Model Selection with Low Complexity Priors

Understand

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated.

• A line of recent work has studied regularization models with various types of low-dimensional structures.
• In such settings, the general approach is to solve a regularized optimization problem, which combines a data fidelity term and some regularization penalty that promotes the assumed low-dimensional/simple structure.
• This paper provides a general framework to capture this low-dimensional structure through what we coin partly smooth functions relative to a linear manifold.