Fast algorithms for high-order sparse linear prediction with applications to speech processing

Abstract

In speech processing applications, imposing sparsity constraints on high-order linear prediction coefficients and prediction residuals has proven successful in overcoming some of the limitation of conventional linear predictive modeling. However, this modeling scheme, named sparse linear prediction, is generally formulated as a linear programming problem that comes at the expenses of a much higher computational burden compared to the conventional approach. In this paper, we propose to solve the optimization problem by combining splitting methods with two approaches: the Douglas-Rachford method and the alternating direction method of multipliers. These methods allow to obtain solutions with a higher computational efficiency, orders of magnitude faster than with general purpose software based on interior-point methods. Furthermore, computational savings are achieved by solving the sparse linear prediction problem with lower accuracy than in previous work. In the experimental analysis, we clearly show that a solution with lower accuracy can achieve approximately the same performance as a high accuracy solution both objectively, in terms of prediction gain, as well as with perceptually relevant measures, when evaluated in a speech reconstruction application.

Computational analysis of a fast algorithm for high-order sparse linear prediction

“…Similarly to what was done in [38], we processed only the vowel and semivowel phones [45] from the TIMIT database (sampled at 16 kHz), belonging to 3696 sentences from 462 speakers. We chose the ones of duration of at least 640 samples (40 ms) for a total of about 40,000 voiced speech frames.…”

“…We chose the ones of duration of at least 640 samples (40 ms) for a total of about 40,000 voiced speech frames. We extend the analysis in [38] by investigating the prediction gain from the ADMM solution with a different number of iterations and compare with the IP solution obtained through the CVX+SeDuMi interface and solver. In both formulation of the SLP problem (5), we chose γ = 0.12 obtained through a modified version of the L-curve [46] by using all except 50 frames picked randomly that will be used as a test set.…”

“…While theoretically achieving the highest prediction gain, it can be seen that the solution was quite similar to the ones obtained with SLP with a significant lower number of non-zero coefficients. In particular, the cardinality of the solutions obtained through ADMM and IP were truncated to the 21 largest values to compare to traditional two step LP and LTP while the 2-norm unconstrained LP retains all 250 nonzero coefficients [38]. FFT IP ADMM HO2 Fig.…”

“…This paper deals with understanding the trade-offs occurring in choosing a proper and fixed number of iterations for the ADMM algorithm and extends the analysis and algorithms presented in [30,38]. We note that we will apply an ADMM algorithm in its straightforward form but several variants and extensions may be useful for solving the sparse linear prediction problem efficiently and may be considered for further investigations.…”

A variational EM method for pole-zero modeling of speech with mixed block sparse and Gaussian excitation

“…Motivated by the compressive sensing research, a least 1-norm criterion is proposed for voiced speech analysis [9], where sparse priors on both the excitation signals and prediction coefficients are utilized. Fast methods and the stability of the 1-norm cost function for spectral envelope estimation are further investigated in [10], [11]. More recently, in [12], the excitation signal of speech is formulated as a combination of block sparse and white noise components to capture the block sparse or white This work was funded by the Danish Council for Independent Research, grant ID: DFF 4184-00056 noise excitation separately or simultaneously.…”