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Adapted and adaptive linear timefrequency representations: a synthesis point of view
, 2013
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Gabor dual windows using convex optimization
"... Abstract—Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal `2norm dual window, is widely used. This window function however, might lack desirable properties, such as good timefrequency concentration, small suppor ..."
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Abstract—Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal `2norm dual window, is widely used. This window function however, might lack desirable properties, such as good timefrequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the WexlerRaz equations and optimizing various constraints. Numerical experiments show that alternate dual windows with considerably improved features can be found. I.
Recovery of Discontinuous Signals Using Group Sparse Higher Degree Total Variation
"... AbstractWe introduce a family of novel regularization penalties to enable the recovery of discrete discontinuous piecewise polynomial signals from undersampled or degraded linear measurements. The penalties promote the group sparsity of the signal analyzed under a nth order derivative. We introduc ..."
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AbstractWe introduce a family of novel regularization penalties to enable the recovery of discrete discontinuous piecewise polynomial signals from undersampled or degraded linear measurements. The penalties promote the group sparsity of the signal analyzed under a nth order derivative. We introduce an efficient alternating minimization algorithm to solve linear inverse problems regularized with the proposed penalties. Our experiments show that promoting group sparsity of derivatives enhances the compressed sensing recovery of discontinuous piecewise linear signals compared with an unstructured sparse prior. We also propose an extension to 2D, which can be viewed as a group sparse version of higher degree total variation, and illustrate its effectiveness in denoising experiments.
EMPLOYING PHASE INFORMATION FOR AUDIO DENOISING
"... Spectral audio denoising methods usually make use of the magnitudes of a timefrequency representation of the signal. However, if the timefrequency frame consists of quadrature pairs of atoms (as in the shorttime Fourier transform), then the phases of the coefficients also follow a predictable p ..."
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Spectral audio denoising methods usually make use of the magnitudes of a timefrequency representation of the signal. However, if the timefrequency frame consists of quadrature pairs of atoms (as in the shorttime Fourier transform), then the phases of the coefficients also follow a predictable pattern, for which simple models are viable. In this paper, we propose a scheme that takes into account the phase information of the signals for the audio denoising problem. The scheme requires to minimize a cost function composed of a diagonally weighted quadrature data term and a fusedlasso type penalty. We formulate the problem as a saddle point search problem and propose an algorithm that numerically finds the solution. Based on the optimality conditions of the problem, we present a guideline on how to select the parameters of the problem. We discuss the performance and the influence of the parameters through experiments. Index Terms — Audio denoising, nonnegative garrote, total variation, fused lasso, audio phase.
SIMILARITY INDUCED GROUP SPARSITY FOR NONNEGATIVE MATRIX FACTORISATION
"... Nonnegative matrix factorisations are used in several branches of signal processing and data analysis for separation and classification. Sparsity constraints are commonly set on the model to promote discovery of a small number of dominant patterns. In group sparse models, atoms considered to belo ..."
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Nonnegative matrix factorisations are used in several branches of signal processing and data analysis for separation and classification. Sparsity constraints are commonly set on the model to promote discovery of a small number of dominant patterns. In group sparse models, atoms considered to belong to a consistent group are permitted to activate together, while activations across groups are suppressed, reducing the number of simultaneously active sources or other structures. Whereas most group sparse models require explicit division of atoms into separate groups without addressing their mutual relations, we propose a constraint that permits dynamic relationships between atoms or groups, based on any defined distance measure. The resulting solutions promote approximation with components considered similar to each other. Evaluation results are shown for speech enhancement and noise robust speech and speaker recognition. Index Terms — nonnegative matrix factorization, group sparsity, sparse representations, speech recognition, speaker recognition 1.
DESIGNING GABOR WINDOWS USING CONVEX OPTIMIZATION
"... Abstract. Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal `2norm dual window, is widely used. This window function however, might lack desirable properties, such as good timefrequency concentration, small suppor ..."
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Abstract. Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal `2norm dual window, is widely used. This window function however, might lack desirable properties, such as good timefrequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the WexlerRaz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found. 1.
1Forest Sparsity for Multichannel Compressive Sensing
, 2014
"... In this paper, we investigate a new compressive sensing model for multichannel sparse data where each channel can be represented as a hierarchical tree and different channels are highly correlated. Therefore, the full data could follow the forest structure and we call this property as forest spars ..."
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In this paper, we investigate a new compressive sensing model for multichannel sparse data where each channel can be represented as a hierarchical tree and different channels are highly correlated. Therefore, the full data could follow the forest structure and we call this property as forest sparsity. It exploits both intra and inter channel correlations and enriches the family of existing modelbased compressive sensing theories. The proposed theory indicates that only O(Tk+ log(N/k)) measurements are required for multichannel data with forest sparsity, where T is the number of channels, N and k are the length and sparsity number of each channel respectively. This result is much better than O(Tk + T log(N/k)) of tree sparsity, O(Tk + k log(N/k)) of joint sparsity, and far better than O(Tk + Tk log(N/k)) of standard sparsity. In addition, we extend the forest sparsity theory to the multiple measurement vectors problem, where the measurement matrix is a blockdiagonal matrix. The result shows that the required measurement bound can be the same as that for dense random measurement matrix, when the data shares equal energy in each channel. A new algorithm is developed and applied on four example applications to validate the benefit of the proposed model. Extensive experiments demonstrate the effectiveness and efficiency of the proposed theory and algorithm. Index Terms forest sparsity, structured sparsity, compressed sensing, modelbased compressive sensing, tree sparsity, joint sparsity Copyright (c) 2013 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubspermissions@ieee.org.
HYBRID MODEL AND STRUCTURED SPARSITY FOR UNDERDETERMINED CONVOLUTIVE AUDIO SOURCE SEPARATION
, 2014
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.