Online system identification under non-negativity and ℓ1-norm constraints algorithm and weight behavior analysis

Information processing with ℓ₁-norm constraint has been a topic of considerable interest during the last five years since it produces sparse solutions. Non-negativity constraints are also desired properties that can usually be imposed due to inherent physical characteristics of real-life phenomena. In this paper, we investigate an online method for system identification subject to these two families of constraints. Our approach differs from existing techniques such as projected-gradient algorithms in that it does not require any extra projection onto the feasible region. The mean weight-error behavior is analyzed analytically. Experimental results show the advantage of our approach over some existing algorithms. Finally, an application to hyperspectral data processing is considered.