Research – Michael B. Wakin

Research Interests

    • Signal processing and machine learning using sparse, low-rank, tensor, and manifold-based models

    • Sensing, compression, inference, and reconstruction

    • Inverse problems, compressive sensing, and quantum state tomography

    • Convex and non-convex optimization algorithms and theory

    • Approximation theory and computational harmonic analysis

Research Group

 

Current Students in my Group

Alumni

    • Anna Titova, Ph.D. 2025 (co-advised with Ali Tura), now Postdoctoral Fellow, The University of Texas at Austin
    • Yifan Wu, Postdoc 2024, now Assistant Professor, Harvey Mudd College
    • Dan Rosen, Ph.D. 2024 (co-advised with Gongguo Tang), now Statistical Signal Processing Researcher, ICR, Inc. (thesis)
    • Marc Valdez, Ph.D. 2024 (co-advised with Jacob Rezac) (thesis)
    • Patipan Saengduean, Ph.D. 2022 (co-advised with Roel Snieder), now Data Scientist at Government Big Data Institute, Thailand (thesis)
    • Shuang Li, Ph.D. 2020 (co-advised with Gongguo Tang), now Assistant Professor of Electrical and Computer Engineering, Iowa State University, formerly 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 Software Engineer, Oklo, Inc., formerly Software Engineer, Uber, formerly Machine Learning Researcher at Software Engineering Institute, Carnegie Mellon University (thesis)
    • Dehui Yang, Ph.D. 2018, now Assistant Professor, Xi’an Jiaotong-Liverpool University, formerly Applied Scientist at Uber, formerly Data Scientist at Root Insurance Co. (thesis)
    • 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, formerly 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 (thesis)
    • 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 Associate Professor, Department of Electronics, Universidad Técnica Federico Santa María (UTFSM), Chile, formerly Professor, Biomedical Engineering, Universidad de Valparaiso, Chile (thesis)
    • Borhan Sanandaji, Ph.D. 2012 (co-advised with Tyrone Vincent), now Manager and Staff Applied Machine Learning Scientist at Uber, formerly Postdoctoral Scholar, UC Berkeley (thesis)
    • Michael Coco, M.S. 2012 (co-advised with Lawrence Wiencke), now Staff Engineer at Booz Allen Hamilton (thesis)

Overview

Effective techniques for signal and data processing often rely on models that capture the expected structure of signals and data. In many cases, such models emphasize conciseness: signals may be sparse or compressible in an appropriate domain, data may be organized into a low-rank or tensor representation, or high-dimensional samples may lie near a low-dimensional manifold.

Our research group focuses on developing:

  • concise mathematical models for signals and data sets that describe intrinsic structure using as few degrees of freedom as possible

  • optimization algorithms that exploit these models to enable efficient sensing and compression, accurate parameter inference, and robust signal/data reconstruction from limited or indirect measurements

  • theoretical guarantees that characterize the performance of models and algorithms in terms of sample complexity, recovery accuracy, stability, and computational efficiency

Some of our work has grown out of the topic area of Compressive Sensing, where sparse models allow signals to be reconstructed from surprisingly few random measurements. More recently, these same core ideas—low-complexity models and algorithms that exploit them—have found impact in a broad range of new areas: quantum state tomography, seismic and acoustic wavefield reconstruction, inverse problems in imaging and sensing, and machine learning with structured data. Our ongoing efforts aim to broaden both the scope and the theoretical understanding of low-complexity models and algorithms across science and engineering applications.

Topic Areas and Selected Publications

A list of selected publications is below. A complete list of publications is available here.

Signal Processing

Ultra-Fast Optics

Quantum State Tomography

Modal Analysis, Super-resolution, and Deconvolution

Dynamical Systems and Time-Series Analysis

Radar and Array Processing

Time-frequency Analysis

Machine Learning

Optimization

Matrix Completion, Matrix Recovery, and Subspace Tracking

Randomness in Computation

Compressive Sensing

Introductory Papers

Compressive Measurement Systems & Hardware

Theoretical Foundations and Sparse Signal Embeddings

Manifold Embeddings

Sparse Signal Recovery

Distributed, Multi-signal, and Video Compressive Sensing

Signal Inference from Compressive Measurements

Fundamentals

Matrices and Linear Operators

Multiscale Geometric Analysis

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.