Abstract:
Many material and biological samples in scientific imaging are characterized by nonlocal repeating structures. These are studied using scanning electron microscopy and el...Show MoreMetadata
Abstract:
Many material and biological samples in scientific imaging are characterized by nonlocal repeating structures. These are studied using scanning electron microscopy and electron tomography. Sparse sampling of individual pixels in a two-dimensional image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography experiment, can enable high speed data acquisition and minimize sample damage caused by the electron beam. In this paper, we present an algorithm for electron tomographic reconstruction and sparse image interpolation that exploits the nonlocal redundancy in images. We adapt a framework, termed plug-and-play priors, to solve these imaging problems in a regularized inversion setting. The power of the plug-and-play approach is that it allows a wide array of modern denoising algorithms to be used as a “prior model” for tomography and image interpolation. We also present sufficient mathematical conditions that ensure convergence of the plug-and-play approach, and we use these insights to design a new nonlocal means denoising algorithm. Finally, we demonstrate that the algorithm produces higher quality reconstructions on both simulated and real electron microscope data, along with improved convergence properties compared to other methods.
Published in: IEEE Transactions on Computational Imaging ( Volume: 2, Issue: 4, December 2016)
Funding Agency:
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
Suhas Sreehari (S’15) received the B.E. degree in
telecommunications engineering from Businayana Mukundadas Sreenivasaiah College of Engineering, Visveswaraiah
Technological University, Belgaum, India, in 2010, and the M.A.Sc. degree in electrical and computer engineering from
the University of Windsor, Windsor, ON, Canada, in 2012. He is currently working toward the Ph.D. degree in the School
of Electrical and Comput...Show More
Suhas Sreehari (S’15) received the B.E. degree in
telecommunications engineering from Businayana Mukundadas Sreenivasaiah College of Engineering, Visveswaraiah
Technological University, Belgaum, India, in 2010, and the M.A.Sc. degree in electrical and computer engineering from
the University of Windsor, Windsor, ON, Canada, in 2012. He is currently working toward the Ph.D. degree in the School
of Electrical and Comput...View more
Lawrence Berkeley National Laboratory, Berkeley, CA, USA
S. V. Venkatakrishnan received the B.Tech. degree in
electronics and communication engineering from the National Institute of Technology Tiruchirappalli, Tiruchirappalli,
India, in 2007, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Purdue University, West
Lafayette, IN, USA, in 2009 and 2014, respectively. He is currently a Postdoctoral Fellow at the Advanced Light
Source, Lawrence B...Show More
S. V. Venkatakrishnan received the B.Tech. degree in
electronics and communication engineering from the National Institute of Technology Tiruchirappalli, Tiruchirappalli,
India, in 2007, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Purdue University, West
Lafayette, IN, USA, in 2009 and 2014, respectively. He is currently a Postdoctoral Fellow at the Advanced Light
Source, Lawrence B...View more
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
Brendt Wohlberg (SM’13) received the B.Sc. (Hons.) degree
in applied mathematics, the M.Sc. degree in applied science, and the Ph.D. degree in electrical engineering from the
University of Cape Town, Cape Town, South Africa, in 1990, 1993, and 1996, respectively. He is currently a Staff
Scientist in the Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA. His research interest
includes signal and...Show More
Brendt Wohlberg (SM’13) received the B.Sc. (Hons.) degree
in applied mathematics, the M.Sc. degree in applied science, and the Ph.D. degree in electrical engineering from the
University of Cape Town, Cape Town, South Africa, in 1990, 1993, and 1996, respectively. He is currently a Staff
Scientist in the Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA. His research interest
includes signal and...View more
Department of Mathematics, Purdue University, West Lafayette, IN, USA
Gregery T. Buzzard received the degrees in violin
performance, computer science, and mathematics from Michigan State University, East Lansing, MI, USA, and the Ph.D.
degree in mathematics from the University of Michigan, Ann Arbor, MI, in 1995. He held postdoctoral positions at
Indiana University and Cornell University before joining the mathematics faculty, in 2002, at the Purdue University,
West Lafayette, IN, USA,...Show More
Gregery T. Buzzard received the degrees in violin
performance, computer science, and mathematics from Michigan State University, East Lansing, MI, USA, and the Ph.D.
