Research

Research Experience
Research experience is in the application of statistical modeling and inference to problems in computational imaging and signal analysis. Conducted pioneering work in the area of multi-frame blind deconvolution with physical system-constraints. Recent work has included: system design and analysis for computational sensing and imaging; image restoration and synthesis with system uncertainties; active imaging with sparse arrays; multispectral mine detection; and image recovery from intensity measurements. Work in these areas has been supported by the Defense Advanced Research Projects Agency, the Army Research Laboratory, the Space Telescope Science Institute, the Air Force Phillips Laboratory, the Army Night Vision Laboratory, the Maui High Performance Computing Center, the Air Force Office of Scientific Research, the State of Michigan, the Environmental Research Institute of Michigan, and by the National Science Foundation through a Faculty Early Career Development Award.

Publications
“Optimal sharpness function for SAR autofocus,” T.J. Schulz, accepted for publication in IEEE
Signal Processing Letters, 2006.

“Characterizing static aberrations in liquid crystal spatial light modulators using phase retrieval,”
N. Hart, M.C. Roggemann, A. Sergeyev, and T.J. Schulz, submitted to Optical Engineering, 2006.

“Distance-based and neural net-based approaches for classifying satellites using spectral measurements,”
M.-A. Cauquy and M.C. Roggemann and T.J. Schulz, Optical Engineering, 45(3), 2006.

“Optimal beams for propagation through random media”, T.J. Schulz, Optics Letters, vol. 30, no. 10, pp. 1093-1095, 2005.

“Multi-frame Image Restoration”, T.J. Schulz, The Image and Video Processing Handbook,
pp. 175-190, 2005.

“Signal recovery from auto- and cross-correlation data”, T.J. Schulz and D.G. Voelz, J. Opt. Soc.
Am. A, vol. 22, issue 4, pp. 616-624, 2004.

“Iterative transform algorithm for the computation of optimal beams”, T.J. Schulz, J. Opt. Soc.
Am. A, vol. 21, issue 10, pp. 1970-1974, 2004.

“Experimental estimation of the spatial statistics of turbulence-induced index of refraction fluctuations
in the upper atmosphere”, J.T. Beyer, M.C. Roggemann, L.J. Otten, T.J. Schulz, T.C. Havens, W.W. Brown, Applied Optics, vol. 42, issue 6, pp. 908-921, 2003.

“Measurement and data-processing approach for detecting anisotropic spatial statistics of the
turbulence-induced index of refraction fluctuations in the upper atmosphere”, T.C. Havens,
M.C. Roggemann, T.J. Schulz, W.W. Brown, J.T. Beyer, and L.J. Otten, Applied Optics, vol. 41,
no. 15, pp. 2800-2808, 2002.

“Measurement and data-processing approach for estimating the spatial statistics of turbulenceinduced
index of refraction fluctuations in the upper atmosphere”, W.W. Brown, M.C. Roggemann,
T.J. Schulz, T.C. Havens, J.T. Beyer, and L.J. Otten, Applied Optics, vol. 40, no. 12, pp.. 1863-
1871, 2001.

“Joint processing of Hartmann sensor and conventional image measurements to estimate large
aberrations: theory and experimental results”, M.C. Roggemann, T.J. Schulz, C.W. Ngai, and
J.T. Kraft, Applied Optics, vol. 38, no. 11, pp. 2249-2255, 1999.

“Maximum Likelihood Imaging”, T.J. Schulz, Encyclopedia of Electrical and Electronics Engineering,
pp. 438-448, 1999.

“Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor
measurements”, M. C. Roggemann and T. J. Schulz, Applied Optics, vol. 37, no. 20, pp. 4321-
4329, 1998.

“Performance bounds for high-light-level amplitude and intensity interferometry”, T. J. Schulz
and N. K. Gupta, Journal of the Optical Society of America A, vol. 15, no. 6, pp. 1619-1625,
1998.

“Penalized maximum-likelihood estimation of covariance matrices with linear structure”, T.J.
Schulz, IEEE Transactions on Signal Processing, vol. 45, no. 12, pp. 3027-3038, 1997.

“Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope”, T.J.
Schulz, B.E. Stribling, and J.J. Miller, Optics Express, vol. 1, no. 11, pp. 355-362, 1997.

