Yosemite National Park
Research Interests:

Research Activities: 
The interdisciplinary field of Inverse Problems is thriving in exciting and unexpected ways. Without even knowing it, you are inevitably surrounded by inverse problems on a daily basis. In an inverse problem, an observation is your data and you aim to determine what set of circumstances led to that data. For example, if you observe contaminated water in a river at point B, you aim to determine where, point A, the contamination originates. Advances in technology have made data measurements from nanoscale, in medical fields, to astronomical scale, in space exploration, modern realities. Coupled with grand advancements in computing power, it is now possible to ask and answer a tremendous variety of interesting questions. The nature of such questions are inherently interdisciplinary bringing together scientists from varying fields such as mathematics, engineering, physics, biology, chemistry, statistics, astronomy, and medicine, etc.
My main area of research involves the use of nonlinear inversion methods for an imaging modality called Electrical Impedance Tomography, or EIT for short. In EIT, the goal is to reconstruct the conductivity distribution inside of a conductive body by using only current and voltage measurements taken at the boundary. The reconstruction task is a highly illposed nonlinear inverse problem and requires the use of mathematical techniques from functional and complex analysis, inverse scattering and PDE theory, and numerical analysis. The CGO solutions and Dbar techniques honed during my PhD studies and Postdoctoral work serve as a springboard into a sea of new, exciting, and diverse problems including integrable systems (Davey Stewartson II, Novikov Vesilov), image processing, and seismic imaging. Please see my Research Statement (from 2014, new projects have not yet been included) , and visit the Projects website, for a more detailed description of my past and future projects
My main area of research involves the use of nonlinear inversion methods for an imaging modality called Electrical Impedance Tomography, or EIT for short. In EIT, the goal is to reconstruct the conductivity distribution inside of a conductive body by using only current and voltage measurements taken at the boundary. The reconstruction task is a highly illposed nonlinear inverse problem and requires the use of mathematical techniques from functional and complex analysis, inverse scattering and PDE theory, and numerical analysis. The CGO solutions and Dbar techniques honed during my PhD studies and Postdoctoral work serve as a springboard into a sea of new, exciting, and diverse problems including integrable systems (Davey Stewartson II, Novikov Vesilov), image processing, and seismic imaging. Please see my Research Statement (from 2014, new projects have not yet been included) , and visit the Projects website, for a more detailed description of my past and future projects
Journal Articles
S. J. Hamilton ``EIT Imaging of admittivities with a Dbar method and spatial prior: experimental results for absolute and difference imaging’’, Physiological Measurement. 2017 May 22;38(6):11761192. doi: 10.1088/13616579/aa63d7.
M. Alsaker, S. J. Hamilton, and A. Hauptmann, ``A Direct Dbar Method for Partial Boundary Data Electrical Impedance Tomography with A Priori Information’’, Inverse Problems and Imaging, Volume 11, No. 3, 2017, 427454, doi: 10.3934/ipi.2017020.
S. J. Hamilton, J. L. Mueller, and M. Alsaker “Incorporating a Spatial Prior into Nonlinear Dbar EIT Imaging for Complex Admittivities”, IEEE Transactions on Medical Imaging, 36(2): 457466, 2017. doi: 10.1109/TMI.2016.2613511
S. J. Hamilton, J. M. Reyes, S. Siltanen, and X. Zhang, “A Hybrid Segmentation and Dbar Method for Electrical Impedance Tomography”,
SIAM J. on Imaging Sciences, 9(2):770793, 2016.
Michelle M. Mellenthin, Jennifer L. Mueller, Erick Dario Leon Bueno de Camargo, Fernando Silva de Moura, Sarah J. Hamilton, and Raul Gonzalez Lima, “The ACE1 Thoracic Electrical Impedance Tomography System for Ventilation and Perfusion”, 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, MiCo, Milano Conference Center, Milano, Italy, August 2529, 2015.
