# Deterministic guarantees for $L^{1}$-reconstruction: A large sieve approach with geometric flexibility

## TL;DR

This paper develops large sieve methods to provide deterministic guarantees for $L^{1}$-reconstruction across various geometries, enabling reliable recovery from incomplete or corrupted data.

## Contribution

It introduces a geometric large sieve approach to establish $L^{1}$-reconstruction guarantees on multiple geometries, expanding the theoretical framework for signal recovery.

## Key findings

- Derived $p$-concentration ratio estimates for different geometries
- Established $L^{1}$-reconstruction guarantees using large sieve techniques
- Applied methods to line, sphere, plane, and hyperbolic disc geometries

## Abstract

We present estimates of the $p$-concentration ratio for various function spaces on different geometries including the line, the sphere, the plane, and the hyperbolic disc, using large sieve methods. Thereby, we focus on $L^{1}$-estimates which can be used to guarantee the reconstruction from corrupted or partial information.