“Statistical analysis for coherent optical-imaging systems with registration errors,” T.T.H. Simarmata
and T.J. Schulz, Journal of the Optical Society of America A, vol. 14, no. 7, pp. 1439-1447,
1997.

“Estimation of polarization parameters in radar meteorology,” T.J. Schulz and A.B. Kostinski,
IEEE Transactions on Geoscience and Remote Sensing, vol. 35, no. 2, pp. 248-255, 1997.

“Estimation of the squared modulus of the mutual intensity from high light-level intensity measurements,”
T.J. Schulz, Journal of the Optical Society of America A, vol. 12, pp. 1331-1337, 1995.

“Multi-frame blind deconvolution of astronomical images,” T.J. Schulz, Journal of the Optical
Society of America A, vol. 10, pp. 1064-1073, 1993.

“Hubble Space Telescope characterized using phase-retrieval algorithms,” J.R. Fienup, J.C. Marron,
T.J. Schulz, and J.H. Seldin, Applied Optics, vol. 32, pp. 1747-1776, 1993.

“Image recovery from correlations,” T.J. Schulz and D.L. Snyder, Journal of the Optical Society
of America A, vol. 9, pp. 1266-1272, 1992.

“Joint estimation of object and aberrations using phase diversity,” R.G. Paxman, T.J. Schulz, and
J.R. Fienup, Journal of the Optical Society of America A, vol. 9, pp. 1072-1085, 1992.

“Deblurring subject to nonnegativity constraints,” D.L. Snyder, T.J. Schulz, and J.A. O’Sullivan,
IEEE Transactions on Signal Processing, vol. 40, pp. 1143-1150, 1992.

“Three dimensional, fine-resolution imaging using laser frequency diversity,” J.C. Marron and T.J.
Schulz, Optics Letters, vol. 17, pp. 285-287, 1992.

“Imaging a randomly moving object from quantum-limited data: applications to image recovery
from second- and third-order autocorrelations,” T.J. Schulz and D.L. Snyder, Journal of the
Optical Society of America A, vol. 8, pp. 801-807, 1991.

“High resolution imaging at low light levels through weak turbulence,” D.L. Snyder and T.J.
Schulz, Journal of the Optical Society of America A, vol. 7, pp. 1251-1265, 1990.

Conference and workshop proceedings
“Bootsrap beacon creation for dynamic wavefront compensation,” A.V. Sergeyev, M.C. Roggemann,
and T.J. Schulz, Proc. SPIE on Advanced Wavefront Control: Methods, Devices, and
Applications IV, 2006.

Performance bounds for the estimation of the degree of polarization from active laser illumination,”
T.J. Schulz, Proc. SPIE on Polarization Science and Remote Sensing II, pp. 189-196,
2005.

“Optimal coherence for beam propagation through random media,” T.J. Schulz and B. Liu, Proc.
SPIE on Free-Space Laser Communications V, pp. 165-172, 2005.

“Eigen-focus beam control for target-in-the-loop,” T.J. Schulz, M.C. Roggemann, and B. Liu,
Proc. SPIE on Target-in-the-Loop: Atmospheric Tracking, Imaging, and Compensation II, pp. 89-
92, 2005.

“Beacon creation and characterization for beam control in strong turbulence,” M.C. Roggemann,
T.J. Schulz, A. Sergeyev, and G. Soehnel, Proc. SPIE on Target-in-the-Loop: Atmospheric
Tracking, Imaging, and Compensation II, pp. 26-33, 2005.

“Prediction of the space-varying point spread function for reconstruction of anisoplanatic adaptive
optics images,” M. Aubailly, M.C. Roggemann, and T.J. Schulz, Astronomical Adaptive Optics
Systems and Applications II, pp. 63-74, 2005.

“Prediction of the off-axis point spread function for large field of view astronomical adaptive optics
images,” M. Aubailly, M.C. Roggemann, and T.J. Schulz, Enabling Photonics Technologies for
Defense, Security, and Aerospace Applications, pp. 262-267, 2005.

“Spectral unmixing to estimate materials on satellite surfaces,” M.A. Cauquy, M.C. Roggemann,
and T.J. Schulz, Proc. of the 36th Southeastern Symposium on System Theory, pp. 11-15, 2004.

“Approaches for processing spectral measurements of reflected sunlight for space situational awareness”,
M.A. Cauquy, M.C. Roggemann, and T.J. Schulz, Proc. SPIE on Signal and Data Processing
of Small Targets, vol. 5428, pp. 48-57, 2004.