S. J. Hamilton, A. Hauptman, and S. Siltanen, “A DataDriven EdgePreserving Dbar Method for Electrical Impedance Tomography”,
Inverse Problems in Imaging, 8(4):10531072, 2014.
S. J. Hamilton, M. Lassas, and S. Siltanen, “A Direct Reconstruction Method for Anisotropic Articles Electrical Impedance Tomography”, Inverse Problems, 30(075007):133, 2014.
S. J. Hamilton and S. Siltanen, “Nonlinear Inversion from Partial EIT Data: Computational Experiments”, Contemporary Mathematics: Inverse Problems and Applications, 615:105129 (2014).
S. J. Hamilton and J. L. Mueller, “Direct EIT reconstruction of complex admittivities on a chestshaped domain in 2D”, IEEE Transactions on Medical Imaging, 32: 757769. 2013.
S. J. Hamilton, C. N. L. Herrera, J. L. Mueller, and A. Von Herrmann, “A direct Dbar reconstruction algorithm for recovering a complex conductivity in 2D”, Inverse Problems, 28 (2012) 095005.
M. Buhnerkempe, N. Burch, S. Hamilton, K. Byrne, E. Childers, L. Davis, P. Doherty, Jr., K. Holfelder, M. Pyne, and G. Schroeder, “The Utility of Transient Sensitivity for Wildlife Management and Conservation: Bison as a Case Study”, Biological Conservation, 144(6):18081815. 2011.
M. Pyne, M. Buhnerkempe, N. Burch, K. Byrne, E. Childers, L. Davis, P. Doherty, Jr., S. Hamilton, K. Holfelder, and G. Schroeder, “Survival and Breeding Transitions for a Reintroduced Bison Population: a Multistate Approach”, Journal of Wildlife Management, 74(7):1463 1471. 2010.
A. Dean, J. EllisMonaghan, S. Hamilton, and G. Pangborn, “Unit rectangle visibility graphs”, Electronic Journal of Combinatorics, 15 (2008), #R79, 124.
M. Alsaker, S. J. Hamilton, and A. Hauptmann, ``A Direct Dbar Method for Partial Boundary Data Electrical Impedance Tomography with A Priori Information’’, Inverse Problems and Imaging, Volume 11, No. 3, 2017, 427454, doi: 10.3934/ipi.2017020.
S. J. Hamilton, J. L. Mueller, and M. Alsaker “Incorporating a Spatial Prior into Nonlinear Dbar EIT Imaging for Complex Admittivities”, IEEE Transactions on Medical Imaging, 36(2): 457466, 2017. doi: 10.1109/TMI.2016.2613511
S. J. Hamilton, J. M. Reyes, S. Siltanen, and X. Zhang, “A Hybrid Segmentation and Dbar Method for Electrical Impedance Tomography”,
SIAM J. on Imaging Sciences, 9(2):770793, 2016.
Michelle M. Mellenthin, Jennifer L. Mueller, Erick Dario Leon Bueno de Camargo, Fernando Silva de Moura, Sarah J. Hamilton, and Raul Gonzalez Lima, “The ACE1 Thoracic Electrical Impedance Tomography System for Ventilation and Perfusion”, 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, MiCo, Milano Conference Center, Milano, Italy, August 2529, 2015.
S. J. Hamilton, A. Hauptman, and S. Siltanen, “A DataDriven EdgePreserving Dbar Method for Electrical Impedance Tomography”,
Inverse Problems in Imaging, 8(4):10531072, 2014.
S. J. Hamilton, M. Lassas, and S. Siltanen, “A Direct Reconstruction Method for Anisotropic Articles Electrical Impedance Tomography”, Inverse Problems, 30(075007):133, 2014.
S. J. Hamilton and S. Siltanen, “Nonlinear Inversion from Partial EIT Data: Computational Experiments”, Contemporary Mathematics: Inverse Problems and Applications, 615:105129 (2014).
