A Novel Regularization Based on the Error Function for Sparse Recovery

Weihong Guo, Yifei Lou, Jing Qin, Ming Yan

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norms. This paper proposes a novel regularization framework that uses the error function to approximate the unit step function. It can be considered as a surrogate function for the L norm. The asymptotic behavior of the error function with respect to its intrinsic parameter indicates that the proposed regularization can approximate the standard L, L1 norms as the parameter approaches to 0 and ∞, respectively. Statistically, it is also less biased than the L1 approach. Incorporating the error function, we consider both constrained and unconstrained formulations to reconstruct a sparse signal from an under-determined linear system. Computationally, both problems can be solved via an iterative reweighted L1 (IRL1) algorithm with guaranteed convergence. A large number of experimental results demonstrate that the proposed approach outperforms the state-of-the-art methods in various sparse recovery scenarios.

Original languageEnglish
Article number31
JournalJournal of Scientific Computing
Issue number1
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Biaseness
  • Compressed sensing
  • Error function
  • Iterative reweighted L
  • Sparsity

ASJC Scopus subject areas

  • Software
  • General Engineering
  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics
  • Numerical Analysis
  • Computational Theory and Mathematics


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