On the Global-Local Dichotomy in Sparsity Modeling

Understand

The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches.

• While producing state-of-the-art results, this methodology is suboptimal, as it does not attempt to model the entire global signal in any meaningful way - a nontrivial task by itself.
• In this paper we propose a way to bridge this theoretical gap by constructing a global model from the bottom up.
• Given local sparsity assumptions in a dictionary, we show that the global signal representation must satisfy a constrained underdetermined system of linear equations, which can be solved efficiently by modern optimization methods such as Alternating Direction Method of Multipliers (ADMM).