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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(More)
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(More)
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 multiple signal classification (MUSIC) estimation criterion. The presented method, termed HMUSIC, is shown to have an efficient implementation using fast Fourier transforms (FFTs). Furthermore, refined(More)
We study the numerical and computational performance of three implementations of orthogonal matching pursuit: one using the QR matrix decomposition, one using the Cholesky matrix decomposition, and one using the matrix inversion lemma. We find that none of these implementations suffer from numerical error accumulation in the inner products or the solution.(More)
In this paper, the problem of noise reduction is addressed as a linear filtering problem in a novel way by using concepts from subspace-based enhancement methods, resulting in variable span linear filters. This is done by forming the filter coefficients as linear combinations of a number of eigenvectors stemming from a joint diagonalization of the(More)
We consider the problem of determining the order of a parametric model from a noisy signal based on the geometry of the space. More specifically, we do this using the nontrivial angles between the candidate signal subspace model and the noise subspace. The proposed principle is closely related to the subspace orthogonality property known from the MUSIC(More)
We present a distance measure between audio files designed to identify cover songs, which are new renditions of previously recorded songs. For each song we compute the chromagram, remove phase information and apply exponentially distributed bands in order to obtain a feature matrix that compactly describes a song and is insensitive to changes in(More)
This paper describes a novel speech coding concept created by introducing sparsity constraints in a linear prediction scheme both on the residual and on the prediction vector. The residual is efficiently encoded using well known multi-pulse excitation procedures due to its sparsity. A robust statistical method for the joint estimation of the short-term and(More)
In this article, we present a novel method for high-resolution joint direction-of-arrivals (DOA) and multi-pitch estimation based on subspaces decomposed from a spatio-temporal data model. The resulting estimator is termed multi-channel harmonic MUSIC (MC-HMUSIC). It is capable of resolving sources under adverse conditions, unlike traditional methods, for(More)