S. J. Hamilton and J. L. Mueller, “Direct EIT reconstruction of complex admittivities on a chestshaped domain in 2D”, IEEE Transactions on Medical Imaging, 32: 757769. 2013.
S. J. Hamilton, C. N. L. Herrera, J. L. Mueller, and A. Von Herrmann, “A direct Dbar reconstruction algorithm for recovering a complex conductivity in 2D”, Inverse Problems, 28 (2012) 095005.
M. Buhnerkempe, N. Burch, S. Hamilton, K. Byrne, E. Childers, L. Davis, P. Doherty, Jr., K. Holfelder, M. Pyne, and G. Schroeder, “The Utility of Transient Sensitivity for Wildlife Management and Conservation: Bison as a Case Study”, Biological Conservation, 144(6):18081815. 2011.
M. Pyne, M. Buhnerkempe, N. Burch, K. Byrne, E. Childers, L. Davis, P. Doherty, Jr., S. Hamilton, K. Holfelder, and G. Schroeder, “Survival and Breeding Transitions for a Reintroduced Bison Population: a Multistate Approach”, Journal of Wildlife Management, 74(7):1463 1471. 2010.
A. Dean, J. EllisMonaghan, S. Hamilton, and G. Pangborn, “Unit rectangle visibility graphs”, Electronic Journal of Combinatorics, 15 (2008), #R79, 124.
Selected Conference and Invited Talks
"Direct Absolute EIT Imaging on Experimental Data", 18th International Conference on Biomedical Applications of Electrical Impedance Tomography, Dartmouth College, USA, June 22, 2017.
"Improving Image Quality for Practical Electrical Impedance Tomography Imaging with Direct Dbar Methods", Mathematics, Statistics, and Computer Science Colloquium, Marquette University, Milwaukee, WI, USA, March 9, 2017.
“Improving image quality for complex Electrical Impedance Imaging: Incorporating a priori in formation into a direct nonlinear Dbar method”, BCAM Scientific Seminar, Basque Center for Applied Mathematics, Bilbao, Spain, June 23, 2016.
“A Nonlinear Reconstruction Method with A Priori Data for EIT”, 16th International Conference on Electrical BioImpedance / 17th Conference on Electrical Impedance Tomography, Stockholm, Sweden, June 22, 2016.
“Incorporating a Spatial Prior into Nonlinear DBar Eit Imaging for Complex Admittivities”, SIAM Conference on Imaging Science 2016 (IS16), Albuquerque, New Mexico, USA, May 25, 2016.
“Improving images for Electrical Impedance Imaging with a spatial prior”, Applied and Computational Mathematics Seminar, University of WisconsinMilwaukee, Milwaukee, Wisconsin, USA, February 11, 2016.
“Direct Dbar Reconstructions for Experimental EIT Data with Boundary Shape Determination”, Applied Inverse Problems conference (AIPC) 2015, University of Helsinki, Helsinki, Finland, May 29, 2015.
“Pulmonary imaging using Electrical Impedance Tomography with a Direct Dbar Admittivity Method”, Joint Mathematics Meeting 2015: Special Session on Inverse Problems, San Antonio, Texas, January 11, 2015.
“A Novel DataDriven Dbar Reconstruction Algorithm for Experimental 2D Electrical Impedance Tomography Data”, The 7th International Conference Inverse Problems: Modeling and Simulation (IPMS2014), Fethiye, Turkey, May 27, 2014.
“A Novel DataDriven Edge Sharpening Dbar Reconstruction Algorithm for 2D Electrical Impedance Tomography Imaging”, SIAM Imaging Science Conference 2014, Minisymposium: Advances in Electrical Impedance Tomography, Hong Kong, Hong Kong, May 14, 2014.
“A Variety of Dbar Methods in Electrical Impedance Tomography: Not Just for 2D Isotropic Conductivities!”, Shanghai Jiao Tong University, Shanghai, China, May 9, 2014.
