Successive approximation algorithm for LPC estimation using sparse residual constraint

Estimation of linear prediction coefficients under the sparsity constraint of the prediction residue, is a modification of the traditional minimum mean square error linear predictor formulation, which accounts for the impulse nature of the residual signal for voiced speech signals. This is solved using the 1-norm minimization approach under sparsity constraints. In this paper, we develop a successive approximation algorithm for estimating the linear predictor coefficients and the sparse residual signal. We illustrate the usefulness of the proposed approach using synthetic, and also real speech examples. Experimental results in a multi-pulse based analysis-synthesis show that the proposed approach can provide better perceptual quality speech reconstruction than the orthogonal matching pursuit based algorithm, with computational time much lower than convex optimization based techniques.