# On partial sparse recovery

arXiv: https://arxiv.org/abs/1304.2809 · HTML: https://mlsanity.com/paper/1304.2809/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2013.

## Built on by (most cited first, 1 of 1)

- [Distributional Hardness Against Preconditioned Lasso via Erasure-Robust Designs](https://mlsanity.com/paper/2203.02824/) (2022)

## Abstract (arXiv)

We consider the problem of recovering a partially sparse solution of an underdetermined system of linear equations by minimizing the ℓ1-norm of the part of the solution vector which is known to be sparse. Such a problem is closely related to a classical problem in Compressed Sensing where the ℓ1-norm of the whole solution vector is minimized. We introduce analogues of restricted isometry and null space properties for the recovery of partially sparse vectors and show that these new properties are implied by their original counterparts. We show also how to extend recovery under noisy measurements to the partially sparse case.