“Alternative uses for Dbar Methods in Electrical Impedance Tomography”, Inverse Problems Seminar, University College London, London, England, UK, April 23, 2014.
“A DataDriven Edge Sharpening Dbar Reconstruction Algorithm for 2D EIT Imaging”, Inverse Problems Seminar, Colorado State University, Fort Collins, CO USA, February 20, 2014.
“A Direct Dbar Reconstruction Method for 2D Anisotropic Electrical Impedance Tomography”, Inverse Days 2013, Inari, Finland, December 12, 2013.
“Direct Dbar Methods for 2D Electrical Impedance Tomography”, Danmarks Tekniske Universitet, Copenhagen, Denmark, October 30, 2013.
“Computational Results for the Semiclassical Limit of the Defocusing DSII Equation”, Exceptional Circle Helsinki Workshop, University of Helsinki, Helsinki, Finland, August 13, 2013.
“NonIterative Dbar Reconstructions of 2D Conductivities and Permittivities from Experimental EIT Data”, Minisymposium: Inverse problems with experimental data, Applied Inverse Problems Conference, Daejeon, Korea, July 2, 2013.
“An Introduction to Partial Data EIT with CGOs”, Technische Universitat Graz, Graz, Austria, June 18, 2013.
“Reconstructing conductivity and permittivity on chest shaped domains in 2D EIT with nonlinear direct Dbar methods”, XV International Conference on Electrical BioImpedance (ICEBI) and the XIV Conference on Electrical Impedance Tomography 2013 (EIT), Heilbad Heiligenstadt, Germany, April 23, 2013.
“Dbar Methods in Direct and Inverse Problems”, Applied Mathematics & Inverse Problems Joint Seminar, Colorado State University, Fort Collins, Colorado, USA, April 11, 2013.
“A direct, nonlinear reconstruction algorithm for the 2D EIT problem using a partial data DN map”, Conference on Inverse Problems and Applications, Linkoping University, Linkoping, Sweden, April 5, 2013.
“A Numerical Move Towards Nonlinear Inversion from Partial EIT Data in 2D”, Institut MittagLeffler, Djursholm, Sweden, March 25, 2013.
“Direct Dbar reconstructions of complex admittivities on a chestshaped domain in 2D EIT”, Inverse Days 2012, University of Jyvaskyla, Jyvaskyla, Finland, December 18, 2012.
“Electrical Impedance Tomography”, SalWe: Mind and Body Program Seminar, GE Healthcare, Helsinki, Finland, November 7, 2012.
“A Direct Dbar Method for the Reconstruction of Complex Admittivities from EIT Data on NonCircular Domains”, Inverse Problems Seminar, University of Helsinki, Helsinki, Finland, August 20, 2012.
“A Direct Dbar Method for the Reconstruction of Complex Admittivities from EIT Data”, SIAM Conference on Imaging Science (IS12), Philadelphia, Pennsylvania, USA, May 22, 2012.
“Implementation of a Direct Dbar Reconstruction Algorithm for Recovering a Complex Admittivity Distribution from Electrical Impedance Tomography Data”, Joint Mathematics Meeting, Boston, Massachusetts, USA, January 8, 2012.
”A Direct Nonlinear Dbar Reconstruction Algorithm for Complex Admittivities in the 2D EIT Problem”, FinnishJapaneseKorean Workshop on Inverse Problems, Helsinki, Finland, December 14, 2012.
“Oh the Things You Can Do and the Places You’ll See With a Mathematics Degree From SMC!”, Saint Michael’s College, Colchester, Vermont, USA, November 28, 2011.
“A Direct Dbar Reconstruction Method for Complex Admittivities in 2D Electrical Impedance Tomography”, Inverse Problems Seminar, Department of Mathematics, Colorado State University, Fort Collins, Colorado, USA, November 10, 2011.
“Simulation of Voltages on Electrodes for the 2D EIT forward admittivity problem by the Continuum and Complete Electrode Models”, Inverse Problems Seminar, Department of Mathematics, Colorado State University, Fort Collins, Colorado, USA, April 16, 2009.
