title: A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D.
abstract: A direct reconstruction algorithm for complex conductivities inW2,∞(Ω), where Ω is a bounded, simply connected Lipschitz domain in ℝ2, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems202000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.
authors: Department of Mathematics, Colorado State University, USA.
authors: S J
authors: SJ
authors: Hamilton
authors: C N L
authors: CN
authors: Herrera
authors: J L
authors: JL
authors: Mueller
authors: A
authors: A
authors: Von Herrmann
references: IEEE Trans Med Imaging. 2002 Jun;21(6):555-9
references: 12166850
references: J Appl Physiol (1985). 2002 Aug;93(2):660-6
references: 12133877
references: IEEE Trans Biomed Eng. 1994 Aug;41(8):729-34
references: 7927395
references: IEEE Trans Biomed Eng. 1991 Nov;38(11):1106-10
references: 1748445
references: Eur J Appl Physiol. 2004 Jun;92(1-2):45-9
references: 14985995
references: IEEE Trans Biomed Eng. 1989 Sep;36(9):918-24
references: 2777280
references: Neuroimage. 2001 Feb;13(2):283-94
references: 11162269
references: IEEE Trans Biomed Eng. 1998 Jul;45(7):899-908
references: 9644899
references: IEEE Trans Med Imaging. 2002 Jun;21(6):638-45
references: 12166860
references: Physiol Meas. 2010 Feb;31(2):221-32
references: 20057005
references: Am J Respir Crit Care Med. 2004 Apr 1;169(7):791-800
references: 14693669
references: IEEE Trans Med Imaging. 2004 Jul;23(7):821-8
references: 15250634
references: IEEE Trans Med Imaging. 2002 Jun;21(6):646-52
references: 12166861
references: Physiol Meas. 2006 May;27(5):S43-50
references: 16636419
references: Curr Opin Crit Care. 2009 Feb;15(1):18-24
references: 19186406
references: Crit Care Med. 2008 Apr;36(4):1230-8
references: 18379250
references: IEEE Trans Med Imaging. 2008 Dec;27(12):1762-8
references: 19033092
references: IEEE Trans Med Imaging. 2008 Oct;27(10):1439-48
references: 18815096
references: Physiol Meas. 2001 Feb;22(1):177-85
references: 11236878
references: Physiol Meas. 2007 Jul;28(7):S101-14
references: 17664628
references: Physiol Meas. 2007 Jul;28(7):S261-7
references: 17664640
references: Physiol Meas. 2003 May;24(2):391-401
references: 12812424
references: IEEE Trans Biomed Eng. 1997 Nov;44(11):1051-60
references: 9353984