Department of Mathematics

Publications

Journal Articles

  1. Simone Brugiapaglia, Rafael Chiclana, Tim Hoheisel, and M.A. Iwen, On Continuous Terminal Embeddings of Sets of Positive Reach (preprint), Submitted, 2024.
  2. Cullen Haselby, M. A. Iwen, Santhosh Karnik, and Rongrong Wang, Tensor Deli: Tensor Completion for Low CP-Rank Tensors via Random Sampling (preprint, code), Submitted, 2024.
  3. Cullen Haselby, M. A. Iwen, Deanna Needell, Elizaveta Rebrova, and William Swartworth, Fast and Low-Memory Compressive Sensing Algorithms for Low Tucker-Rank Tensor Approximation from Streamed Measurements (preprint, code), Submitted, 2023.
  4. Craig Gross and M.A. Iwen,
    Sparse Spectral Methods for Solving High-Dimensional and Multiscale Elliptic PDEs (preprint, code), Foundations of Computational Mathematics, to appear.
  5. Rafael Chiclana, M.A. Iwen, and Mark Roach,
    On Outer Bi-Lipschitz Extensions of Linear Johnson-Lindenstrauss Embeddings of Subsets of RN (preprint, code), Numerische Mathematik, Vol. 156, pages 2111 -- 2130, 2024.
  6. M.A. Iwen, Benjamin Schmidt, Arman Tavakoli,
    On Fast Johnson-Lindenstrauss Embeddings of Compact Submanifolds of RN with Boundary (preprint), Discrete & Computational Geometry, Vol. 71, pages 498 -- 555, 2024.
  7. Santhosh Karnik, Rongrong Wang, and M. A. Iwen,
    Neural Network Approximation of Continuous Functions in High Dimensions with Applications to Inverse Problems (preprint), Journal of Computational and Applied Mathematics, Vol. 438, article 115557, 2024.
  8. Cullen Haselby, M.A. Iwen, Deanna Needell, Michael Perlmutter, Elizaveta Rebrova, Modewise Operators, the Tensor Restricted Isometry Property, and Low-Rank Tensor Recovery (preprint, code), Applied and Computational Harmonic Analysis, Vol. 66, pages 161 -- 192, 2023.
  9. Ali Zare, Roland Wirth, Cullen Haselby, Heiko Hergert, M. A. Iwen,
    Modewise Johnson-Lindenstrauss Embeddings for Nuclear Many-Body Theory (preprint), European Physical Journal A, Vol. 59, Issue 5, article 95, 2023.
  10. M.A. Iwen, Benjamin Schmidt, Arman Tavakoli,
    Lower Bounds on the Low-Distortion Embedding Dimension of Submanifolds of Rn (preprint), Applied and Computational Harmonic Analysis, Vol. 65, pages 170 -- 180, 2023.
  11. M.A. Iwen, Michael Perlmutter, Mark Roach,
    Toward Fast and Provably Accurate Near-field Ptychographic Phase Retrieval (preprint, code), Sampling Theory, Signal Processing, and Data Analysis, Vol. 21, Issue 1, article 6, 2023.
  12. M.A. Iwen, Michael Perlmutter, Nada Sissouno, Aditya Viswanathan,
    Phase Retrieval for L2([-π,π]) via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements (preprint, code), Journal of Fourier Analysis and Applications, Vol. 29, Issue 1, article 8, 2023.
  13. Craig Gross, M.A. Iwen, Lutz Kämmerer, Toni Volkmer,
    Sparse Fourier Transforms on Rank-1 Lattices for the Rapid and Low-Memory Approximation of Functions of Many Variables (preprint, code), Sampling Theory, Signal Processing, and Data Analysis, Vol. 20, Issue 1, article 1, 2022.
  14. Craig Gross, M.A. Iwen, Lutz Kämmerer, Toni Volkmer,
    A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of Near-Optimal Size (preprint, code), Advances in Computational Mathematics, Vol. 47, Issue 6, article 86, 2021.
  15. Michael Perlmutter, Sami Merhi, Aditya Viswanathan, and Mark Iwen,
    Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization (preprint, code), Information and Inference: A Journal of the IMA, Vol. 10, Issue 4, pages 1491 -- 1531, 2021.
  16. Bosu Choi, M.A. Iwen, Toni Volkmer,
    Sparse Harmonic Transforms II: Best s-Term Approximation Guarantees for Bounded Orthonormal Product Bases in Sublinear-Time (preprint, code),
    Numerische Mathematik, Vol. 148, Issue 2, pages 293 -- 362, 2021.
