Work

Is the 1-norm the best convex sparse regularization?

Year: 2018

Type: preprint

Abstract: The 1-norm is a good convex regularization for the recovery of sparse vectors from under-determined linear measurements. No other convex regularization seems to surpass its sparse recovery performance. How can this be explained? To answer this question, we define several notions of "best" (convex) regulariza-tion in the context of general low-dimensional recovery and show that indeed the 1-norm is an optimal convex sparse regularization within this framework.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1806.08690

Authors: Traonmilin, Yann, Vaiter, Samuel, Gribonval, Rémi

Institutions: Centre National de la Recherche Scientifique, Institut de Mathématiques de Bordeaux, Université de Bourgogne, Institut de Mathématiques de Bourgogne

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2998747330

Cites: 8

Cited by:

Related to: 10