We propose a unified non-linear approach that offers an ef- ficient closed-form solution for the problem of sparse linear prediction analysis. The approach is based on our previous work for minimization of the weighted l2 -norm of the prediction error. The weighting of the l2 -norm is done in a way that less emphasis is given to the prediction error around the Glottal Closure Instants (GCI) as they are expected to attain the largest values of error and hence, the resulting cost function approaches the ideal l0 -norm cost function for sparse residual recovery. As such, the method requires knowledge of the GCIs. In this paper we use our recently developed GCI detection algorithm which is particularly suitable for this problem as it does not rely on residuals themselves for detection of GCIs. We show that our GCI detection algorithm provides slightly better sparsity properties in comparison to a recent powerful GCI detection algorithm. Moreover, as the computational cost of our GCI detection algorithm is quite low, the computational cost of the overall solution is considerably lower.