  17. Theodore Faust, Mark Iwen, Rayan Saab, Rongrong Wang,
    On the l∞-norms of the Singular Vectors of Arbitrary Powers of a Difference Matrix with Applications to Sigma-Delta Quantization (preprint), Linear Algebra and its Applications, Vol. 626, pages 79 -- 151, 2021.
  18. M.A. Iwen, Felix Krahmer, Sara Krause-Solberg, Johannes Maly,
    On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds (preprint), Discrete & Computational Geometry, Vol. 65, Issue 4, pages 953 -- 998, 2021.
  19. Bosu Choi, M.A. Iwen, Felix Krahmer,
    Sparse Harmonic Transforms: A New Class of Sublinear-time Algorithms for Learning Functions of Many Variables (preprint, code),
    Foundations of Computational Mathematics, Vol. 21, Issue 2, pages 275 -- 329, 2021.
  20. M.A. Iwen, Deanna Needell, Elizaveta Rebrova, Ali Zare,
    Lower Memory Oblivious (Tensor) Subspace Embeddings with Fewer Random Bits: Modewise Methods for Least Squares (preprint), SIAM Journal on Matrix Analysis and Applications, Vol. 42-1, pages 376 -- 416, 2021.
  21. Nada Sissouno, Florian Bossmann, Frank Filbir, Mark Iwen, Maik Kahnt, Rayan Saab, Christian Schroer, and Wolfgang zu Castell,
    A Direct Solver for the Phase Retrieval Problem in Ptychographic Imaging (preprint),
    Mathematics and Computers in Simulation, Vol. 176, pages 292 -- 300, 2020.
  22. M.A. Iwen, Brian Preskitt, Rayan Saab, and Aditya Viswanathan,
    Phase Retrieval from Local Measurements: Improved Robustness via Eigenvector-Based Angular Synchronization (preprint, code),
    Applied and Computational Harmonic Analysis, Vol. 48, Issue 1, pages 415 -- 444, 2020.
  23. M.A. Iwen, Sami Merhi, and Michael Perlmutter,
    Lower Lipschitz Bounds for Phase Retrieval from Locally Supported Measurements (preprint),
    Applied and Computational Harmonic Analysis, Vol. 47, Issue 2, pages 526 -- 538, 2019.
  24. Sami Merhi, Ruochuan Zhang, Mark A. Iwen, and Andrew Christlieb,
    A New Class of Fully Discrete Sparse Fourier Transforms: Faster Stable Implementations with Guarantees (preprint, code),
    Journal of Fourier Analysis and Applications, Vol. 25, Issue 3, pages 751 -- 784, 2019.
  25. Sina Bittens, Ruochuan Zhang, and Mark A. Iwen,
    A Deterministic Sparse FFT for Functions with Structured Fourier Sparsity (preprint, code),
    Advances in Computational Mathematics, Vol. 45, Issue 2, pages 519 -- 561, 2019.
  26. Ali Zare, Alp Ozdemir, Mark A. Iwen, and Selin Aviyente,
    Extension of PCA to Higher Order Data Structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA (preprint),
    Proceedings of the IEEE, Vol. 106, Number 8, pages 1341 -- 1358, 2018.
  27. Xianfeng Hu, M.A. Iwen, and Hyejin Kim,
    Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms (preprint, code),
    Numerical Algorithms, Vol. 74, Issue 4, pages 1029 -- 1059, 2017.
  28. M.A. Iwen, Aditya Viswanathan, and Yang Wang,
    Robust Sparse Phase Retrieval Made Easy (preprint, code),
    Applied and Computational Harmonic Analysis, Vol. 42, Issue 1, pages 135 -- 142, 2017.
  29. M.A. Iwen, Aditya Viswanathan, and Yang Wang,
    Fast Phase Retrieval from Local Correlation Measurements (preprint, code),
    SIAM J. on Imaging Sciences, Vol. 9, Number 4, pages 1655 -- 1688, 2016.
  30. M.A. Iwen and B.W. Ong,
    A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks (preprint, code),
    SIAM Journal on Matrix Analysis and Applications, Vol. 37, Issue 4, pages 1699-1718, 2016.
  31. M.A. Iwen & Felix Krahmer,
    Fast Subspace Approximation via Greedy Least-Squares (preprint),
    Constructive Approximation, Volume 42, Issue 2, pages 281 -- 301, 2015.
