John Bardsley's Publications Page
Scientific Papers in Progress
"A Computational Framework for Total Variation-Regularized Positron Emission Tomography", submitted PDF.
"Structured Linear Algebra Problems in Adaptive Optics Imaging", with Sarah Knepper and Jim Nagy, submitted PDF
"A Nonnegatively Constrained Iterative Method for Positron Emission Tomography", submitted PDF.
"Hierarchical Regularization for Edge-Preserving Reconstruction of PET Images", submitted with Daniela Calvetti and Erkki Somersalo, PDF.
Refereed Journal Articles
Poisson Inverse Problems, Theory: consult #4 first, as it corrects various small errors and omissions found in #1-3, and provides a proof that the approaches of #1-3 define regularization schemes.
4. "A Theoretical Framework for the Regularization of Poisson Likelihood Estimation Problems," accepted in Inverse Problems in Imaging, PDF.
3. "An Analysis of Regularization by Diffusion for Ill-Posed Poisson Likelihood Estimation," with N'djekornom Laobeul, Inverse Problems in Science and Engineering, Volume 17, Issue 4, June 2009 , pages 537 - 550. PDF.
2. "Tikhonov Regularized Poisson Likelihood Estimation: Theoretical Justification and a Computational Method," with N'djekornom Laobeul, Inverse Problems in Science and Engineering, Volume 16, Issue 2 January 2008 , pages 199 - 215 PDF.
1. "Total Variation-Penalized Poisson Likelihood Estimation for Ill-Posed Problems," with Aaron Luttman, Advances in Computational Mathematics, Volume 31, Issue 1, (2009), Page 35-59. PDF.
Poisson Inverse Problems, Computation: computational methods we have found to be efficient, various regularization functions, and regularization parameter selection methods (see MATLAB codes here).
8. "Regularization Parameter Selection Methods for Ill-Posed Poisson Maximum Likelihood Estimation", with John Goldes, Inverse Problems, 25 (2009) 095005, doi: 10.1088/0266-5611/25/9/095005 PDF.
7. "An Iterative Method for Edge-Preserving MAP Estimation when Data-Noise is Poisson," with John Goldes, accepted in SIAM Journal on Scientific Computing PDF.
6. "Stopping Rules for a Nonnegatively Constrained Iterative Method for Ill-Posed Poisson Imaging Problems," BIT Numerical Mathematics, Volume 48, Number 4, December, 2008, pp. 651-664 PDF.
5. "An Efficient Computational Method for Total Variation-Penalized Poisson Likelihood Estimation," Inverse Problems and Imaging, vol. 2, no. 2, 2008, pp. 167 - 185 PDF.
4. "Covariance-Preconditioned Iterative Methods for Nonnegatively Constrained Astronomical Imaging," with Jim Nagy, SIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 4, 2006, pp. 1184-1198, PDF.
3. "Least-Squares methods with Poissonian noise: analysis and
a comparison with the Richardson-Lucy algorithm," with R. Vio and W. Wamsteker,
Astronomy and Astrophysics, 436, 2005, pp. 741-755 PDF.
2. "A Limited Memory, Quasi-Newton Preconditioner for Nonnegatively Constrained
Image Reconstruction," Journal of the Optical
Society of America A, vol. 21, no. 5, 2004, pp. 724-731.
PDF
1. "A Nonnnegatively Constrained Convex Programming Method for Image
Reconstruction," with C.R. Vogel, SIAM Journal on
Scientific Computing, vol. 25, no. 4, 2004, pp. 1326-1343.
PDF.
Other Refereed Journal Articles: topics include Kalman filtering, adaptive optics, image reconstruction, image segmentation and analysis, and theoretical and computational electromagnetics (see MATLAB codes here).
15. "Large-Scale Kalman Filtering Using the Limited Memory BFGS Method", with H. Auvinen, H. Haario, and T. Kauranne, accepted in Electronic Transactions in Numerical Analysis, PDF.
14. "A Fixed Point Formulation of the k-Means Algorithm and a Connection to Mumford-Shaw", with Aaron Luttman, accepted in Applied Math E-Notes, UM Tech. Report \#36, 2008 PDF.
13. "The variational Kalman filter and an efficient implementation using limited memory BFGS", with H. Auvinen, H. Haario, and T. Kauranne, accepted in International Journal for Numerical Methods in Fluids PDF
12. "The Stabilizing Properties of Nonnegativity Constraints in Least-Squares Image Reconstruction," with Jorma Merikoski and Roberto Vio, International Journal of Pure and Applied Mathematics, vol. 43, no. 1, 2008, pp. 95-109 PDF.