“Compensation of laser beam projection through turbulence in multimirror adaptive optics system
with phase retrieval method”, Y. Zhang, M.C. Roggemann, T.J. Schulz, and R. Kizito, Proc. SPIE
on Free-Space Laser Communication and Active Laser Illumination III, vol. 5160, pp. 98-106, 2004.

“Image sharpness metric-based deformable mirror control for beam projection systems operating
in strong scintillation”, R. Kizito, M.C. Roggemann, T.J. Schulz, and Y. Zhang, Proc. SPIE on
Free-Space Laser Communication and Active Laser Illumination III, vol. 5160, pp. 406-416, 2004.

“Sensor expansion through integration of microscanning and superresolution algorithms”,
R.W. Reynolds, D. Talcott, M.C. Roggemann, J.W. Hilgers, and T.J. Schulz, Proc. SPIE on
Passive Millimeter-Wave Imaging, vol. 4373, pp. 117-131, 2001.

“Cramer-Rao bounds for estimation of turbulence-induced wavefront aberrations”, T.J. Schulz,
W. Sun, and M.C. Roggemann, Proc. SPIE on Propagation and Imaging through the Atmosphere
III, vol. 3763, pp. 23-28, 1999.

“Experimental results of joint processing of Hartmann sensor and conventional image measurements
to estimate large aberrations”, M.C. Roggemann, T.J. Schulz, C.W. Ngai, and J.T. Kraft,
Proc. SPIE on Digital Image Recovery and Synthesis IV, vol. 3815, pp. 208-216, 1999.

“Joint processing of image plane and wave front sensor information to measure large aberrations
in optical systems”, M.C. Roggemann, T.J. Schulz, B.M. Welsh, C.W. Ngai, and J.T. Kraft, Proc.
SPIE on Novel Optical Systems and Large Aperture Imaging, vol. 3430, pp. 272-281, 1998.

“Comparison of image reconstruction algorithms using adaptive optics instrumentation”,
D.W. Tyler, S.D. Ford, B.R. Hunt, R.G. Paxman, M.C. Roggemann, J.C. Rountree, T.J. Schulz,
K.J. Schulze, J.H. Seldin, D.G. Sheppard, B.E. Stribling, W.C. van Kampen, B.M. Welch, Proc.
SPIE on Adaptive Optical System Technologies, vol. 3353, pp. 160-171, 1998.

“Superresolved imaging sensors with field-of-view preservation”, W.R. Reynolds, J.W. Hilgers,
T.J. Schulz, and S.A. Amphay, Proc. SPIE on Passive Millimeter-Wave Imaging Techniques,
vol. 3378, pp. 134-147, 1998.

“A fast algorithm for maximum-likelihood imaging with coherent speckle measurements”, T.J.
Schulz, Proc. of the 1997 IEEE International Conference on Image Processing, Santa Barbara,
CA, pp. 679-682, October 1997.

“Nonlinear models and methods for space-object imaging through atmospheric turbulence,” (invited
paper), T.J. Schulz, 1997 IEEE Nonlinear Signal and Image Processing Workshop, Mackinac
Island, Michigan, September, 1997.

“Phase-error compensation through multiframe blind deconvolution”, T.J. Schulz, J.J. Miller, and
B.E. Stribling, Proc. of the 1996 IEEE International Conference on Image Processing, Lausanne,
Switzerland, September, 1996.

“Blind deconvolution,” (invited paper), T.J. Schulz, in Signal Recovery and Synthesis V, Vol.
11, 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp.
68-69. (also presented)

“Coherent array imaging with sparse arrays,” T.J. Schulz, Proc. of the 1995 IEEE International
Conference on Image Processing, pp. 133-135, Washington, DC, October, 1995. (also presented)

“Phase-error correction for coherent array imaging systems,” T.J. Schulz, Proc. of the 1994 IEEE
International Conference on Image Processing, pp. 314-318, Austin, Texas, November, 1994.
(also presented)

“Multiframe blind deconvolution with high photon noise,” S. Sandven, D.C. Dayton, T.J. Schulz,
and J.D. Gonglewski, Proc. of the 1994 SPIE Symposium on Astronomical Telescopes & Instrumentation
for the 21st Century, Kona, Hawaii, March, 1994.

