A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing
This work addresses the problem of efficiently solving linear systems with sparse or minimal-TV solutions, particularly for scenarios where linear measurements are slow and expensive to obtain, representing an incremental advancement in optimization methods.
The paper proposed an algorithmic framework for computing sparse or minimal-TV solutions of linear systems, including new methods like a sparse Kaczmarz solver, and demonstrated its utility in applications such as online compressed sensing, TV tomographic reconstruction, and radio interferometry.
An algorithmic framework to compute sparse or minimal-TV solutions of linear systems is proposed. The framework includes both the Kaczmarz method and the linearized Bregman method as special cases and also several new methods such as a sparse Kaczmarz solver. The algorithmic framework has a variety of applications and is especially useful for problems in which the linear measurements are slow and expensive to obtain. We present examples for online compressed sensing, TV tomographic reconstruction and radio interferometry.