[Amath-seminars] Jan. 26 - Special AMATH Seminar - Dominique Zosso (UCLA)

Ulrich Hetmaniuk hetmaniu at uw.edu
Wed Jan 20 11:24:41 PST 2016

Dear All,

We hope you can join us for our special AMATH seminar on Tuesday January

Speaker: Dominique Zosso, UCLA
Time: January 26th, 16h00
Location: DEM 004

Title: From Sparsity in Images and Information Science to Efficient PDE

There is a strong convergence between problems and methods in imaging, data
science and machine learning. Maybe more unexpectedly, elliptic PDEs
equally bear strong similarities with these imaging and data problems. In
this talk, I will present recent and ongoing research on numerical schemes
associated with optimization problems in imaging/data science, and
naturally related to elliptic PDEs. Recently, the primal-dual hybrid
gradients (PDHG) method has been revived. In our work, we realize that in
the particular yet frequent case of Dirichlet-energy problems, the proximal
update of the dual problem has an immediate, simple solution, and the dual
variable can be eliminated altogether. The resulting scheme is reduced to a
primal update problem that contains a momentum term, which significantly
boosts the convergence over standard gradient descent. Since elliptic PDEs
describe the minimizers of associated convex minimization problems, this
algorithm extends to the explicit, fast solution of elliptic PDE problems
without operator inversion. I will describe our algorithm in detail on a
simple Laplace problem and briefly analyze the dynamics of the resulting
optimization scheme. We then look at more interesting PDE and optimization
problems, ranging from classical image denoising, motion by mean curvature,
the obstacle problem, to nonconvex problems such as eigenfunctions of the
Schrödinger operator and pagerank on graphs. The proposed algorithms are
derived in a disciplined way, are simple to interpret and implement, and
generally fast.

Speaker webpage
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