Vancouver, 7 - 10 décembre 2018
This work is done in collaboration with Prof. Eldad Haber (UBC), Dr. Christoph Schwarzbach (Computational Geosciences, Inc), and Dr. Wenke Wilhelms (UBC).
Our algorithms are based on the alternating direction method of multipliers and apply to models/images/video on small 2D and large 3D grids because we exploit computational similarity between constraint sets, coarse and fine-grained parallelism, and we also present a multilevel accelerated version.
To obtain more flexible descriptions of prior knowledge, we introduce a formulation that allows constraint sets to be the sum of intersections of sets, which is essentially an extension of a Minkowski set. This formulation builds on the success of additive image descriptions that are usually based on penalty methods, such as cartoon-texture decomposition and robust principal component analysis.
We show applications where we use multiple constraint sets to regularize partial-differential-equation based parameter estimation problems such as seismic waveform inversion, as well as various image and video processing and segmentation tasks.