Research – Models and Algorithms for
Signal and Data Processing
Research Interests
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- 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
Postdocs
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- Yifan Wu
Current Students in my Group
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- Alireza Goldar, Ph.D. student
- Dan Rosen, Ph.D. student (co-advising with Gongguo Tang)
- Anna Titova, Ph.D. student (co-advising with Ali Tura)
- Marc Valdez, Ph.D. student (co-advising with Jacob Rezac)
- Qiaojie (Grant) Zheng, Ph.D. student (co-advising with Xiaoli Zhang)
- Patrick Barringer, M.S. student
- Additional collaborations and informal co-advising
Alumni
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- Patipan Saengduean, Ph.D. 2022 (co-advised with Roel Snieder), now Data Scientist at Government Big Data Institute, Thailand
- 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.
Compressive Sensing
Introductory Papers
- M. B. Wakin, Compressive Sensing Fundamentals, in M. Amin (Ed.), Compressive Sensing for Urban Radar, CRC Press, 2014.
- 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. Snieder and M. B. Wakin, When Randomness Helps in Undersampling, SIAM Review, vol. 64, no. 4, pp. 1062-1080, November 2022. (code)
- 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 Measurement Systems & Hardware
- A. Titova, M. B. Wakin, and A. C. Tura, Achieving Robust Compressive Sensing Seismic Acquisition with a Two-Step Sampling Approach, Sensors, vol. 23, no. 23, 9519, 2023.
- 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.
- 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.
- See also: Team website for Analog to Information project
Theoretical Foundations and Sparse Signal Embeddings
- 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)
- 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.
- 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)
- 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.
Manifold Embeddings
- A. Eftekhari and M. B. Wakin, What Happens to a Manifold Under a Bi-Lipschitz Map?, Discrete & Computational Geometry, vol. 57, no. 3, pp. 641-673, April 2017. (authors’ copy)
- 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)
- 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.
- 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.
- C. Hegde, M. Wakin, and R. Baraniuk, Random Projections for Manifold Learning, in Neural Information Processing Systems — NIPS, Vancouver, Canada, December 2007.
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)
- 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.
- 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)
- C. W. Lim and M. B. Wakin, Reconstruction of Frequency Hopping Signals From Multi-Coset Samples, Arxiv preprint arXiv:1603.06886, 2016.
- 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.
Distributed, Multi-signal, and Video Compressive Sensing
- R. G. Baraniuk, T. Goldstein, A. C. Sankaranarayanan, C. Studer, A. Veeraraghavan, and M. B. Wakin, Compressive Video Sensing: Algorithms, Architectures, and Applications, in IEEE Signal Processing Magazine, vol. 34, no. 1, pp. 52-66, January 2017.
- 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.
- 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.
- 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, 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)
- 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.
Machine Learning
Optimization
- Z. Qin, M. B. Wakin, and Z. Zhu, Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery, preprint, 2023.
- S. Li, G. Tang, and M. B. Wakin, Landscape Correspondence of Empirical and Population Risks in the Eigendecomposition Problem, IEEE Transactions on Signal Processing, vol. 70, pp. 2985-2999, 2022. (authors’ copy)
- S. Li, Q. Li, Z. Zhu, G. Tang, and M. B. Wakin, The Global Geometry of Centralized and Distributed Low-rank Matrix Recovery without Regularization, IEEE Signal Processing Letters, vol. 27, pp. 1400-1404, July 15, 2020. (authors’ copy)
- Q. Li, Z. Zhu, G. Tang, and M. B. Wakin, Provable Bregman-divergence based Methods for Nonconvex and Non-Lipschitz Problems, preprint, 2019.
- Z. Zhu, Q. Li, X. Yang, G. Tang, and M. B. Wakin, Distributed Low-rank Matrix Factorization with Exact Consensus, Thirty-third Conference on Neural Information Processing Systems (NeurIPS), Vancouver, Canada, December 2019. (authors’ copy)
- Z. Zhu, D. Soudry, Y. C. Eldar, and M. B. Wakin, The Global Optimization Geometry of Shallow Linear Neural Networks, Journal of Mathematical Imaging and Vision, May 31, 2019. (authors’ copy)
- Z. Zhu, Q. Li, G. Tang, and M. B. Wakin, The Global Optimization Geometry of Low-Rank Matrix Optimization, IEEE Transactions on Information Theory, vol. 67, no. 2, pp. 1308-1331, February 2021. (authors’ copy)
- Z. Zhu, Q. Li, G. Tang, and M. B. Wakin, Global Optimality in Low-rank Matrix Optimization, IEEE Transactions on Signal Processing, vol. 66, no. 13, pp. 3614-3628, July 2018. (authors’ copy)
Matrix Completion, Matrix Recovery, and Subspace Tracking
- S. Li and M. B. Wakin, Recovery Guarantees for Time-varying Pairwise Comparison Matrices with Non-transitivity, preprint, 2021.
