# A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing

arXiv: https://arxiv.org/abs/1403.7543 · HTML: https://mlsanity.com/paper/1403.7543/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2014.

## Built on by (most cited first, 4 of 4)

- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [Iterative regularization for low complexity regularizers](https://mlsanity.com/paper/2202.00420/) (2022)
- [A Note on Randomized Kaczmarz Algorithm for Solving Doubly-Noisy Linear Systems](https://mlsanity.com/paper/2308.16904/) (2023)
- [ALS: Augmented Lagrangian Sketching Methods for Linear Systems](https://mlsanity.com/paper/2208.06152/) (2022)

## Abstract (arXiv)

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.