# Total Variation Minimization in Compressed Sensing

## TL;DR

This paper reviews recovery guarantees for total variation minimization in compressed sensing, highlighting the limitations of synthesis sparse approaches and extending results from Gaussian to subgaussian measurements.

## Contribution

It provides a comprehensive overview of total variation minimization in compressed sensing and introduces generalized guarantees for subgaussian measurement scenarios.

## Key findings

- Total variation minimization has specific recovery guarantees in compressed sensing.
- Synthesis sparse signal approaches are inadequate for total variation minimization.
- Recent results are extended from Gaussian to subgaussian measurement models.

## Abstract

This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is common for synthesis sparse signals fails and different techniques are necessary. Lastly, we discuss a generalizations of recent results for Gaussian measurements to the subgaussian case.