Sparse constraint affine projection algorithm with parallel implementation and application in compressive sensing

Based on affine projection algorithm (APA) in adaptive filtering and the technique of parallel computing, we propose a novel algorithm called ℓ₀-APA with its parallel implementation for sparse system identification and sparse signal recovery. For sparse system identification, parallel ℓ₀-APA can serve as an effective approach for practical hardware implementation, since it lowers the requirement on the processors´ clock speed. For sparse signal recovery, it can significantly reduce the convergence time. Prior algorithms such as ℓ₀-LMS and ℓ₀-ZAP can be seen as special cases of ℓ₀-APA. Finally the performance of the proposed algorithm is analyzed and verified by numerical experiments.