# Recovering linear images of sparse signals from indirect observations

arXiv: https://arxiv.org/abs/2609.06182 · HTML: https://mlsanity.com/paper/2609.06182/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theory](https://mlsanity.com/paper/1301.4240/) (2013)
- [High-dimensional simultaneous inference with the bootstrap](https://mlsanity.com/paper/1606.03940/) (2016)
- [Statistical Inference and Large-scale Multiple Testing for High-dimensional Regression Models](https://mlsanity.com/paper/2301.10392/) (2023)
- [On Design of Polyhedral Estimates in Linear Inverse Problems](https://mlsanity.com/paper/2212.12516/) (2022)
- [On Robust Recovery of Signals from Indirect Observations](https://mlsanity.com/paper/2309.06563/) (2023)

## Abstract (arXiv)

In this paper, we develop and analyze techniques for recovering a linear image Bx of an unknown signal x from indirect noisy observation ω=Ax+xi. It is em a priori known that x∈ cX, a given convex compact set, and that x is s-sparse---has at most s nonvanishing entries. The proposed estimates belong to a large family of recovery routines by ℓ1-minimization. However, unlike the classical result describing performance of such estimates, we do not make any special (and hard to check) assumptions about the sensing matrix A such as nullspace or Restricted Isometry condition and the like. As a consequence, parameters of the estimates and the upper bounds on their risks are not available in a closed analytic form, but are delivered instead by efficient computation as solutions to explicit convex optimization problems.