# On the strong convergence of forward-backward splitting in reconstructing jointly sparse signals

arXiv: https://arxiv.org/abs/1711.02591 · HTML: https://mlsanity.com/paper/1711.02591/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2017.

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

- [Orthogonally weighted ℓ2,1 regularization for rank-aware joint sparse recovery: algorithm and analysis](https://mlsanity.com/paper/2311.12282/) (2023)

## Abstract (arXiv)

We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be infinite-dimensional, and [28], which extends the aforementioned work to the joint sparse recovery of finite number of infinite-dimensional vectors. In our case, to take account of the joint sparsity and promote the coupling of nonvanishing components, we employ a convex relaxation approach with mixed norm penalty ℓ2,1. This paper discusses the computation of the solutions of linear inverse problems with such relaxation by a forward-backward splitting algorithm. However, since the solution matrix possesses infinitely many columns, the arguments of [17] no longer apply. As such, we establish new strong convergence results for the algorithm, in particular when the set of jointly sparse vectors is infinite.