degree in mathematics from the University of Michigan, Ann Arbor, MI, in 1995. He held postdoctoral positions at
Indiana University and Cornell University before joining the mathematics faculty, in 2002, at the Purdue University,
West Lafayette, IN, USA,...View more
Air Force Research Laboratory, Dayton, OH, USA
Lawrence F. Drummy received the B.S. degree in physics
from Rensselaer Polytechnic Institute, Troy, NY, USA, in 1998, while developing image processing tools for scanning
tunneling microscopy, and the Ph.D. degree from the Department of Materials Science and Engineering, University of
Michigan, Ann Arbor, MI, USA, in 2003, performing research on flexible electronic materials. He is a Materials
Engineer in the Soft Ma...Show More
Lawrence F. Drummy received the B.S. degree in physics
from Rensselaer Polytechnic Institute, Troy, NY, USA, in 1998, while developing image processing tools for scanning
tunneling microscopy, and the Ph.D. degree from the Department of Materials Science and Engineering, University of
Michigan, Ann Arbor, MI, USA, in 2003, performing research on flexible electronic materials. He is a Materials
Engineer in the Soft Ma...View more
Air Force Research Laboratory, Dayton, OH, USA
Jeffrey P. Simmons (M’96) received the B.S. degree
in metallurgical engineering from New Mexico Institute of Mining and Technology, Socorro, NM, USA, in 1983, the M.S.
degree in metallurgical engineering and materials science, and the Ph.D. degree in materials science and engineering
from Carnegie Mellon University, Pittsburgh, PA, USA, in 1985 and 1992, respectively. He is a Research Scientist in
the Structural Mate...Show More
Jeffrey P. Simmons (M’96) received the B.S. degree
in metallurgical engineering from New Mexico Institute of Mining and Technology, Socorro, NM, USA, in 1983, the M.S.
degree in metallurgical engineering and materials science, and the Ph.D. degree in materials science and engineering
from Carnegie Mellon University, Pittsburgh, PA, USA, in 1985 and 1992, respectively. He is a Research Scientist in
the Structural Mate...View more
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
Charles A. Bouman
(S’86–M’89–SM’97–F’01) received the B.S.E.E. degree from the University of
Pennsylvania, Philadelphia, PA, USA, in 1981, the M.S. degree from the University of California, Berkeley, CA, USA, in
1982, and the Ph.D. degree in electrical engineering from Princeton University, Princeton, NJ, USA, in 1989. From 1982
to 1985, he was a Full Staff Member at the MIT Lincoln Laboratory. In 1989, he joined the...Show More
Charles A. Bouman
(S’86–M’89–SM’97–F’01) received the B.S.E.E. degree from the University of
Pennsylvania, Philadelphia, PA, USA, in 1981, the M.S. degree from the University of California, Berkeley, CA, USA, in
1982, and the Ph.D. degree in electrical engineering from Princeton University, Princeton, NJ, USA, in 1989. From 1982
to 1985, he was a Full Staff Member at the MIT Lincoln Laboratory. In 1989, he joined the...View more
Contents School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
Suhas Sreehari (S’15) received the B.E. degree in
telecommunications engineering from Businayana Mukundadas Sreenivasaiah College of Engineering, Visveswaraiah
Technological University, Belgaum, India, in 2010, and the M.A.Sc. degree in electrical and computer engineering from
the University of Windsor, Windsor, ON, Canada, in 2012. He is currently working toward the Ph.D. degree in the School
of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA. His research interests include
inverse imaging problems, computational imaging, and mathematical modeling.
Suhas Sreehari (S’15) received the B.E. degree in
telecommunications engineering from Businayana Mukundadas Sreenivasaiah College of Engineering, Visveswaraiah
Technological University, Belgaum, India, in 2010, and the M.A.Sc. degree in electrical and computer engineering from
the University of Windsor, Windsor, ON, Canada, in 2012. He is currently working toward the Ph.D. degree in the School
of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA. His research interests include
inverse imaging problems, computational imaging, and mathematical modeling.View more
Lawrence Berkeley National Laboratory, Berkeley, CA, USA
S. V. Venkatakrishnan received the B.Tech. degree in
electronics and communication engineering from the National Institute of Technology Tiruchirappalli, Tiruchirappalli,
India, in 2007, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Purdue University, West
Lafayette, IN, USA, in 2009 and 2014, respectively. He is currently a Postdoctoral Fellow at the Advanced Light
Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. His research interests include statistical
information processing, inverse problems, computational imaging, and machine learning.
