Research – Models and Algorithms for
Signal and Data Processing

Research Interests

    • 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

    • Yifan Wu

 

Current Students in my Group

    • 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

    • 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

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

Machine Learning

Optimization

Matrix Completion, Matrix Recovery, and Subspace Tracking

Randomness in Computation

Application Areas

Ultra-Fast Optics

Quantum State Tomography

Modal Analysis, Super-resolution, and Deconvolution

Dynamical Systems and Time-Series Analysis

Radar and Array Processing

Fundamentals

Time-frequency Analysis

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.