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.
|Journal||Journal of Scientific Computing|
|State||Published - Apr 2021|
Bibliographical notePublisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Compressed sensing
- Error function
- Iterative reweighted L
ASJC Scopus subject areas
- Theoretical Computer Science
- Numerical Analysis
- Engineering (all)
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics