We are looking to recruit talented Ph.D. students with research interests in mathematical signal processing, data science, sensing systems, quantum information,
and machine learning. Financial support may be available via research assistantships and/or departmental teaching assistantships.
Prospective students are encouraged to email Prof. Wakin with the subject line "Wakin group".
Signal and data processing using sparse, low-rank, and manifold-based models
Sensing, compression, inference, and reconstruction
Inverse problems and compressive sensing
Convex and non-convex optimization for signal processing and machine learning
Approximation theory and computational harmonic analysis
Research Group
Current students in my group:
Daniel Rosen, Ph.D. student (co-advising with Gongguo Tang)
Patipan Saengduean, Ph.D. student (co-advising with Roel Snieder)
Anna Titova, Ph.D. student (co-advising with Ali Tura)
Marc Valdez, Ph.D. student (co-advising with NIST)
Patrick Barringer, M.S. student
Additional collaborations and informal co-advising
Alumni:
Shuang Li, Ph.D. 2020 (co-advised with Gongguo Tang), now Hedrick Assistant Adjunct Professor, Department of Mathematics, UCLA (thesis)
Xinshuo Yang, Postdoc 2018-19 (co-supervised with Gongguo Tang), now Postdoc at Princeton, formerly Postdoc at National Renewable Energy Laboratory
Jonathan Helland, M.S. 2019, now Associate Machine Learning Researcher at Software Engineering Institute, Carnegie Mellon University
Dehui Yang, Ph.D. 2018, now Applied Scientist at Uber, formerly Data Scientist at Root Insurance Co.
Zhihui Zhu, Ph.D. 2017, now Assistant Professor of Computer Science and Engineering at Ohio State, formerly Assistant Professor ECE at the University of Denver, formerly Postdoc at Johns Hopkins University (thesis)
Armin Eftekhari, Ph.D. 2015, now Assistant Professor at Umea Math in Sweden, formerly Research Fellow at the Alan Turing Institute (thesis)
Chia Wei Lim, Ph.D. 2015, now at DSO National Laboratories Singapore
Jae Young Park, Ph.D. 2013, University of Michigan (co-advised with Anna Gilbert), now Video Processing Architect at Apple
Alejandro Weinstein, Ph.D. 2013, now Professor, Biomedical Engineering, Universidad de Valparaiso, Chile (thesis)
Borhan Sanandaji, Ph.D. 2012 (co-advised with Tyrone Vincent), now Data Scientist II at Uber, formerly Postdoctoral Scholar, UC Berkeley
Michael Coco, M.S. 2012 (co-advised with Lawrence Wiencke), now Staff Engineer at Booz Allen Hamilton
Overview
Effective techniques for signal and data processing often rely on some sort of model that characterizes the expected behavior of the signals/data. In many
cases, the model conveys a notion of constrained structure or conciseness: signals may be bandlimited or sparse in some transform domain, data sets may be organized into a
low-rank matrix, and so on.
Our research group focuses on developing
concise mathematical models for signals and data sets that capture the intrinsic structure in as few degrees of freedom as possible
optimization algorithms for signal and data processing that exploit concise models to sense and compress as efficiently as possible, learn models and infer parameters as
accurately as possible, and reconstruct signals/data from partial information
theory to characterize the performance of these models and algorithms in terms of approximation and compression performance, sample complexity, and so on
Some of our work has focused on the topic area of Compressive Sensing, where sparse models are used to reconstruct signals from small numbers of random linear measurements.
More recently, however, many of the same core ideas (low-complexity models and optimization algorithms that exploit these models) have demonstrated their potential in a broad
variety of new applications: medical imaging, radar imaging, super-resolution, dynamical systems analysis, low-rank matrix completion, machine learning, and so on. Our work
aims to expand the relevance and understanding of low-complexity models and algorithms in these and other contexts.
Topic Areas and Selected Publications
A list of selected publications is below. A complete list of publications is available here.
M.B. Wakin, Concise Signal Models, Connexions modules endorsed by the IEEE Signal Processing Society.
Compressive Measurement Systems & Hardware
M. Wakin, S. Becker, E. Nakamura, M. Grant, E. Sovero, D. Ching, J. Yoo, J. Romberg, A. Emami-Neyestanak, and E. Candès, A Non-Uniform Sampler for Wideband Spectrally-Sparse Environments, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, vol. 2, no. 3, pp. 516-529, September 2012. (authors' copy)
M. B. Wakin, J. N. Laska, M. F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, An Architecture for Compressive Imaging, in IEEE 2006 International Conference on Image Processing -- ICIP 2006, Atlanta, GA, Oct. 2006.
M. J. Rubin, M. B. Wakin, and T. Camp, Lossy Compression for Wireless Seismic Data Acquisition, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing (JSTARS), vol. 9, no. 1, pp. 236-252, January 2016.
R. G. Baraniuk and M. B. Wakin, Random Projections of Smooth Manifolds, Foundations of Computational Mathematics, vol. 9, no. 1, pp. 51-77, February 2009.
C. Hegde, M. Wakin, and R. Baraniuk, Random Projections for Manifold Learning, in Neural Information Processing Systems -- NIPS, Vancouver, Canada, December 2007.
D. Baron, M. F. Duarte, M. B. Wakin, S. Sarvotham, and R. G. Baraniuk, Distributed Compressive Sensing, Arxiv preprint arXiv:0901.3403, 2009.
Signal Inference from Compressive Measurements
M. A. Davenport, P. T. Boufounos, M. B. Wakin, and R. G. Baraniuk, Signal processing with compressive measurements, IEEE Journal of Selected Topics in Signal Processing, vol. 4, no. 2, pp. 445-460, April 2010.
B.M. Sanandaji, T.L. Vincent, M.B. Wakin, R. Toth, and K. Poolla, Compressive System Identification of LTI and LTV ARX Models, IEEE 2011 Conference on Decision and Control and European Control Conference -- CDC-ECC, Orlando, Florida, December 2011.
S. Karnik, Z. Zhu, M. B. Wakin, J. Romberg, and M. A. Davenport, The Fast Slepian Transform, Applied and Computational Harmonic Analysis, vol. 46, no. 3, pp. 624-652, May 2019. (authors' copy)
