On this page: Research Interests | Research Group | Motivation | Projects and Contributions | Additional Information & Resources
Signal and image processing using sparse, low-dimensional, and manifold-based signal models
Multiscale geometric analysis for image processing, compression, estimation, and computer vision
Low-rate signal sensing and acquisition; signal recovery from partial information; compressive sensing
Multiple signal processing, compression, acquisition, and recovery; light field imaging; sensor networks
Approximation theory and computational harmonic analysis; wavelets, curvelets, and wedgelets
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 Postdoctoral Scholar, UC Berkeley ( thesis)
Michael Coco, M.S. 2012 (co-advised with Lawrence Wiencke)
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. B. Wakin, Compressive Sensing Fundamentals, in M. Amin (Ed.), , CRC Press, 2014.
Compressive Sensing for Urban Radar E. J. Candès and M. B. Wakin, An introduction to compressive sampling, in IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 2130, March 2008.
R. G. Baraniuk, V. Cevher, and M. B. Wakin, Low-dimensional models for dimensionality reduction and signal recovery: A geometric perspective, Proceedings of the IEEE, vol. 98, no. 6, pp. 959-971, June 2010.
M.B. Wakin, Concise Signal Models, Connexions modules endorsed by the IEEE Signal Processing Society.
Compressive Sensing of Analog Signals; Compressive Measurement Systems & Hardware
M. J. Rubin, M. B. Wakin, and T. Camp, A Comparison of On-Mote Lossy Compression Algorithms for Wireless Seismic Data Acquisition, IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS), Marina Del Rey, California, May 2014.
M. A. Davenport and M. B. Wakin, Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences, Applied and Computational Harmonic Analysis, vol. 33, no. 3, pp. 438-472, November 2012. ( authors' copy)
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)
J. Yoo, C. Turnes, E. Nakamura, C. Le, S. Becker, E. Sovero, M. Wakin, M. Grant, J. Romberg, A. Emami-Neyestanak, and E. Candès, A Compressed Sensing Parameter Extraction Platform for Radar Pulse Signal Acquisition, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, vol. 2, no. 3, pp. 626-638, 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.
See also: Team website for Analog to Information project
See also: Compressive Imaging: A New Single Pixel Camera
Manifold-based Compressive Sensing and Manifold Learning
A. Eftekhari and M. B. Wakin, New Analysis of Manifold Embeddings and Signal Recovery from Compressive Measurements, Applied and Computational Harmonic Analysis, vol. 39, no. 1, pp. 67-109, July 2015. ( authors' copy)
H. L. Yap, M. B. Wakin, and C.J. Rozell, Stable Manifold Embeddings with Structured Random Matrices, IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 4, pp. 720-730, August 2013. ( authors' copy)
L. Carin, R.G. Baraniuk, V. Cevher, D. Dunson, M.I. Jordan, G. Sapiro, and M.B. Wakin, Learning Low-Dimensional Signal Models: A Bayesian Approach Based on Incomplete Measurements, IEEE Signal Processing Magazine, vol. 28, no. 2, pp. 39-51, March 2011.
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 and Multi-image Compressive Sensing
J. Y. Park, A. C. Gilbert, and M. B. Wakin, Compressive Measurement Bounds for Wireless Sensor Networks in Structural Health Monitoring, World Conference on Structural Control and Monitoring (WCSCM), Barcelona, Spain, July 2014.
J. Y. Park, M. B. Wakin, and A. C. Gilbert, Modal Analysis with Compressive Measurements, IEEE Transactions on Signal Processing, vol. 62, no. 7, pp. 1655-1670, April 2014. ( authors' copy)
M. F. Duarte, M. B. Wakin, D. Baron, S. Sarvotham, and R. G. Baraniuk, Measurement Bounds for Sparse Signal Ensembles via Graphical Models, IEEE Transactions on Information Theory, vol. 59, no. 7, pp. 4280-4289, July 2013. ( authors' copy)
J. Y. Park and M. B. Wakin, A Multiscale Algorithm for Reconstructing Videos from Streaming Compressive Measurements, Journal of Electronic Imaging, vol. 22, no. 2, pages 021001, 2013. ( authors' copy) (See also: companion technical report.)
M. B. Wakin, A Study of the Temporal Bandwidth of Video and its Implications in Compressive Sensing, Colorado School of Mines Technical Report 2012-08-15, August 2012.
J. Y. Park and M. B. Wakin, A Geometric Approach to Multi-view Compressive Imaging, EURASIP Journal on Advances in Signal Processing, vol. 2012, article 37, 2012.
Algorithms for Sparse Signal Recovery
M. A. Davenport, D. Needell, and M. B. Wakin, Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries, IEEE Transactions on Information Theory, vol. 59, no. 10, pp. 6820-6829, October 2013. ( authors' copy)
A. J. Weinstein and M. B. Wakin, Recovering a Clipped Signal in Sparseland, Sampling Theory in Signal and Image Processing, vol. 12, no. 1, pp. 55-69, 2013. ( authors' copy)
A.J. Weinstein and M.B. Wakin, Online Search Orthogonal Matching Pursuit, in IEEE Statistical Signal Processing Workshop -- SSP 2012, Ann Arbor, Michigan 2012.
