Reduced complexity online sparse signal reconstruction using projections onto weighted ℓ1 balls

This paper presents a novel online method for sparse signal reconstruction. In particular, the notion of sub-dimensional projections is introduced, which allows a significant complexity reduction in the Adaptive Projection-based Algorithm using Weighted ℓ₁ balls (APWL1). This is achieved without sacrificing performance. The proposed method is evaluated in both stationary and time-varying environments and its performance is compared with state-of-the-art online and batch LASSO-based methods.