• A novel fidelity and regularity in image reconstruction
• On the Consistency of Feature SelectionWith Lasso for Non-linear Targets

A novel fidelity and regularity in image reconstruction

• joint work with: Weihong Guo (CWRU), Guohui Song (Clarkson Univ.).
• Presented at SIAM conference on Imaging Science, 2016, Minisymposia 38: recent developments in image reconstruction and restoration.
• Abstract. We propose a general framework for image reconstruction. The contributions are two-fold: instead of the traditional fidelity in measurement domain, we measure the closeness in a processing domain; for regularity, we selectively choose TV and fractional-order total variation in different regions to fuse the power and avoid drawbacks of each individual. Image measurements are projected onto one frame domain while regularizing the solution in another domain. Numerical experiments in non-uniform Fourier reconstruction show its advantages.
  • Code: in progress.

On the Consistency of Feature SelectionWith Lasso for Non-linear Targets

• Joint work with: Soumya Ray (CWRU), Weihong Guo (CWRU).
• Accepted: ICML 2016.
• Abstract. An important question in feature selection is whether a selection strategy recovers the “true” set of features, given enough data. We study this question in the context of the popular Least Absolute Shrinkage and Selection Operator (Lasso) feature selection strategy. In particular, we consider the scenario when the model is misspecified so that the learned model is linear while the underlying real target is nonlinear. Surprisingly, we prove that under certain conditions, Lasso is still able to recover the correct features in this case. We also carry out numerical studies to empirically verify the theoretical results and explore the necessity of the conditions under which the proof holds.
  • Code: in progress.