- A. Eftekhari, M. B. Wakin, and R. A. Ward, MC^2: A Two-Phase Algorithm for Leveraged Matrix Completion, Information and Inference: A Journal of the IMA, vol. 7, no. 3, pp. 581-604, 19 September 2018. (authors’ copy)
- A. Eftekhari, D. Yang, and M. B. Wakin, Weighted Matrix Completion and Recovery with Prior Subspace Information, IEEE Transactions on Information Theory, vol. 64, no. 6, pp. 4044–4071, June 2018. (authors’ copy)
- A. Eftekhari, G. Ongie, L. Balzano, and M. B. Wakin, Streaming Principal Component Analysis From Incomplete Data, Journal of Machine Learning Research, vol. 20, no. 86, pp. 1-62, 2019. (authors’ copy)
- A. Eftekhari, L. Balzano, and M. B. Wakin, What to Expect When You Are Expecting on the Grassmannian, IEEE Signal Processing Letters, vol. 24, no. 6, pp. 872-876, June 2017. (authors’ copy)
Randomness in Computation
- A. Eftekhari, M. B. Wakin, P. Li, and P. G. Constantine, Randomized Learning of the Second-moment Matrix of a Smooth Function, Foundations of Data Science, vol. 1, no. 3, pp. 329-387, 2019. (authors’ copy)
- P. G. Constantine, A. Eftekhari, and M. B. Wakin, Computing Active Subspaces Efficiently with Gradient Sketching, IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Cancun, Mexico, December 2015. (authors’ copy)
- A. C. Gilbert, J. Y. Park, and M. B. Wakin, Sketched SVD: Recovering Spectral Features from Compressive Measurements, Arxiv preprint arXiv:1211.0361, 2012.
Application Areas
Ultra-Fast Optics
- D. Rosen and M. B. Wakin, Bivariate Retrieval from Intensity of Cross-Correlation, Signal Processing, vol. 215, 109267, February 2024.
Quantum State Tomography
- Z. Qin, C. Jameson, Z. Gong, M. B. Wakin, and Z. Zhu, Stable Tomography for Structured Quantum States, preprint, 2023.
- A. Lidiak, C. Jameson, Z. Qin, G. Tang, M. B. Wakin, Z. Zhu, and Z. Gong, Quantum state tomography with tensor train cross approximation, preprint, 2022.
- Z. Qin, A. Lidiak, Z. Gong, G. Tang, M. B. Wakin, and Z. Zhu, Error Analysis of Tensor-Train Cross Approximation, Conference on Neural Information Processing Systems (NeurIPS), 2022.
Modal Analysis, Super-resolution, and Deconvolution
- J. Jayne, M. B. Wakin, and R. Snieder, Green’s function estimation by seismic interferometry from limited frequency samples, Signal Processing, vol. 205, 108863, April 2023.
- S. Li, M. B. Wakin, and G. Tang, Atomic Norm Denoising for Complex Exponentials with Unknown Waveform Modulations, IEEE Transactions on Information Theory, vol. 66, no. 6, pp. 3893-3913, June 2020. (authors’ copy)
- Y. Xie, M. B. Wakin, and G. Tang, Support Recovery for Sparse Signals With Unknown Non-Stationary Modulation, IEEE Transactions on Signal Processing, vol. 68, February 24, 2020. (authors’ copy)
- Y. Xie, M. B. Wakin, and G. Tang, Simultaneous Sparse Recovery and Blind Demodulation, IEEE Transactions on Signal Processing, vol. 67, no. 19, pp. 5184-5199, October 1, 2019. (authors’ copy)
- D. Yang, G. Tang, and M. B. Wakin, Super-Resolution of Complex Exponentials from Modulations with Unknown Waveforms, IEEE Transactions on Information Theory, vol. 62, no. 10, pp. 5809-5830, October 2016. (authors’ copy)
- S. Li, H. Mansour, and M. B. Wakin, Recovery analysis of damped spectrally sparse signals and its relation to MUSIC, Information and Inference: A Journal of the IMA, vol. 11, no. 1, pp. 355-383, March 2022. (authors’ copy, code)
- Z. Zhu, D. Yang, M. B. Wakin, and G. Tang, A Super-Resolution Algorithm for Multiband Signal Identification, 51st Asilomar Conference on Signals, Systems and Computers, Pacific Grove, California, October 2017.
- S. Li, D. Yang, G. Tang, and M. B. Wakin, Atomic Norm Minimization for Modal Analysis from Random and Compressed Samples, IEEE Transactions on Signal Processing, vol. 66, no. 7, pp. 1817-1831, April 1, 2018. (authors’ copy)
- 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)
- Z. Zhu, M. Lopez-Santillana, and M. Wakin, Super-Resolution of Complex Exponentials from Modulations with Known Waveforms, IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Curaçao, December 2017.
