comm. in Math. Sci., 9 (2011), 903-928.doi: 10.4310/CMS.2011.v9.n3.a11. |
[11] |
Y. Li and S. Osher, Coordinate descent optimization for L1 minimization with application to compressed sensing; A greedy algorithm, Inverse Problems and Imaging, 3 (2009), 487–-503.doi: 10.3934/ipi.2009.3.487. |
[12] |
G. Li, Y. Tan, J. Cheng and X. Wang, Determining magnitude of groundwater pollution sources by data compatibility analysis, Inverse Problem in Science and Engineering, 14 (2006), 287-300.doi: 10.1080/17415970500485153. |
[13] |
L. Ling and T. Takeuchi, Point sources identification problems for heat equations, Communications in Computational Physics, 5 (2009), 897-913. |
[14] |
L. Ling, M. Yamamoto, Y. Hon and T. Takeuchi, Identification of source locations in two-dimensional heat equations, Inverse Problems, 22 (2006), 1289-1305.doi: 10.1088/0266-5611/22/4/011. |
[15] |
A. V. Mamonov and Y.-H. R. Tsai, Point source identification in non-linear advection-diffusion-reaction systems, Inverse Problems, 29 (2013).doi: 10.1088/0266-5611/29/3/035009. |
[16] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, An iterative regularization method for total variation-based image restoration, MMS, 4 (2005), 460-489.doi: 10.1137/040605412. |
[17] |
Z. Wen, W. Yin, D. Goldfarb and Y. Zhang, A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation, SIAM J. Scientific Computing, 32 (2010), 1832-1857.doi: 10.1137/090747695. |
[18] |
W. Yin, S. Osher, D. Goldfarb and J. Darbon, Bregman iterative algorithms for $l_1$-minimization with applications to compressed sensing, SIAM J. Imaging Sciences, (2008), 143-168.doi: 10.1137/070703983. |