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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.

In this paper, we present a novel method for joint estimation of the fundamental frequency and order of a set of harmonically related sinusoids based on the MUSIC estimation criterion. The presented method, termed HMUSIC, is shown to have an efficient implementation using FFTs. Furthermore, refined estimates can be obtained using a gradient-based method. Illustrative examples of the application of the algorithm to real-life speech and audio signals are given, and the statistical performance of the estimator is evaluated using synthetic signals, demonstrating its good statistical properties.

We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.

We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to μ-strongly convex objective functions with L-Lipschitz continuous gradient. In the framework of Nesterov both μ and L are assumed known-an assumption that is seldom satisfied in practice. We propose to incorporate mechanisms to estimate locally sufficient μ and L during the iterations. The mechanisms also allow for the application to non-strongly convex functions. We discuss the convergence rate and iteration complexity of several first-order methods, including the proposed algorithm, and we use a 3D tomography problem to compare the performance of these methods. In numerical simulations we demonstrate the advantage in terms of faster convergence when estimating the strong convexity parameter μ for solving ill-conditioned problems to high accuracy, in comCommunicated by Erkki Somersalo. 330 T.L. Jensen et al.parison with an optimal method for non-strongly convex problems and a first-order method with Barzilai-Borwein step size selection.

This paper describes new algorithms and related software for total variation (TV) image reconstruction, more specifically: denoising, inpainting, and deblurring. The algorithms are based on one of Nesterov's first-order methods, tailored to the image processing applications in such a way that, except for the mandatory regularization parameter, the user needs not specify any parameters in the algorithms. The software is written in C with interface to Matlab (version 7.5 or later), and we demonstrate its performance and use with examples.

In this contribution we focus on the problem of power spectral density (PSD) estimation from multiple microphone signals in reverberant and noisy environments. The PSD estimation method proposed in this paper is based on the maximum likelihood (ML) methodology. In particular, we derive a novel ML PSD estimation scheme that is suitable for sound scenes which besides speech and reverberation consist of an additional noise component whose second-order statistics are known. The proposed algorithm is shown to outperform an existing similar algorithm in terms of PSD estimation accuracy. Moreover, it is shown numerically that the mean squared estimation error achieved by the proposed method is near the limit set by the corresponding Cramér-Rao lower bound. The speech dereverberation performance of a multi-channel Wiener filter (MWF) based on the proposed PSD estimators is measured using several instrumental measures and is shown to be higher than when the competing estimator is used. Moreover, we perform a speech intelligibility test where we demonstrate that both the proposed and the competing PSD estimators lead to similar intelligibility improvements.

Psychoacoustical models have been used extensively within audio coding applications over the past decades. Recently, parametric coding techniques have been applied to general audio and this has created the need for a psychoacoustical model that is specifically suited for sinusoidal modelling of audio signals. In this paper, we present a new perceptual model that predicts masked thresholds for sinusoidal distortions. The model relies on signal detection theory and incorporates more recent insights about spectral and temporal integration in auditory masking. As a consequence, the model is able to predict the distortion detectability. In fact, the distortion detectability defines a (perceptually relevant) norm on the underlying signal space which is beneficial for optimisation algorithms such as rate-distortion optimisation or linear predictive coding. We evaluate the merits of the model by combining it with a sinusoidal extraction method and compare the results with those obtained with the ISO MPEG-1 Layer I-II recommended model. Listening tests show a clear preference for the new model. More specifically, the model presented here leads to a reduction of more than 20% in terms of number of sinusoids needed to represent signals at a given quality level