M. A. Davenport and M. B. Wakin, Analysis of Orthogonal Matching Pursuit using the Restricted Isometry Property, IEEE Transactions on Information Theory, vol. 56, no. 9, pp. 4395--4401, September 2010. ( authors' copy)
E. J. Candès, M. B. Wakin, and S. P. Boyd, Enhancing Sparsity by Reweighted L1 Minimization, Journal of Fourier Analysis and Applications, vol. 14, no. 5, pp. 877--905, December 2008.
Theoretical Foundations and Analysis of Randomized Operators
R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, A Simple Proof of the Restricted Isometry Property for Random Matrices, Constructive Approximation, vol. 28, no. 3, pp. 253--263, December 2008.
J.Y. Park, H.L. Yap, C.J. Rozell, and M.B. Wakin, Concentration of Measure for Block Diagonal Matrices with Applications to Compressive Signal Processing, IEEE Transactions on Signal Processing, vol. 59, no. 12, pp. 5859-5875, December 2011.
A. Eftekhari, H. L. Yap, C. J. Rozell, and M. B. Wakin, The Restricted Isometry Property for Random Block Diagonal Matrices, Applied and Computational Harmonic Analysis, vol. 38, no. 1, pp. 1-31, January 2015. ( authors' copy)
Information Scalability; Estimation and Detection
C. W. Lim and M. B. Wakin, Compressive Temporal Higher Order Cyclostationary Statistics, IEEE Transactions on Signal Processing, vol. 63, no. 11, pp. 2942-2956, June 2015. (See also companion technical report)
A. Eftekhari, J. Romberg, and M. B. Wakin, Matched Filtering from Limited Frequency Samples, IEEE Transactions on Information Theory, vol. 59, no. 6, pp. 3475-3496, June 2013. ( authors' copy)
C. W. Lim and M. B. Wakin, Automatic Modulation Recognition for Spectrum Sensing using Nonuniform Compressive Samples, in IEEE International Conference on Communications -- ICC 2012, Ottawa, Canada, June 2012.
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. Davenport, M. Duarte, M. Wakin, J. Laska, D. Takhar, K. Kelly, and R. Baraniuk, The Smashed Filter for Compressive Classification and Target Recognition, in Computational Imaging V at IS&T/SPIE Electronic Imaging, San Jose, California, January 2007.
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.
Compressive System Identification
B. M. Sanandaji, M. B. Wakin, and T. L. Vincent, Observability with Random Observations, IEEE Transactions on Automatic Control, vol. 59, no. 11, pp. 3002-3007, October 2014. (See also companion technical report)
B. M. Sanandaji, T. L. Vincent, and M. B. Wakin, Concentration of Measure Inequalities for Toeplitz Matrices with Applications, IEEE Transactions on Signal Processing, vol. 61, no. 1, pp. 109-117, January 2013. ( authors' copy) (See also companion technical report.)
B.M. Sanandaji, T.L. Vincent, and M.B. Wakin, Compressive Topology Identification of Interconnected Dynamic Systems via Clustered Orthogonal Matching Pursuit, IEEE 2011 Conference on Decision and Control and European Control Conference -- CDC-ECC, Orlando, Florida, December 2011.
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.
Randomness in Computation
P. G. Constantine, A. Eftekhari, and M. B. Wakin, Computing Active Subspaces Efficiently with Gradient Sketching, preprint, 2015.
A. C. Gilbert, J. Y. Park, and M. B. Wakin, Sketched SVD: Recovering Spectral Features from Compressive Measurements, Arxiv preprint arXiv:1211.0361, 2012.
Manifolds and Multi-Image Processing
Non-differentiable Image Manifolds & Parameter Estimation
Single-Signal and Single-Image Processing and Compression
Approximations and Representations for Sampled Signals
Multiscale Geometric Models for Approximation and Compression
Generalizations and Extensions to Higher Dimensions
A. J. Weinstein and M. B. Wakin, Recovering a Clipped Signal in Sparseland, to appear in Sampling Theory in Signal and Image Processing. (Old draft available here; final version to be posted soon.)
Fundamentals of Representing and Encoding Information
M. B. Wakin, M. T. Orchard, R. G. Baraniuk, and V. Chandrasekaran, Phase and Magnitude Perceptual Sensitivities in Nonredundant Complex Wavelet Representations, in Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, November 2003.
R.M. Castro, M.B. Wakin, and M.T. Orchard, On the Problem of Simultaneous Encoding of Magnitude and Location Information, in Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, November 2002.
Additional Information & Resources
Email: mwakin (at) mines (dot) e d u