11. "An Efficient Phase and Object Estimation Scheme for Phase-Diversity Time Series Data," IEEE Transactions on Image Processing, volume 17, issue 1, 2008, p. 9-15 PDF.
10. "An Analysis of Methods for Wavefront Reconstruction From Gradient Measurements in Adaptive Optics," International Journal of Pure and Applied Mathematics, Vol. 42, No. 1, 2008, pp. 71-81 PDF.
09. "Wavefront Reconstruction Methods for Adaptive Optics Systems on Ground-Based Telescopes," SIAM Journal on Matrix Analysis and Application, Volume 30 Issue 1, 2008, pp. 67-83 PDF.
08. "Analysis of Pattern Formation on the Surface of Respiring Leaves," with Aaron Luttman and Emily Stone, Physica D, Vol 232, Issue 2, 2007, pp. 142-155. PDF.
07. "A Variational Approach to Image Segmentation for Botanical Data," with Aaron Luttman, SIAM Journal on Scientific Computing, Vol 29, Issue 4, 2007, pp. 1550-1566.PDF. This paper was featured in Science Magazine's Editors' Choice column. PDF. Erratum in SISC Vol 30, Issue 1, p. 548 PDF.
06. "A Computational Method for the Restoration of Images With an Unknown, Spatially-Varying Blur," with Stuart Jeffries, Jim Nagy and Bob Plemmons, Optics Express, vol. 14, Iss. 5, 2006, pp. 1767-1782, PDF.
05. "Dealing with edge effects in least-squares image deconvolution problems," with R. Vio, M. Donatelli, and W. Wamsteker, Astronomy and Astrophysics, vol. 442, pp. 397-403, 2005. PDF
04. "A Nonnegatively Constrained Trust Region Algorithm for the
Restoration of Images with an Unknown Blur," Electronic Transactions in
Numerical Analysis, vol. 20, 2005, pp. 139-153.
PDF.
03. "Parameter Identification for a Dispersive Dielectric
in 2D Electromagnetics: Forward and Inverse Methodology with Statistical
Considerations," with H. T. Banks, International Journal of Computational
and Numerical Analysis and Applications, vol. 5, No. 1, 2004, pp. 13--49.
PDF.
02. "Wellposedness for Systems Arising in Time Domain Electromagnetics in Dielectrics," with H. T. Banks, International Journal of Pure and Applied Mathematics 46 (2008), no. 1, 1--18.PDF.
01. "Computational Methods for a Large-Scale Inverse Problem Arising in
Atmospheric Optics," with Luc Gilles and C.R. Vogel, Inverse Problems,
18, 2002, pp. 237-252.
PDF.
Non-refereed Conference Proceedings, Technical Reports, and Abandoned Papers.
5. "A Matrix Theoretic Derivation of the Kalman Filter," University of Montana Technical Report #32, 2008, PDF.
4. "Wavefront Estimation for Adaptive Optics Systems on Ground-Based Telescopes," PAMM Volume 7, Issue 1 , Pages 1021701 - 1021702, 2008, Proceedings of the 2007 International Conference of Industrial and Applied Mathematics, PDF.
3. "Blind Iterative Restoration of Images with Spatially-Varying Blur," with Stuart Jeffries, Jim Nagy and Bob Plemmons, 2005 AMOS Technical Conference Proceedings, PDF.
2. "An Inverse Problem in X-Ray Radiography," with V. Korostyshevskiy,
L.C. Parra, S. LaVoie, T.J. Leiterman, J. Reese, B. Song, Technical Report,
Center for Research in Scientific Computation, CRSC-TR01-27, NCSU, 2001.
1. "A Bound-Constrained Levenburg-Marquardt Algorithm for a Class of Parameter Identification
Problems Arising in Electromagnetics," PDF. See MATLAB code here.
Reflections on Research
(6/09) Seven years beyond the PhD: (i) some of the papers I'm writing reference my own work too heavily -- it's time to move on from those topics; (ii) quantity increasingly means less to me and quality more; (iii) the relationships I've built are at least as important as the work that I've done; (iv) my impatience has been both a blessing and a curse; and (v) working with students has been the most challenging, rewarding, and (it seems to me) impactful part of the job.