References
- Klibanov, MV, Su, J, Pantong, N, Shan, H, and Liu, H, 2010. A globally convergent numerical method for an inverse elliptic problem of optical tomography, Appl. Anal. 89 (2010), pp. 861–891.
- Pantong, N, Su, J, Shan, H, Klibanov, MV, and Liu, H, 2009. A globally accelerated reconstruction algorithm for diffusion tomography with continuous-wave source in arbitrary convex shape domain, J. Opt. Soc. Am. A 26 (2009), pp. 456–472.
- Shan, H, Klibanov, MV, Su, J, Pantong, N, and Liu, H, 2008. A globally accelerated numerical method for optical tomography with continuous wave source, J. Inverse Ill-Posed Prob. 16 (2008), pp. 765–792.
- Su, J, Shan, H, Liu, H, and Klibanov, MV, 2006. Reconstruction method from a multiplesite continuous-wave source for three-dimensional optical tomography, J. Opt. Soc. Am. A 23 (2006), pp. 2388–2395.
- Gilbarg, D, and Trudinger, NS, 1983. Elliptic Partial Differential Equations of the Second Order. New York: Springer-Verlag; 1983.
- Arridge, S, 1999. Optical tomography in medical imaging, Inverse Prob. 15 (1999), pp. 841–893.
- Kuzhuget, AV, Beilina, L, and Klibanov, MV, 2012. Approximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattering data, J. Math. Sci. 181 (2012), pp. 126–163.
- Beilina, L, and Klibanov, MV, 2012. Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems. New York: Springer; 2012.
- Beilina, L, and Klibanov, MV, 2008. A globally convergent numerical method for a coefficient inverse problem, SIAM J. Sci. Comp. 30 (2008), pp. 478–509.
- Beilina, L, and Klibanov, MV, 2010. A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem, Inverse Prob. 26 (2010), 045012.
- Beilina, L, and Klibanov, MV, 2010. Reconstruction of dielectrics from experimental data via a hybrid globally convergent/adaptive inverse algorithm, Inverse Prob. 26 (2010), 125009.
- Klibanov, MV, Fiddy, MA, Beilina, L, Pantong, N, and Schenk, J, 2010. Picosecond scale experimental verification of a globally convergent numerical method for a coefficient inverse problem, Inverse Prob. 26 (2010), 045003.
- Kuzhuget, AV, Beilina, L, Klibanov, MV, Sullivan, A, Nguyen, L, and Fiddy, MA, 2012. Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm, Inverse Prob. 28 (2012), 095007.
- Alexeenko, NV, Burov, VA, and Rumyantseva, OD, 2008. Solution of a three-dimensional acoustical inverse scattering problem: II. Modified Novikov algorithm, Acoust. Phys. 54 (2008), pp. 407–419.
- Burov, VA, Morozov, SA, and Rumyantseva, OD, 2002. Reconstruction of fine-scale structure of acoustical scatterers on large scale contrast background, Acoust. Imaging 26 (2002), pp. 231–238.
- Isaacson, D, Mueller, JL, Newell, JC, and Siltanen, S, 2004. Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography, IEEE Trans. Med. Imaging 23 (2004), pp. 821–828.
- Mueller, J, and Siltaren, S, 2003. Direct reconstruction of conductivities from boundary measurements, SIAM J. Sci. Comp. 24 (2003), pp. 1232–1266.
- Novikov, RG, 2005. The ∂-bar approach to approximate inverse scattering at fixed energy in three dimensions, Int. Math. Res. Papers 6 (2005), pp. 287–349.
- Novikov, RG, and Santacesaria, M, Monochromatic reconstruction algorithms for two-dimensional multi-channel inverse problems, preprint (2011), to appear in Int. Math. Res. Notices, preprint available at arXiv:1105.4086 [math.AP].
- Bakushinskii, AB, and Kokurin, MYu, 2004. Iterative Methods for Approximate Solutions of Inverse Problems. New York: Springer; 2004.
- Tikhonov, AN, Goncharsky, AV, Stepanov, VV, and Yagola, AG, 1995. Numerical Methods for Solutions of Ill-Posed Problems. London: Kluwer; 1995.
- Alfano, RR, Pradhan, RR, and Tang, GC, 1989. Optical spectroscopic diagnosis of cancer and normal breast tissues, J. Opt. Soc. Am. B 6 (1989), pp. 1015–1023.
- Abramowitz, M, and Stegun, A, 1964. Handbook of Mathematical Functions. Washington, DC: National Bureau of Standards; 1964.
- Engl, HW, Hanke, M, and Neubauer, A, 2000. Regularization of Inverse Problems. Boston, MA: Kluwer Academic Publishers; 2000.
- Kabanikhin, SI, and Shishlenin, MA, 2011. Numerical algorithm for two-dimensional inverse acoustic problem based on Gel'fand–Levitan–Krein equation, J. Inverse Ill-Posed Prob. 18 (2011), pp. 979–995.
- Born, M, and Wolf, E, 1970. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. New York: Cambridge University Press; 1970.
- Ciarlet, PG, 2002. The Finite Element Method for Elliptic Problems. Philadelphia, PA: SIAM; 2002.