Tuesday, October 15, 2019 - 4:15pm - 6:00pm
- On Non-Convex Regularization for Convex Signal Processing
Ivan Selesnick (New York University)
Some effective and systematic approaches for nonlinear signal processing are based on sparse and low-rank signal models. Often, the L1 norm (or nuclear norm) is used, but this tends to underestimate the true values. We present non-convex alternatives to the L1 norm (and nuclear norm). Unlike other non-convex regularizers, the proposed regularizer is designed to maintain the convexity of the objective function to be minimized. Thus, we can retain beneficial properties of both convex and non-convex regularization. The new regularizer can be understood in terms of a generalized Moreau envelope. We present new results applying these ideas to total variation signal denoising.
- The iterative convolution-thresholding method (ICTM) for image segmentation
Dong Wang (The University of Utah)
We propose a novel iterative convolution-thresholding method (ICTM) that is applicable to a range of variational models for image segmentation. A variational model usually minimizes an energy functional consisting of a fidelity term and a regularization term. In the ICTM, the interface between two different segment domains is implicitly represented by their characteristic functions. The fidelity term is then written as a linear functional of the characteristic functions and the regularized term is approximated by a functional of characteristic functions in terms of heat kernel convolution. This allows us to design an iterative convolution-thresholding method to minimize the approximate energy. The method is simple, efficient and enjoys the energy-decaying property. Numerical experiments show that the method is easy to implement, robust and applicable to various image segmentation models.