  32. Anna Gilbert, Piotr Indyk, M.A. Iwen, and Ludwig Schmidt,
    Recent Developments in the Sparse Fourier Transform (preprint),
    IEEE Signal Processing Magazine, Vol. 31, Issue 5, pages 91 -- 100, 2014.
  33. M.A. Iwen,
    Compressed Sensing with Sparse Binary Matrices: Instance Optimal Error Guarantees in Near-Optimal Time (preprint),
    Journal of Complexity, Vol. 30, Issue 1, pages 1 -- 15, 2014.
  34. M.A. Iwen & Rayan Saab,
    Near-Optimal Encoding for Sigma-Delta Quantization of Finite Frame Expansions (preprint),
    Journal of Fourier Analysis and Applications, Vol. 19, Issue 6, pages 1255 -- 1273, 2013.
  35. M. A. Iwen & Mauro Maggioni,
    Approximation of Points on Low-Dimensional Manifolds via Random Linear Projections (preprint),
    Information and Inference: A Journal of the IMA, Vol. 2, Issue 1, pages 1 -- 31, 2013.
  36. I.B. Segal* & M.A. Iwen,
    Improved Sparse Fourier Approximation Results: Faster Implementations and Stronger Guarantees (preprint, code),
    Numerical Algorithms, Vol. 63, Issue 2, pages 239 -- 263, 2013. *Undergraduate Student
    Please also see this scholarship established in Ben's honor.
  37. M. A. Iwen, Fadil Santosa, and Rachel Ward,
    A Symbol-based Bar Code Decoding Algorithm (preprint),
    SIAM Journal on Imaging Sciences, Vol. 6, Issue 1, pages 56 -- 77, 2013.
  38. M. A. Iwen,
    Improved Approximation Guarantees for Sublinear-Time Fourier
    Algorithms     (preprint, code),
    Applied and Computational Harmonic Analysis, Vol. 34, Issue 1, pages 57 -- 82, 2013.
  39. M. A. Iwen & A. H. Tewfik,
    Adaptive Strategies for Target Detection and Localization in Noisy Environments (preprint),
    IEEE Transactions on Signal Processing, Vol. 60, Issue 5, pages 2344 -- 2353, 2012.
  40. J. Bailey*, M. A. Iwen, and C. V. Spencer,
    On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions (preprint, code),
    SIAM J. Matrix Anal. Appl., Vol. 33, No. 1, pages 263 -- 289, 2012. *Undergraduate Student
  41. M. A. Iwen,
    Combinatorial Sublinear-Time Fourier Algorithms (preprint, code),
    Foundations of Computational Mathematics, Vol. 10, Issue 3, pages 303 -- 338, 2010.
    Additional notes on Lemma 6 can be found here.
  42. M. A. Iwen & C. V. Spencer,
    A Note on Compressed Sensing and the Complexity of Matrix Multiplication (preprint),
    Information Processing Letters, Vol. 109, Issue 10, April, 2009.
  43. Farrell, B., Yi Huang, Mark Iwen, Ting Wang, Lisa Zhang, and Jintong Zheng,
    Wavelength Assignment in Optical Network Design (preprint),
    Mathematics-in-Industry Case Studies (MICS), Vol. 1, 2008.
  44. M. A. Iwen, Anna Gilbert, and Martin Strauss,
    Empirical Evaluation of a Sub-Linear Time Sparse DFT Algorithm (preprint, code),
    Communications in Mathematical Sciences, Vol. 5, No. 4, December, 2007.

Refereed Conference Proceedings

  1. Santhosh Karnik, Anna Veselovska, Mark Iwen, Felix Krahmer,
    Implicit Regularization for Tubal Tensor Factorizations via Gradient Descent (preprint), Submitted, 2024.
  2. Cullen Haselby, Santhosh Karnik, and Mark Iwen,
    Tensor Sandwich: Tensor Completion for Low CP-Rank Tensors via Adaptive Random Sampling (preprint), Sampling Theory and Applications (SampTA), 2023.
  3. Michael Perlmutter, Jieqian He, Mark A. Iwen, and Matthew Hirn
    A Hybrid Scattering Transform for Signals with Isolated Singularities (preprint), Asilomar Conf. on Signals, Systems, and Computers (ACSSC), 2021.