“Simultaneous phase retrieval and deblurring for the Hubble Space Telescope,” T.J. Schulz and
S.C. Cain, Proc. of the 1993 Image Restoration Workshop for Hubble Space Telescope Imagery,
The Restoration of HST Images and Spectra II, pp. 206-211, Space Telescope Science Institute,
Baltimore, MD, Nov. 1993. (also presented)

“Multispectral evaluation of vehicle signatures,” T.J. Schulz, Proc. of the Fourth Annual Ground
Target Modeling & Validation Conference, pp. 72-78, Houghton, MI, August, 1993. (also presented)

“Low order adaptive optics with blind deconvolution post processing,” D. Dayton, S. Sandven,
T.J. Schulz, and J.G. Gonglewski, Proc. of the ICO - 16 Satellite Conference on Active and
Adaptive Optics, Garching, Germany, August, 1993.

“Estimation-theoretic approach to the deconvolution of atmospherically degraded images with
wavefront sensor measurements,” T.J. Schulz, in Digital Image Recovery and Synthesis II, Paul
S. Idell, Editor, Proc. SPIE 2029, pp. 311-320 (1993). (also presented)

“Imaging using fourth-order correlation of coherent fields,” J.D. Gonglewski, D.G. Voelz, D.C.
Dayton, and T.J. Schulz, in Digital Image Recovery and Synthesis II, Paul S. Idell, Editor, Proc.
SPIE 2029, pp. 185-191 (1993).

" Image recovery from a sequence of atmospherically degraded images with unknown point-spread
functions,” T.J. Schulz, in Signal Recovery and Synthesis IV, Vol. 11, 1995 OSA Technical Digest
Series (Optical Society of America, Washington D.C., 1992), pp. 55-57. (also presented)

“Phase-diverse speckle interferometry,” R.G. Paxman, T.J. Schulz, and J.R. Fienup, in Signal
Recovery and Synthesis IV, Vol. 11, 1995 OSA Technical Digest Series (Optical Society of
America, Washington D.C., 1992), pp. 5-7.

“Image recovery from photon differences,” (invited paper), T.J. Schulz and D.L. Snyder, Proc.
of the Twenty-fifth Annual Conference on Information Sciences and Systems, The Johns Hopkins
University, Baltimore, MD, pp. 649-653, March, 1991. (also presented)

“Heterodyne array phasing by digital shearing laser interferometry,” J.R. Fienup, J.N. Cederquist,
J.C. Marron, T.J. Schulz, and J.H. Seldin, Proc. of the Infrared Information Symposium (IRIS)
Specialty Group on Active Systems, Ann Arbor, MI, October, 1990.

“A new method for the recovery of images from their triple-correlation functions,” A. Hammoud,
T.J. Schulz, and D.L. Snyder, Proc. of the Twenty-eighth Annual Allerton Conf. on Communication,
Control, and Computing, Univ. of Illinois, September, 1990.

“A new method for the recovery of objects from their Fourier magnitude,” T.J. Schulz and D.L.
Snyder, Proc. of the SPIE Conference on Digital Image Synthesis and Inverse Optics, San Diego,
CA, July, 1990. (also presented)

“Imaging a randomly moving object,” D.L. Snyder and T.J. Schulz, Proc. of the Twenty-fourth
Annual Conference on Information Sciences and Systems, Princeton University, Princeton, New
Jersey, March, 1990.

“Density estimation in correlated noise,” T.J. Schulz and D.L. Snyder, Proc. of the Twentyseventh
Annual Allerton Conf. on Communication, Control, and Computing, Univ. of Illinois,
September, 1989. (also presented)

“High resolution imaging at low light-levels through weak turbulence,” D.L. Snyder and T.J.
Schulz, Quantum-Limited Imaging and Information Processing, 1989 Technical Digest Series, vol.
13, Optical Society of America, Washington, D.C., 1989.

“A parametric form for sieve-constrained maximum-likelihood density estimation from noisy data,”
T.J. Schulz and D.L. Snyder, Proc. of the Twenty-sixth Annual Allerton Conf. on Communication,
Control, and Computing, Univ. of Illinois, September, 1988. (also presented)

“Constrained probability-density estimation from noisy data,” D.L. Snyder, M.I. Miller, and T.J.
Schulz, Proc. of the Twenty-second Annual Conference on Information Sciences and Systems,
Princeton University, Princeton, New Jersey, March, 1988.