The SINE Center is an interdisciplinary effort in research and education, bringing together three faculty from Computer Science and three faculty from Electrical
Engineering. Research activities focus on topics related to information collection and processing in signals and networks. Example projects include wireless
sensor networks for geosystems; compressive sensing and optimization in imaging and signal acquisition; incentive mechanisms and enforcement strategies for
efficient spectrum sharing; control, identification, and tracking of dynamical systems; community detection and mobility monitoring via social media; and building
energy monitoring and control using wireless sensor networks. Educational activities include providing professional development opportunities for Colorado high
school teachers and a wide range of STEM outreach activities to K-12 students.
Armin Eftekhari, Ph.D. 2015, now Research Fellow at the Alan Turing Institute, formerly postdoc at Rutgers and ICES Postdoc Fellow at UT Austin (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 at Schlumberger Research
Alejandro Weinstein, Ph.D. 2013, now Associate Professor, Biomedical Engineering, Universidad de Valparaiso, Chile (thesis)
Borhan Sanandaji, Ph.D. 2012 (co-advised with Tyrone Vincent), now Scientific Programmer at RMS, formerly Postdoctoral Scholar, UC Berkeley (thesis)
Michael Coco, M.S. 2012 (co-advised with Lawrence Wiencke), now Staff Engineer at Booz Allen Hamilton
Motivation
Effective techniques for processing and understanding data and information often rely on some sort of model that characterizes the expected behavior of the information. In many cases, the model conveys a notion of constrained structure or conciseness to the information; one may believe, for example, that a length-N data vector (or signal) has few degrees of freedom relative to its size N. Examples include bandlimited signals, images containing low-dimensional geometric features, or collections of signals observed from multiple viewpoints in a camera or sensor network.
The notion of conciseness is a very powerful assumption, and it suggests the potential for developing highly accurate and efficient data processing algorithms that capture and exploit the inherent structure of the model. In some cases, for example, the signals of interest can be expressed as sparse linear combinations of elements from some dictionary---the sparsity of the representation directly reflects the conciseness of the model and permits efficient algorithms for signal processing. Sparsity also forms the core of the emerging theory of Compressive Sensing, which states that a sparse signal can be recovered from a small number of random linear measurements.
In other cases, however, sparse representations may not suffice to truly capture the underlying structure of a signal. Instead, the conciseness of the signal model may impose a low-dimensional geometric (often manifold-like) structure to the signal class as a subset of the high-dimensional ambient signal space. To date, the importance and utility of manifolds for signal processing has been acknowledged largely through a research effort into learning manifold structure from a collection of data points. While these methods have proved effective for certain tasks (such as classification and recognition), they also tend to be quite generic and fail to consider the geometric nuances of specific signal classes.
Projects and Contributions
The purpose of my research is to develop new methods and understanding for signal and data processing based on low-dimensional signal models, with a particular focus on the role of geometry. Below is a list of key topics (with links to selected publications):
Compressive Sensing and Randomized Dimensionality Reduction
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.
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.
J. A. Tropp, M. B. Wakin, M. F. Duarte, D. Baron, and R. G. Baraniuk, Random Filters for Compressive Sampling and Reconstruction, in IEEE 2006 International Conference on Acoustics, Speech, and Signal Processing -- ICASSP 2006, Toulouse, France, May 2006.
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.
Multi-signal, Multi-image, and Video Compressive Sensing
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.
M. F. Duarte, M. A. Davenport, M. B. Wakin, and R. G. Baraniuk, Sparse Signal Detection from Incoherent Projections, in IEEE 2006 International Conference on Acoustics, Speech, and Signal Processing -- ICASSP 2006, Toulouse, France, May 2006.
Dynamical Systems; Compressive System Identification
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.