  4. Michael Perlmutter, Nada Sissouno, Aditya Viswanathan, and Mark A. Iwen,
    A Provably Accurate Algorithm for Recovering Compactly Supported Smooth Functions from Spectrogram Measurements (preprint),
    European Signal Processing Conference (EUSIPCO), 2020.
  5. Mark A. Iwen, Eric Lybrand, Aaron A. Nelson, and Rayan Saab,
    New Algorithms and Improved Guarantees for One-Bit Compressed Sensing on Manifolds (preprint),
    Sampling Theory and Applications (SampTA), 2019.
  6. Sjoerd Dirksen, Mark A. Iwen, Sara Krause-Solberg, and Johannes Maly,
    Robust One-bit Compressed Sensing With Manifold Data (preprint),
    Sampling Theory and Applications (SampTA), 2019.
  7. Alp Ozdemir, Ali Zare, Mark A. Iwen, and Selin Aviyente,
    Multiscale Analysis for Higher-order Tensors (preprint),
    Proc. of SPIE Optical Engineering + Applications, San Diego, CA, 2019.
  8. Sami Merhi, Aditya Viswanathan, and Mark A. Iwen,
    Recovery of Compactly Supported Functions from Spectrogram Measurements via Lifting (preprint),
    Sampling Theory and Applications (SampTA), 2017.
    ~Slides with additional experiments are available here.~
  9. Mark A. Iwen, Brian Preskitt, Rayan Saab, and Aditya Viswanathan,
    Phase Retrieval from Local Measurements in Two Dimensions (preprint),
    Proc. of SPIE Optical Engineering + Applications, San Diego, CA, 2017.
  10. Jade Larriva-Latt*, Angela Morrison*, Alison Radgowski*, Joseph Tobin*, Mark Iwen, and Aditya Viswanathan,
    Edge-Augmented Fourier Partial Sums with Applications to Magnetic Resonance Imaging (MRI) (preprint, code),
    Proc. of SPIE Optical Engineering + Applications, San Diego, CA, 2017. *Undergraduate Student
  11. Alp Ozdemir, Marisel Villafane-Delgado, David Zhu, Mark A. Iwen, and Selin Aviyente,
    Multi-Scale Higher Order Singular Value Decomposition (MS-HOSVD) for Resting-State FMRI Compression and Analysis (preprint),
    IEEE Internl Conf on Acoustics, Speech, and Signal Proc. (ICASSP), 2017.
  12. Alp Ozdemir, Mark A. Iwen, and Selin Aviyente,
    Multiscale Tensor Decomposition (preprint),
    50th Asilomar Conf. on Sig., Sys., and Comp., Pacific Grove, CA, 2016.
  13. Alp Ozdemir, Mark A. Iwen, and Selin Aviyente,
    A Multiscale Approach for Tensor Denoising (preprint),
    IEEE Statistical Signal Processing Workshop (SSP), 2016.
  14. Alp Ozdemir, Mark A. Iwen, and Selin Aviyente,
    Locally Linear Low-rank Tensor Approximation (preprint),
    GlobalSIP, 2015.
  15. Aditya Viswanathan & Mark A. Iwen,
    Fast Compressive Phase Retrieval (preprint),
    49th Asilomar Conf. on Sig., Sys., and Comp., Pacific Grove, CA, 2015.
  16. Aditya Viswanathan & Mark A. Iwen,
    Fast Angular Synchronization for Phase Retrieval via Incomplete
    Information     (preprint),
    Proc. of SPIE Optics + Photonics, San Diego, CA, 2015.
  17. M.A. Iwen & Rayan Saab,
    Random encoding of quantized finite frame expansions (preprint),
    Proc. of SPIE Wavelets XV, San Diego, CA, 2013.
  18. Guangliang Chen, Mark Iwen, Sang Chin, and Mauro Maggioni,
    A Fast Multiscale Framework for Data in High-Dimensions: Measure Estimation, Anomaly Detection, and Compressive Measurements (preprint),
    Visual Comm. and Image Proc. (VCIP), 2012.
  19. M. A. Iwen and A. H. Tewfik,
    Adaptive Compressed Sensing for Sparse Signals in Noise (preprint),
    45th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, 2011.
  20. I.B. Segal* and M.A. Iwen,
    Signal Approximation via the Gopher Fast Fourier Transform (preprint, code),
    AIP Conf. Proc., Vol. 1301, pp. 494 -- 504, June, 2010. *Undergraduate Student.
    Please also see this scholarship established in Ben's honor.