S. V. Venkatakrishnan received the B.Tech. degree in
electronics and communication engineering from the National Institute of Technology Tiruchirappalli, Tiruchirappalli,
India, in 2007, and the M.S. and Ph.D. degrees in electrical and computer engineering from the Purdue University, West
Lafayette, IN, USA, in 2009 and 2014, respectively. He is currently a Postdoctoral Fellow at the Advanced Light
Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. His research interests include statistical
information processing, inverse problems, computational imaging, and machine learning.View more
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
Brendt Wohlberg (SM’13) received the B.Sc. (Hons.) degree
in applied mathematics, the M.Sc. degree in applied science, and the Ph.D. degree in electrical engineering from the
University of Cape Town, Cape Town, South Africa, in 1990, 1993, and 1996, respectively. He is currently a Staff
Scientist in the Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA. His research interest
includes signal and image processing inverse problems, with an emphasis on sparse representations and exemplar-based
methods. He was an Associate Editor of the IEEE Transactions on Image Processing from 2010 to 2014, and is
currently the Chair of the Computational Imaging Special Interest Group of the IEEE Signal Processing Society and an
Associate Editor of the IEEE Transactions on Computational Imaging.
Brendt Wohlberg (SM’13) received the B.Sc. (Hons.) degree
in applied mathematics, the M.Sc. degree in applied science, and the Ph.D. degree in electrical engineering from the
University of Cape Town, Cape Town, South Africa, in 1990, 1993, and 1996, respectively. He is currently a Staff
Scientist in the Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA. His research interest
includes signal and image processing inverse problems, with an emphasis on sparse representations and exemplar-based
methods. He was an Associate Editor of the IEEE Transactions on Image Processing from 2010 to 2014, and is
currently the Chair of the Computational Imaging Special Interest Group of the IEEE Signal Processing Society and an
Associate Editor of the IEEE Transactions on Computational Imaging.View more
Department of Mathematics, Purdue University, West Lafayette, IN, USA
Gregery T. Buzzard received the degrees in violin
performance, computer science, and mathematics from Michigan State University, East Lansing, MI, USA, and the Ph.D.
degree in mathematics from the University of Michigan, Ann Arbor, MI, in 1995. He held postdoctoral positions at
Indiana University and Cornell University before joining the mathematics faculty, in 2002, at the Purdue University,
West Lafayette, IN, USA, where he currently serves as the Head of the Department of Mathematics. His research
interests include dynamical systems, experiment design, and uncertainty quantification.
Gregery T. Buzzard received the degrees in violin
performance, computer science, and mathematics from Michigan State University, East Lansing, MI, USA, and the Ph.D.
degree in mathematics from the University of Michigan, Ann Arbor, MI, in 1995. He held postdoctoral positions at
Indiana University and Cornell University before joining the mathematics faculty, in 2002, at the Purdue University,
West Lafayette, IN, USA, where he currently serves as the Head of the Department of Mathematics. His research
interests include dynamical systems, experiment design, and uncertainty quantification.View more
Air Force Research Laboratory, Dayton, OH, USA
Lawrence F. Drummy received the B.S. degree in physics
from Rensselaer Polytechnic Institute, Troy, NY, USA, in 1998, while developing image processing tools for scanning
tunneling microscopy, and the Ph.D. degree from the Department of Materials Science and Engineering, University of
Michigan, Ann Arbor, MI, USA, in 2003, performing research on flexible electronic materials. He is a Materials
Engineer in the Soft Matter Materials Branch, Functional Materials Division, Materials and Manufacturing Directorate,
Air Force Research Laboratory, Dayton, OH, USA. His research interests include tomography and inverse problems, signal
and image processing, high-resolution transmission electron microscopy, nanocomposites, organic–inorganic
interfaces, structural proteins, metamaterials, and organic electronics.
