Advances in Multiscale Hierarchical Decomposition Methods for Image Restoration
This talk will present the multiscale hierarchical decomposition method (MHDM) for image restoration and scale separation, building on the framework introduced by Tadmor, Nezzar, and me.
Overview
The method utilizes variational techniques and regularization. I will show how to extend the initial MHDM idea to (1) image restoration in the presence of multiplicative noise and (2) the highly ill-posed, challenging blind deblurring problem. I will discuss the existence and uniqueness of solutions for the proposed models, provide convergence properties, and state a discrepancy principle stopping criterion that prevents recovering excess noise in the multiscale reconstruction. Comprehensive numerical experiments and comparisons demonstrate the validity of the models for image denoising and deblurring. Beyond image restoration, these methods have the added benefit of recovering multiple scales of an image, which provide features of interest. This is joint work with Joel Barnett, Stefan Kindermann, Wen Li, Elena Resmerita, and Tobias Wolf.
Presenters
Luminita Vese, Professor of Mathematics, University of California, Los Angeles (UCLA)
Brief Biography
Luminita Vese is a Professor of Mathematics at the University of California, Los Angeles (UCLA). Her research focuses on mathematical image processing, including active contour models, level-set methods, variational image restoration, segmentation, and multiscale analysis. She completed her doctorate at the University of Nice Sophia Antipolis in 1997, joined the UCLA faculty in 2002, and is a recipient of a Sloan Research Fellowship. She is co-author of the textbook “Variational Methods in Image Processing” with Carole Le Guyader.