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Sparse Signal Reconstruction Modeling for MEG Source Localization Using Non-convex Regularizers

Samarasinghe, Kasun M
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439304367

Abstract Details

2015, PhD, University of Cincinnati, Engineering and Applied Science: Electrical Engineering.
This thesis introduces the usage of non-convex based regularizers to solve the underdetermined MEG inverse problem.The signal to be reconstructed is considered to have a structure which entails group-wise sparsity and within group sparsity among its covariates. We discuss the usage of Ι2 norm regularization and smoothed Ι0 (SL0) norm regularization to impose group-wise and within group sparsity respectively. In addition, we introduce a novel criterion which if satisfied, guarantees global optimality while solving this non-convex optimization problem. We use proximal gradient descent as the method of optimization as it promises faster convergence rates. Initially, we show that our algorithm successfully recovers sparse signals with a smaller number of measurements than the conventional Ι1 regularization framework. We also support this claim using MEG source localization simulations and extend the reconstruction for both stationary and non-stationary signals. Next, we formulate a global convergence analysis for the novel algorithm. Finally, we incorporate novel information criteria techniques and concepts of duality to find the best set of regularization parameters and a proper stopping criterion respectively. We were able to successfully illustrate that the regularization parameters (models) with lower information criteria performs better than the ones with higher information criteria. Also, concepts of duality provides the necessary tools to determine when to stop the algorithm, which is an important contribution considering the non- differentiability of the objective function.
H. Howard Fan, Ph.D. (Committee Chair)
Donald French, Ph.D. (Committee Member)
William Wee, Ph.D. (Committee Member)
Jing Xiang, Ph.D. (Committee Member)
Xuefu Zhou, Ph.D. (Committee Member)
166 p.
Engineering
MEG Source Localization; Non-convex optimization; l0 norm; group sparsity; duality; information criteria

Recommended Citations

Citations

  • Samarasinghe, K. M. (2015). Sparse Signal Reconstruction Modeling for MEG Source Localization Using Non-convex Regularizers [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439304367

    APA Style (7th edition)

  • Samarasinghe, Kasun. Sparse Signal Reconstruction Modeling for MEG Source Localization Using Non-convex Regularizers. 2015. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439304367.

    MLA Style (8th edition)

  • Samarasinghe, Kasun. "Sparse Signal Reconstruction Modeling for MEG Source Localization Using Non-convex Regularizers." Doctoral dissertation, University of Cincinnati, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439304367

    Chicago Manual of Style (17th edition)

ucin1439304367
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© 2015, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.