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Rachel A Ward

Associate Professor, Core Faculty
Department of Mathematics, Institute for Computational Engineering and Science

Applied harmonic analysis, statistics, optimization, probability

Office Location
RLM 10.144

Postal Address
The University of Texas at Austin
2515 SPEEDWAY, Stop C1200
AUSTIN, TX 78712-1202

Ph.D., Princeton University (2009)

Research Interests

Applied harmonic analysis, probability and numerical analysis

My research spans signal processing, numerical linear algebra, and statistics. Much of my work is in compressed sensing.

1. Coherent matrix completion (with Srinadh Bhojanapalli, Yudong Chen, and Sujay Sanghavi), submitted.

2. Testing goodness of fit for logistic regression (with Mark Tygert), submitted.

3. Beyond incoherence: stable and robust sampling strategies for compressive imaging (with Felix Krahmer), submitted.

4. A comparison of the discrete Kolmogorov-Smirnov statistic and the Euclidean distance (with Jacob Carruth and Mark Tygert), submitted.

5. Stability for second-order chaotic sigma-delta quantization (with Lauren Bandklayder), submitted.

6. Computing the confidence levels for a root-mean-square test of goodness-of-fit, Part II (with Will Perkins and Mark Tygert), submitted.

Journal Publications

7. Near-optimal compressed sensing guarantees for total variation minimization (with Deanna Needell), IEEE Transactions on Image Processing, 2013.

8. Testing Hardy-Weinberg equilibrium with a simple root-mean-square statistic (with Raymond Carroll), Biostatistics, 2013.

9. Stable image reconstruction using total variation minimization (with Deanna Needell), SIAM Journal on Imaging Science, 2013.

10. Some deficiencies of chi-square and classical exact tests of significance (with Will Perkins and Mark Tygert), Applied and Computational Harmonic Analysis, 2013.

11. A symbol-based bar code decoding algorithm (with Mark Iwen and Fadil Santosa), SIAM Journal on Imaging Science, Volume 6, Issue 1 (2013), 56-77.

12. Two-subspace projection method for coherent overdetermined systems (with Deanna Needell), Journal of Fourier Analysis and Applications, Volume 19, Issue 2 (2013), 256-269.

13. Weighted eigenfunction estimates with applications to compressed sensing (with Nicolas Burq, Semyon Dyatlov, and Maciej Zworski), SIAM Journal on Mathematical Analysis, Volume 44, Issue 5 (2012), 3481-3501 .

14. Sparse Legendre expansions via `1-minimization (with Holger Rauhut), Journal of Approximation Theory, Volume 164, Issue 5 (2012), 517-533.

15. Root-exponential accuracy for coarse quantization of finite frame expansions (with Felix Krahmer and Rayan Saab), IEEE Transactions on Information Theory, Volume 58, Issue 2 (2012), 1069-1079.

16. Lower bounds for the error decay incurred by coarse quantization schemes (with Felix Krahmer), Applied and Computational Harmonic Analysis, Volume 32, Issue 1 (2012), 131-138.

17. Low-rank matrix recovery via iteratively reweighted least squares minimization (with Massimo Fornasier and Holger Rauhut), SIAM Journal on Optimization, Volume 21 (2011), 1614-1640.

18. New and improved Johnson Lindenstrauss embeddings via the Restricted Isometry Property (with Felix Krahmer), SIAM Journal on Mathematical Analysis, Volume 43, Issue 3 (2011), 1269-1281.

19. Computing the confidence levels for a root-mean-square test of goodness-of-fit (with Will Perkins and Mark Tygert), Applied Mathematics and Computation, Volume 217, Issue 22 (2011).

20. On the complexity of Mumford-Shah type regularization, viewed as a relaxed sparsity constraint (with Boris Alexeev), IEEE Transactions on Image Processing, Volume 19, Number 10 (2010), 2787-2789.

21. Quiet sigma delta quantization, and global convergence for a class of asymmetric piecewise affine maps. Nonlinearity, Volume 23, Number 9 (2010).

22. Iterative thresholding meets free discontinuity problems (with Massimo Fornasier,) Foundations of Computational Mathematics, Volume 10, Number 5 (2010). 527-567.

23. Freedom through imperfection: Exploiting the flexibility offered by redundancy in signal processing. PhD thesis, Princeton University, 2009.

24. Compressed sensing with cross validation, IEEE Transactions on Information Theory, Volume 55, Issue 12 (2009), 5773-5782.

25. On robustness properties of golden ratio encoders and beta encoders, IEEE Transactions on Information Theory, Volume 54, Issue 9 (2008). 4324-4334.

26. Subfunctionalization: How often does it occur? How long does it take? (with Richard Durrett) Theoretical Population Biology 66, Issue 2 (2004), 93-100.

  • NSF CAREER Award 2013 - 2018
  • Air Force Young Investigator Award (AFOSR YIP) 2013 - 2016
  • Alfred P. Sloan Fellowship 2012
  • DOD-Navy grant N00014-12-1-0743 2012-2014
  • Harrington Faculty Fellowship 2011-2012
  • NSF Mathematical Sciences Postdoctoral Research Fellowship 2009-2011
  • NSF Graduate Research Fellowship 2005-2008
  • Barry M. Goldwater Scholarship 2004-2005
  • National Merit Finalist 2001