Lawrence F. Drummy received the B.S. degree in physics
from Rensselaer Polytechnic Institute, Troy, NY, USA, in 1998, while developing image processing tools for scanning
tunneling microscopy, and the Ph.D. degree from the Department of Materials Science and Engineering, University of
Michigan, Ann Arbor, MI, USA, in 2003, performing research on flexible electronic materials. He is a Materials
Engineer in the Soft Matter Materials Branch, Functional Materials Division, Materials and Manufacturing Directorate,
Air Force Research Laboratory, Dayton, OH, USA. His research interests include tomography and inverse problems, signal
and image processing, high-resolution transmission electron microscopy, nanocomposites, organic–inorganic
interfaces, structural proteins, metamaterials, and organic electronics.View more
Air Force Research Laboratory, Dayton, OH, USA
Jeffrey P. Simmons (M’96) received the B.S. degree
in metallurgical engineering from New Mexico Institute of Mining and Technology, Socorro, NM, USA, in 1983, the M.S.
degree in metallurgical engineering and materials science, and the Ph.D. degree in materials science and engineering
from Carnegie Mellon University, Pittsburgh, PA, USA, in 1985 and 1992, respectively. He is a Research Scientist in
the Structural Materials Division, Materials and Manufacturing Directorate, Air Force Research Laboratory, Dayton, OH,
USA. He is currently working with developing mathematical algorithms for data analysis of emerging large digital
datasets produced by advances in microscope characterization capabilities.
Jeffrey P. Simmons (M’96) received the B.S. degree
in metallurgical engineering from New Mexico Institute of Mining and Technology, Socorro, NM, USA, in 1983, the M.S.
degree in metallurgical engineering and materials science, and the Ph.D. degree in materials science and engineering
from Carnegie Mellon University, Pittsburgh, PA, USA, in 1985 and 1992, respectively. He is a Research Scientist in
the Structural Materials Division, Materials and Manufacturing Directorate, Air Force Research Laboratory, Dayton, OH,
USA. He is currently working with developing mathematical algorithms for data analysis of emerging large digital
datasets produced by advances in microscope characterization capabilities.View more
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
Charles A. Bouman
(S’86–M’89–SM’97–F’01) received the B.S.E.E. degree from the University of
Pennsylvania, Philadelphia, PA, USA, in 1981, the M.S. degree from the University of California, Berkeley, CA, USA, in
1982, and the Ph.D. degree in electrical engineering from Princeton University, Princeton, NJ, USA, in 1989. From 1982
to 1985, he was a Full Staff Member at the MIT Lincoln Laboratory. In 1989, he joined the faculty of Purdue
University, West Lafayette, IN, USA, where he is currently the Showalter Professor of electrical and computer
engineering and biomedical engineering. His research interests include the use of statistical image models, multiscale
techniques, fast algorithms in applications including tomographic reconstruction, medical imaging, and document
rendering and acquisition. He is a Fellow of the American Institute for Medical and Biological Engineering, a Fellow
of the Society for Imaging Science and Technology, a Fellow of the SPIE Professional Society, and a Fellow of the
National Academy of Inventors.
Charles A. Bouman
(S’86–M’89–SM’97–F’01) received the B.S.E.E. degree from the University of
Pennsylvania, Philadelphia, PA, USA, in 1981, the M.S. degree from the University of California, Berkeley, CA, USA, in
1982, and the Ph.D. degree in electrical engineering from Princeton University, Princeton, NJ, USA, in 1989. From 1982
to 1985, he was a Full Staff Member at the MIT Lincoln Laboratory. In 1989, he joined the faculty of Purdue
University, West Lafayette, IN, USA, where he is currently the Showalter Professor of electrical and computer
engineering and biomedical engineering. His research interests include the use of statistical image models, multiscale
techniques, fast algorithms in applications including tomographic reconstruction, medical imaging, and document
rendering and acquisition. He is a Fellow of the American Institute for Medical and Biological Engineering, a Fellow
of the Society for Imaging Science and Technology, a Fellow of the SPIE Professional Society, and a Fellow of the
National Academy of Inventors.View more
