An efficient solution to sparse linear prediction analysis of speech

Abstract

We propose an efficient solution to the problem of sparse linear prediction analysis of the speech signal. Our method is based on minimization of a weighted l 2 -norm of the prediction error. The weighting function is constructed such that less emphasis is given to the error around the points where we expect the largest prediction errors to occur (the glottal closure instants) and hence the resulting cost function approaches the ideal l 0 -norm cost function for sparse residual recovery. We show that the efficient minimization of this objective function (by solving normal equations of linear least squares problem) provides enhanced sparsity level of residuals compared to the l 1 -norm minimization approach which uses the computationally demanding convex optimization methods. Indeed, the computational complexity of the proposed method is roughly the same as the classic minimum variance linear prediction analysis approach. Moreover, to show a potential application of such sparse representation, we use the resulting linear prediction coefficients inside a multi-pulse synthesizer and show that the corresponding multi-pulse estimate of the excitation source results in slightly better synthesis quality when compared to the classical technique which uses the traditional non-sparse minimum variance synthesizer.

Efficient GCI Detection for Efficient Sparse Linear Prediction

“…We have shown in [16] that a simple minimization of the weighted version of l 2 -norm cost function may lead to better sparsity properties, while avoiding stability issues. Indeed, the use of l 2 -norm cost function preserves the computational efficiency while the weighting function is used to cope with its exaggerative effect on outliers (by careful down-weighting of the cost function at those points).…”

“…(2) is straight-forward. Indeed, setting the derivative of the cost function to zero results in a set of normal equations that can be easily solved as explained in [16]. The weighting function is constructed in a way that it de-emphasizes the exaggerative effect of l 2 -norm on outliers.…”

“…Such sparse representation is beneficial for coding applications [9,13] and also leads in a more accurate estimation of human vocal tract system [11,16].…”

“…We have previously shown in [16] that the minimization of a weighted version of l 2 -norm results in a more sparse solution with less computational burden. In this approach, GCIs are considered as the points that have the potential of attaining largest norms of residuals and then a weighting function is constructed such that the prediction error is relaxed at those points.…”

“…Consequently, the weighted l 2 -norm objective function is minimized by the solution of normal equations of liner least squares problem. In [16] a powerful method called SEDREAMS [7] is employed for detection of GCIs and it is shown that the weighted l 2 -norm minimization achieves better sparsity properties compared to l 1 -norm minimization.…”