A Novel Regularization Based on the Error Function for Sparse Recovery

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 norm, e.g., $L_1$ and $L_2$ norms. In this paper, we propose a novel framework that uses error function to approximate unit step function. It can be considered surrogate for $L_0$ norm. The asymptotic behavior of with respect its intrinsic parameter indicates proposed standard $L_0$, norms approaches $0$ $\infty,$ respectively. Statistically, it is also less biased than approach. We then incorporate into either constrained or unconstrained model when recovering sparse signal from under-determined linear system. Computationally, both solved via iterative reweighted (IRL1) algorithm guaranteed convergence. A large number experimental results demonstrate approach outperforms state-of-the-art methods various recovery scenarios.