Frank-Wolfe Algorithm for the Exact Sparse Problem
This addresses sparse signal recovery for applications like compressed sensing, but it appears incremental as it applies an existing algorithm to a specific problem with theoretical guarantees.
The paper tackles the Exact Sparse reconstruction problem using the Frank-Wolfe algorithm, proving that under quasi-incoherent dictionaries, it selects atoms from the support at each iteration and converges exponentially fast beyond a certain point.
In this paper, we study the properties of the Frank-Wolfe algorithm to solve the \ExactSparse reconstruction problem. We prove that when the dictionary is quasi-incoherent, at each iteration, the Frank-Wolfe algorithm picks up an atom indexed by the support. We also prove that when the dictionary is quasi-incoherent, there exists an iteration beyond which the algorithm converges exponentially fast.