# On recoverability of discrete time signals from sparse observations

## TL;DR

This paper explores conditions under which discrete time signals can be reliably reconstructed from incomplete and sparse observations, demonstrating that many signals are recoverable even with very limited data.

## Contribution

It introduces broad classes of signals that are densely recoverable from sparse, non-periodic observations under mild conditions.

## Key findings

- Wide classes of signals are densely recoverable from sparse observations.
- Robust linear recovery of finite traces is possible with minimal restrictions.
- Recovery is feasible even with arbitrarily sparse, non-periodic data.

## Abstract

The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable signals and such that signals from these classes feature robust linear recoverability of their finite traces under very mild restrictions on the location of the observed data. In particular, the case arbitrarily sparse and non-periodic subsequences of observations are not excluded.