  21. M. A. Iwen
    Group Testing Strategies for Recovery of Sparse Signals in Noise (preprint),
    43rd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, 2009.
  22. M. A. Iwen
    Simple Deterministically Constructible RIP Matrices with Sublinear Fourier Sampling Requirements (preprint),
    43rd Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, 2009.
  23. M. A. Iwen
    Empirical Evaluation of Two Deterministic Sparse Fourier Transforms (preprint, code),
    43rd Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, 2009.
  24. Anna C. Gilbert, M. A. Iwen, and Martin J. Strauss,
    Group Testing and Sparse Signal Recovery (preprint),
    42nd Asilomar Conference on Signals, Systems, and Computers, Monterey, CA, 2008.
  25. M. A. Iwen & C. V. Spencer,
    Improved Bounds for a Deterministic Sublinear-Time Sparse Fourier Algorithm (preprint),
    42nd Annual Conference on Information Sciences and Systems (CISS), Princeton, NJ, 2008.
  26. M. A. Iwen, W. Lang, and J. Patel,
    Scalable Rule-Based Gene Expression Data Classification
    (preprint [Extended Version - BST Classification]),
    IEEE International Conference on Data Engineering (ICDE), 2008.
  27. M. A. Iwen,
    A Deterministic Sub-linear Time Sparse Fourier Algorithm via Non-adaptive Compressed Sensing Methods (preprint, code),
    ACM-SIAM Symposium on Discrete Algorithms (SODA), San Francisco, CA, 2008.
  28. M. A. Iwen, G. S. Mandair, M. D. Morris, M. Strauss,
    Fast Line-Based Imaging of Small Sample Features (preprint),
    IEEE International Conference on Acoustics, Speech, and Signal Processing(ICASSP), Honolulu, Hawaii, April 2007.
  29. Jason Laska, Sami Kirolos, Yehia Massoud, Richard Baraniuk, Anna Gilbert, Mark Iwen, Martin Strauss,
    Random Sampling for Analog-to-Information Conversion of Wideband Signals (preprint),
    IEEE Dallas Circuits and Systems Workshop (DCAS), Dallas, TX, 2006.
  30. Mark Iwen & Amol D. Mali,
    DSatz: A Directional SAT Solver for Planning (preprint.pdf),
    Proceedings of IEEE International Conference on Tools with Artificial Intelligence (ICTAI), Washington D.C., November 2002, pp. 199-208.
  31. Mark Iwen & Amol D. Mali, Distributed Graphplan (preprint.pdf),
    Proceedings of IEEE International Conference on Tools with Artificial Intelligence (ICTAI), Washington D.C., November 2002, pp. 138-145.
  32. Mark Iwen & Amol D. Mali, Automatic Problem Decomposition for Distributed Planning (preprint.pdf),
    Proceedings of the International Conference on Artificial Intelligence (IC-AI), Vol. 1, Las Vegas, June 2002, pp. 411-417.
  33. Mark Iwen & Amol D. Mali, Interaction Graphs for Planning Problem Decomposition (preprint.pdf),
    Proceedings of international conference on autonomous agents and multi-agent systems (AAMAS), Italy, 2002, pp. 984-985.

Technical Reports

  1. M.A. Iwen, Benjamin Schmidt, Arman Tavakoli,
    Characterizing Unit Spheres in Euclidean Spaces via Reach and Volume, Unpublished Report, February 12, 2022.
  2. Jade Larriva-Latt, Angela Morrison, Alison Radgowski, Joseph Tobin, Aditya Viswanathan, and Mark Iwen,
    Technical Report: Improved Fourier Reconstruction using Jump Information with Applications to MRI (preprint, code),
    Unpublished Report, October 12, 2016.
  3. Mark Iwen, Felix Krahmer, and Aditya Viswanathan,
    Technical Note: A Minor Correction of Theorem 1.3 from [1] ,
    Unpublished Note, April 23, 2015.
  4. Shengyuan Chen, Emilie Danna, Kory Hedman, Mark Iwen, Wei Kang, John Marriott, Anders Nottrott, George Yin, and Qing Zhang,
    Battery Storage Control for Steadying Renewable Power Generation (preprint),
    IMA Preprint Series #2373, July, 2011.
  5. Ian Besse, Patrick Campbelly, Julianne Chungz, Malena I. Espanolx, Mark Iwen, Edward Keyes, and Qingshuo Song,
    Integrated Circuit Layout Reconstruction (preprint),
    IMA Mathematical Modeling in Industry Workshop, 2005.