“Unit Rectangle Visibility Graphs (URVGs)”, NASA Goddard Space Flight Station, Greenbelt, Maryland, USA, July, 2007.
“A Sampler of Wave Motion”, Hudson River Undergraduate Mathematics Conference XIV, Siena College Loudonville, New York, USA, April 21, 2007.
“Unit Rectangle Visibility Graphs (URVGs)”, Hudson River Undergraduate Mathematics Conference XIV, Siena College Loudonville, New York, USA, April 21, 2007.
“HIV Modeling”, Hudson River Undergraduate Mathematics Conference XIII, Westfield State College, Westfield, Massachusetts, USA, April 8, 2006.
"Improving Image Quality for Practical Electrical Impedance Tomography Imaging with Direct Dbar Methods", Mathematics, Statistics, and Computer Science Colloquium, Marquette University, Milwaukee, WI, USA, March 9, 2017.
“Improving image quality for complex Electrical Impedance Imaging: Incorporating a priori in formation into a direct nonlinear Dbar method”, BCAM Scientific Seminar, Basque Center for Applied Mathematics, Bilbao, Spain, June 23, 2016.
“A Nonlinear Reconstruction Method with A Priori Data for EIT”, 16th International Conference on Electrical BioImpedance / 17th Conference on Electrical Impedance Tomography, Stockholm, Sweden, June 22, 2016.
“Incorporating a Spatial Prior into Nonlinear DBar Eit Imaging for Complex Admittivities”, SIAM Conference on Imaging Science 2016 (IS16), Albuquerque, New Mexico, USA, May 25, 2016.
“Improving images for Electrical Impedance Imaging with a spatial prior”, Applied and Computational Mathematics Seminar, University of WisconsinMilwaukee, Milwaukee, Wisconsin, USA, February 11, 2016.
“Direct Dbar Reconstructions for Experimental EIT Data with Boundary Shape Determination”, Applied Inverse Problems conference (AIPC) 2015, University of Helsinki, Helsinki, Finland, May 29, 2015.
“Pulmonary imaging using Electrical Impedance Tomography with a Direct Dbar Admittivity Method”, Joint Mathematics Meeting 2015: Special Session on Inverse Problems, San Antonio, Texas, January 11, 2015.
“A Novel DataDriven Dbar Reconstruction Algorithm for Experimental 2D Electrical Impedance Tomography Data”, The 7th International Conference Inverse Problems: Modeling and Simulation (IPMS2014), Fethiye, Turkey, May 27, 2014.
“A Novel DataDriven Edge Sharpening Dbar Reconstruction Algorithm for 2D Electrical Impedance Tomography Imaging”, SIAM Imaging Science Conference 2014, Minisymposium: Advances in Electrical Impedance Tomography, Hong Kong, Hong Kong, May 14, 2014.
“A Variety of Dbar Methods in Electrical Impedance Tomography: Not Just for 2D Isotropic Conductivities!”, Shanghai Jiao Tong University, Shanghai, China, May 9, 2014.
“Alternative uses for Dbar Methods in Electrical Impedance Tomography”, Inverse Problems Seminar, University College London, London, England, UK, April 23, 2014.
“A DataDriven Edge Sharpening Dbar Reconstruction Algorithm for 2D EIT Imaging”, Inverse Problems Seminar, Colorado State University, Fort Collins, CO USA, February 20, 2014.
“A Direct Dbar Reconstruction Method for 2D Anisotropic Electrical Impedance Tomography”, Inverse Days 2013, Inari, Finland, December 12, 2013.
“Direct Dbar Methods for 2D Electrical Impedance Tomography”, Danmarks Tekniske Universitet, Copenhagen, Denmark, October 30, 2013.
“Computational Results for the Semiclassical Limit of the Defocusing DSII Equation”, Exceptional Circle Helsinki Workshop, University of Helsinki, Helsinki, Finland, August 13, 2013.
