Collaborative Research:
Trust-Search Methods for Inverse Problems in Imaging

Principal Investigators:
Roummel Marcia, University of California, Merced
Jennifer Erway, Wake Forest University
Supported by NSF Grants CMMI-1333326 and CMMI-1334042


Abstract. The research objective of this award is to develop and implement first-order trust-search methods for use in large-scale data-generated optimization problems. Data-generated problems arise in applications such as signal and image processing. These problems are especially difficult to solve since the data are often high dimensional and are noisy, incomplete, and/or inexact. This research will develop first-order quasi-Newton trust-search methods for solving large data-generated problems. The methods to be used are trust-search methods, which are hybridizations of the most fundamental types of methods for unconstrained optimization: trust-region methods and line-search methods. Trust-search methods seek to implement line-search strategies in combination with trust-region theoretics to obtain more robust methods.

Publications. This research grant has thus far resulted in the following articles:
  1. Shape-changing L-SR1 trust-region methods,
    Johannes Brust, Oleg Burdakov, Jennifer Erway, Roummel Marcia, and Ya-xiang Yuan,
    Submitted (available here).
  2. Trust-region methods for sparse relaxation,
    Lasith Adhikari, Jennifer Erway, Shelby Lockhart*, and Roummel Marcia,
    Submitted.
  3. On solving limited-memory quasi-Newton equations,
    Jennifer Erway and Roummel Marcia,
    Submitted (paper available here and here).
  4. On solving L-SR1 trust-region subproblems,
    Johannes Brust, Jennifer Erway and Roummel Marcia,
    Accepted to Computational Optimization and Applications (paper available here and here; code available here).
  5. Sparse reconstruction for fluorescence lifetime imaging microscopy with Poisson noise,
    Lasith Adhikari, Arnold Kim, and Roummel Marcia,
    Accepted to the 2016 IEEE Global Conference on Signal and Information Processing in Washington, DC.
  6. Nonconvex sparse Poisson intensity reconstruction for time-dependent bioluminescence tomography,
    Lasith Adhikari, Arnold Kim, and Roummel Marcia,
    Accepted to the 2016 International Symposium on Information Theory and Its Applications in Monterey, CA.
  7. Trust-region methods for nonconvex sparse recovery optimization,
    Lasith Adhikari, Jennifer Erway, Roummel Marcia, and Robert Plemmons,
    Accepted to the 2016 International Symposium on Information Theory and Its Applications in Monterey, CA.
  8. Bounded sparse photon-limited image recovery,
    Lasith Adhikari and Roummel Marcia,
    2016 IEEE International Conference on Image Processing. [doi]
  9. Constrained variant detection with SPaRC: Sparsity, parental relatedness, and coverage,
    Mario Banuelos, Rubi Almanza, Lasith Adhikari, Roummel Marcia, and Suzanne Sindi,
    Proceedings of the 2016 International Conference of the IEEE Engineering in Medicine and Biology Society.
  10. Sparse genomic structural variant detection: Exploiting parent-child relatedness for signal recovery,
    Mario Banuelos, Rubi Almanza, Lasith Adhikari, Roummel Marcia, and Suzanne Sindi,
    Proceedings of the 2016 IEEE Workshop on Statistical Signal Processing.
  11. Sparse signal recovery methods for variant detection in next-generation sequencing data,
    Mario Banuelos, Rubi Almanza, Lasith Adhikari, Suzanne Sindi, and Roummel Marcia,
    Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing.
  12. Analysis of p-norm regularized subproblem minimization for sparse photon-limited image recovery,
    Aramayis Orkusyan*, Lasith Adhikari, Joanna Valenzuela*, and Roummel Marcia,
    Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing.
  13. On efficiently computing the eigenvalues of limited-memory quasi-Newton matrices,
    Jennifer Erway and Roummel Marcia,
    SIAM Journal on Matrix Analysis and Applications, 36:3, pp. 1338-1359, 2015. [doi]
  14. p-th power total variation regularization in photon-limited imaging via iterative reweighting,
    Lasith Adhikari and Roummel Marcia,
    Proceedings of the 2015 European Signal Processing Conference, Nice, France. [link]
  15. Lasith Adhikari, Dianwen Zhu, Changqing Li, and Roummel Marcia,
    Nonconvex reconstruction for low-dimensional fluorescence molecular tomographic Poisson observations,
    Proceedings of the 2015 IEEE International Conference on Image Processing, Quebec City, Quebec, Canada.
  16. Nonconvex relaxation for Poisson intensity reconstruction,
    Lasith Adhikari and Roummel Marcia,
    Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing. [doi]
  17. MSS: MATLAB Software for L-BFGS Trust-Region Subproblems for Large-Scale Optimization,
    Jennifer Erway and Roummel Marcia,
    ACM Transactions on Mathematical Software, 40:4, pp. 1-12, 2014. [doi]
  18. Shifted L-BFGS systems,
    Jennifer Erway, Vibhor Jain*, and Roummel Marcia,
    Optimization Methods and Software, 29:5, pp. 992-1004, 2014. [doi]
  19. Shifted limited-memory DFP systems,
    Jennifer Erway, Vibhor Jain*, and Roummel Marcia,
    Proceedings of 2013 Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA. [doi]
* Undergraduate student

Codes. Software implementation of some of the algorithms above are available here.

Presentations. The results of this grant have been presented at the following conferences, workshops, and seminars:

2016 International Symposium on Information Theory and Its Applications, Monterey, CA, November, 2016 (link)
2016 IEEE International Conference on Image Processing, Phoenix, AZ, September, 2016 (link)
2016 ICCOPT, Tokyo, Japan, August, 2016 (link)
2016 SIAM Annual Conference, Boston, MA, July, 2016 (link here and here)
2016 SIAM Conference on the Life Sciences Boston, MA, July, 2016 (link)
2016 IEEE Statistical Signal Processing Mallorca, Spain, June, 2016 (link here and here)
2016 International Conference on Machine Learning, New York, NY, June, 2016 (link)
2016 IEEE International Conference on Acoustics, Speech and Signal Processing, Shanghai, China, March, 2016 (link here and here)
2015 SIAM Conference in Applied Linear Algebra, Atlanta, GA, October, 2015 (link)
2015 IEEE International Conference in Image Processing, Quebec, Canada, September 2015 (link)
2015 European Signal Processing Conference, Nice, France, August, 2015 (link)
22nd International Symposium on Mathematical Programming, Pittsburgh, PA, July, 2015 (link here, here, and here)
2015 IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, Australia, April, 2015 (link)
Workshop on Multiscale Modeling and Computation of Nano-Optics, East Lansing, MI, August, 2014
2013 Asilomar Conference on Signals, Systems, and Computers, Asilomar, CA November, 2013 (link)
2013 SIAM Annual Meeting, San Diego, CA July, 2013 (link)
2013 ICCOPT, Lisbon, Portugal July, 2013 (link here and here)


2015 REU Supplement.

This grant supported Aramayis Orkusyan, an undergraduate math major at Fresno State
(pictured here with graduate student, Lasith Adhikari, at the 2015 Undergraduate Summer Research Symposium at UC Merced).

Any opinions, findings and conclusions or recommendations expressed in the publications supported by this grant are those of the author(s) and do not necessarily reflect the views of the NSF.