- A. Eftekhari and M. B. Wakin, Greed is Super: A Fast Algorithm for Super-Resolution, Arxiv preprint arXiv:1511.03385, 2015.
- 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.
Dynamical Systems and Time-Series Analysis
- A. Eftekhari, H. L. Yap, M. B. Wakin, and C. J. Rozell, Stabilizing Embedology: Geometry-Preserving Delay-Coordinate Maps, Physical Review E, vol. 97, no. 2, pp. 022222, February 2018. (authors’ copy)
- 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.
Radar and Array Processing
- M. A. Valdez, A. J. Yuffa, and M. B. Wakin, On-grid compressive sampling for spherical field measurements in acoustics, Journal of the Acoustical Society of America, vol. 152, no. 4, October 2022. (authors’ copy)
- M. A. Valdez, A. J. Yuffa, and M. B. Wakin, Compressive Sensing with Wigner D-functions on Subsets of the Sphere, IEEE Transactions on Signal Processing, vol. 70, pp. 5652-5667, 2022. (authors’ copy)
- Y. Wu, M. B. Wakin, and P. Gerstoft, Gridless DOA Estimation with Multiple Frequencies, IEEE Transactions on Signal Processing, vol. 71, pp. 417-432, 2023. (authors’ copy)
- S. Li, P. Nayeri, and M. B. Wakin, Digital Beamforming Robust to Time-Varying Carrier Frequency Offset, preprint, 2021. (code)
- Y. Xie, S. Li, G. Tang, and M. B. Wakin, Radar signal demixing via convex optimization, International Conference on Digital Signal Processing (DSP), London, August 2017.
- Z. Zhu, G. Tang, P. Setlur, S. Gogineni, M. Wakin, and M. Rangaswamy, Super-Resolution in SAR Imaging: Analysis With the Atomic Norm, IEEE Sensor Array and Multichannel Signal Processing (SAM) Workshop, Rio de Janeiro, Brazil, July 2016.
- Z. Zhu and M. B. Wakin, On the Dimensionality of Wall and Target Return Subspaces in Through-the-Wall Radar Imaging, 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa), Aachen, Germany, September 2016.
- Z. Zhu and M. B. Wakin, Wall Clutter Mitigation and Target Detection Using Discrete Prolate Spheroidal Sequences, 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa), Pisa, Italy, June 2015.
Fundamentals
Time-frequency Analysis
- Z. Zhu, S. Karnik, M. B. Wakin, M. A. Davenport, and J. Romberg, ROAST: Rapid Orthogonal Approximate Slepian Transform, IEEE Transactions on Signal Processing, vol. 66, no. 22, pp. 5887-5901, November 15, 2018. (authors’ copy)
- 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)
- Z. Zhu and M. B. Wakin, Approximating Sampled Sinusoids and Multiband Signals Using Multiband Modulated DPSS Dictionaries, Journal of Fourier Analysis and Applications, vol. 23, no. 6, pp. 1263-1310, December 2017. (authors’ copy)
Matrices and Linear Operators
- Z. Zhu and M. B. Wakin, Time-Limited Toeplitz Operators on Abelian Groups: Applications in Information Theory and Subspace Approximation, Pure and Applied Functional Analysis, vol. 8, no. 2, pp. 775-808, 2023. (authors’ copy)
- Z. Zhu, S. Karnik, M. A. Davenport, J. Romberg, and M. B. Wakin, The Eigenvalue Distribution of Discrete Periodic Time-Frequency Limiting Operators, IEEE Signal Processing Letters, vol. 25, no. 1, pp.95–99, January 2018. (authors’ copy)
- Z. Zhu and M. B. Wakin, On the Asymptotic Equivalence of Circulant and Toeplitz Matrices, IEEE Transactions on Information Theory, vol. 63, no. 5, pp. 2975-2992, May 2017. (authors’ copy)
Multiscale Geometric Analysis
- M. B. Wakin, D. L. Donoho, H. Choi, and R. G. Baraniuk, The Multiscale Structure of Non-Differentiable Image Manifolds, in SPIE Wavelets XI, San Diego, California, July 2005.
- V. Chandrasekaran, M. B. Wakin, D. Baron, and R. G. Baraniuk, Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets, IEEE Transactions on Information Theory, vol. 55, no. 1, pp. 374-400, January 2009.
- M. B. Wakin, J. K. Romberg, H. Choi, and R. G. Baraniuk, Wavelet-domain Approximation and Compression of Piecewise Smooth Images, in IEEE Transactions on Image Processing, Vol. 15, No. 5, May 2006.
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.