“NonIterative Dbar Reconstructions of 2D Conductivities and Permittivities from Experimental EIT Data”, Minisymposium: Inverse problems with experimental data, Applied Inverse Problems Conference, Daejeon, Korea, July 2, 2013.
“An Introduction to Partial Data EIT with CGOs”, Technische Universitat Graz, Graz, Austria, June 18, 2013.
“Reconstructing conductivity and permittivity on chest shaped domains in 2D EIT with nonlinear direct Dbar methods”, XV International Conference on Electrical BioImpedance (ICEBI) and the XIV Conference on Electrical Impedance Tomography 2013 (EIT), Heilbad Heiligenstadt, Germany, April 23, 2013.
“Dbar Methods in Direct and Inverse Problems”, Applied Mathematics & Inverse Problems Joint Seminar, Colorado State University, Fort Collins, Colorado, USA, April 11, 2013.
“A direct, nonlinear reconstruction algorithm for the 2D EIT problem using a partial data DN map”, Conference on Inverse Problems and Applications, Linkoping University, Linkoping, Sweden, April 5, 2013.
“A Numerical Move Towards Nonlinear Inversion from Partial EIT Data in 2D”, Institut MittagLeffler, Djursholm, Sweden, March 25, 2013.
“Direct Dbar reconstructions of complex admittivities on a chestshaped domain in 2D EIT”, Inverse Days 2012, University of Jyvaskyla, Jyvaskyla, Finland, December 18, 2012.
“Electrical Impedance Tomography”, SalWe: Mind and Body Program Seminar, GE Healthcare, Helsinki, Finland, November 7, 2012.
“A Direct Dbar Method for the Reconstruction of Complex Admittivities from EIT Data on NonCircular Domains”, Inverse Problems Seminar, University of Helsinki, Helsinki, Finland, August 20, 2012.
“A Direct Dbar Method for the Reconstruction of Complex Admittivities from EIT Data”, SIAM Conference on Imaging Science (IS12), Philadelphia, Pennsylvania, USA, May 22, 2012.
“Implementation of a Direct Dbar Reconstruction Algorithm for Recovering a Complex Admittivity Distribution from Electrical Impedance Tomography Data”, Joint Mathematics Meeting, Boston, Massachusetts, USA, January 8, 2012.
”A Direct Nonlinear Dbar Reconstruction Algorithm for Complex Admittivities in the 2D EIT Problem”, FinnishJapaneseKorean Workshop on Inverse Problems, Helsinki, Finland, December 14, 2012.
“Oh the Things You Can Do and the Places You’ll See With a Mathematics Degree From SMC!”, Saint Michael’s College, Colchester, Vermont, USA, November 28, 2011.
“A Direct Dbar Reconstruction Method for Complex Admittivities in 2D Electrical Impedance Tomography”, Inverse Problems Seminar, Department of Mathematics, Colorado State University, Fort Collins, Colorado, USA, November 10, 2011.
“Simulation of Voltages on Electrodes for the 2D EIT forward admittivity problem by the Continuum and Complete Electrode Models”, Inverse Problems Seminar, Department of Mathematics, Colorado State University, Fort Collins, Colorado, USA, April 16, 2009.
“Unit Rectangle Visibility Graphs (URVGs)”, NASA Goddard Space Flight Station, Greenbelt, Maryland, USA, July, 2007.
“A Sampler of Wave Motion”, Hudson River Undergraduate Mathematics Conference XIV, Siena College Loudonville, New York, USA, April 21, 2007.
“Unit Rectangle Visibility Graphs (URVGs)”, Hudson River Undergraduate Mathematics Conference XIV, Siena College Loudonville, New York, USA, April 21, 2007.
“HIV Modeling”, Hudson River Undergraduate Mathematics Conference XIII, Westfield State College, Westfield, Massachusetts, USA, April 8, 2006.