A Compensated Shrinkage Affine Projection Algorithm for Debiased Sparse Adaptive Filtering

In this paper, we propose a novel sparse adaptive filtering algorithm termed compensated shrinkage affine projection algorithm (CS-APA). Our cost function is the sum of a time-varying data fidelity term and a difference-of-convex (DC) type nonconvex sparse regularizer. The regularizer includes the well known MC and SCAD penalty as special instances, thus leading to sparse estimation with small bias. Leveraging the DC structure of the regularizer, the nonconvex forward-backward splitting algorithm can be applied to the cost function, whereby the proposed CS-APA is derived. We present several favourable properties of CS-APA, including its mean stability analysis. Numerical examples demonstrate the superiority of CS-APA with comparisons to existing methods.