Monday, 16:15 - 16:40 h, Room: H 1012

 

Volkan Cevher
Nonconvex models with exact and approximate projections for constrained linear inverse problems

Coauthor: Anastasios Kyrillidis

 

Abstract:
Many natural and man-made signals exhibit a few degrees of freedom relative to their dimension due to natural parameterizations or constraints. The inherent low-dimensional structure of such signals are mathematically modeled via combinatorial and geometric concepts, such as sparsity, unions-of-subspaces, or spectral sets, and are now revolutionizing the way we address linear inverse problems from incomplete data.
In this talk, we describe a set of low-dimensional, nonconvex models for constrained linear inverse problems that feature exact and epsilon-approximate projections in polynomial time. We pay particular attention to structured sparsity models based on matroids, multi-knapsack, and clustering as well as spectrally constrained models. We describe a hybrid optimization framework which explicitly leverages these non-convex models along with additional convex constraints to improve recovery performance. We then analyze the convergence and approximation guarantees of our framework based on restrictions on the linear operator in conjunction with several well-known acceleration techniques, such as step-size selection, memory, splitting, and block coordinate descent.

 

Talk 3 of the invited session Mon.3.H 1012
"Nonsmooth optimization in imaging sciences I" [...]
Cluster 17
"Nonsmooth optimization" [...]

 

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