Sparse Linear Prediction and Its Applications to Speech Processing

Abstract

The aim of this paper is to provide an overview of Sparse Linear Prediction, a set of speech processing tools created by introducing sparsity constraints into the linear prediction framework. These tools have shown to be effective in several issues related to modeling and coding of speech signals. For speech analysis, we provide predictors that are accurate in modeling the speech production process and overcome problems related to traditional linear prediction. In particular, the predictors obtained offer a more effective decoupling of the vocal tract transfer function and its underlying excitation, making it a very efficient method for the analysis of voiced speech. For speech coding, we provide predictors that shape the residual according to the characteristics of the sparse encoding techniques resulting in more straightforward coding strategies. Furthermore, encouraged by the promising application of compressed sensing in signal compression, we investigate its formulation and application to sparse linear predictive coding. The proposed estimators are all solutions to convex optimization problems, which can be solved efficiently and reliably using, e.g., interior-point methods. Extensive experimental results are provided to support the effectiveness of the proposed methods, showing the improvements over traditional linear prediction in both speech analysis and coding.

Real-time implementations of sparse linear prediction for speech processing

“…Stability is intrinsically guaranteed by the construction of the problem [3] and can be easily preserved by the numerical robustness of the Levinson recursion. Nevertheless, in LPC of speech, sparsity criteria have been shown to provide a valid alternative to the 2-norm minimization criterion, overcoming most of its deficiencies in modeling and coding [4][5][6][7][8]. In particular, in [6], a new formulation for speech coding is introduced that provides not only a sparse approximation of the prediction error, which allows for a simple coding strategy, but also a sparse approximation of a high-order predictor which successfully models jointly short-term and long-term redundancies.…”

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

“…, i − p − 1, and the optimal choice of these M − p indices yields the second term W i−p−1 (M − p). Since the index i − p is not included, the two terms simply add as in (27). The sum is then maximized over all choices of p. For p = 0, the right-hand side of (28) reduces to W i−1 (M ), i.e., the last index is not used.…”

“…Sparse linear prediction for speech coding is proposed in [27] using iteratively reweighted 1 minimization to promote sparsity in the residuals and improve coding performance.…”

An efficient solution to sparse linear prediction analysis of speech

“…The algorithm starts by plain l 1 -norm minimization and then, iteratively, the resulting residuals are used to re-weight the l 1 -norm cost function such that the points having larger residuals (outliers) are less penalized and the points having smaller residuals are penalized heavier. Hence, the optimizer encourages small values to become smaller while augmenting the amplitude of outliers [13].…”