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Simultaneous codeword optimization (SimCO) for dictionary update and learning
 IEEE Trans. Signal Process
, 2012
"... Abstract—We consider the datadriven dictionary learning problem. The goal is to seek an overcomplete dictionary from which every training signal can be best approximated by a linear combination of only a few codewords. This task is often achieved by iteratively executing two operations: sparse cod ..."
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Abstract—We consider the datadriven dictionary learning problem. The goal is to seek an overcomplete dictionary from which every training signal can be best approximated by a linear combination of only a few codewords. This task is often achieved by iteratively executing two operations: sparse coding and dictionary update. In the literature, there are two benchmark mechanisms to update a dictionary. The first approach, for example the MOD algorithm, is characterized by searching for the optimal codewords while fixing the sparse coefficients. In the second approach, represented by the KSVD method, one codeword and the related sparse coefficients are simultaneously updated while all other codewords and coefficients remain unchanged. We propose a novel framework that generalizes the aforementioned two methods. The unique feature of our approach is that one can update an arbitrary set of codewords and the corresponding sparse coefficients simultaneously: when sparse coefficients are fixed, the underlying optimization problem is the same as that in the MOD algorithm; when only one codeword is selected for update, it can be proved that the proposed algorithm is equivalent to the KSVD method; and more importantly, our method allows to update all codewords and all sparse coefficients simultaneously, hence the term simultaneously codeword optimization (SimCO). Under the proposed framework, we design two algorithms, namely the primitive and regularized SimCO. Simulations demonstrate that our approach excels the benchmark KSVD in terms of both learning performance and running speed. I.
Sharp recovery bounds for convex demixing, with applications
, 2014
"... Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a secon ..."
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Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis, and the problem of decomposing an observed matrix into a lowrank matrix plus a sparse matrix. This paper describes and analyzes a framework, based on convex optimization, for solving these demixing problems, and many others. This work introduces a randomized signal model which ensures that the two structures are incoherent, i.e., generically oriented. For an observation from this model, this approach identifies a summary statistic that reflects the complexity of a particular signal. The difficulty of separating two structured, incoherent signals depends only on the total complexity of the two structures. Some applications include (i) demixing two signals that are sparse in mutually incoherent bases; (ii) decoding spreadspectrum transmissions in the presence of impulsive errors; and (iii) removing sparse corruptions from a lowrank matrix. In each case, the theoretical analysis of the convex demixing method closely matches its empirical behavior.
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.
Representations
"... Abstract—Recovering missing or distorted audio signal samples has been recently improved by solving an Audio Inpainting problem. This paper aims to connect this problem with KSVD dictionary learning to improve reconstruction error for missing signal insertion problem. Our aim is to adapt an initia ..."
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Abstract—Recovering missing or distorted audio signal samples has been recently improved by solving an Audio Inpainting problem. This paper aims to connect this problem with KSVD dictionary learning to improve reconstruction error for missing signal insertion problem. Our aim is to adapt an initial dictionary to the reliable signal to be more accurate in missing samples estimation. This approach is based on sparse signals reconstruction and optimization problem. In the paper two staple algorithms, connection between them and emerging problems are described. We tried to find optimal parameters for efficient dictionary learning.
On Inpainting the Adress Algorithm
"... Abstract — The Adress algorithm has been demonstrated to be capable of separating sound sources from instantaneous linear mixtures, provided that the sources have a unique pan position in the stereo field. However, a shortcoming of the Adress algorithm is that all timefrequency bins outside of the ..."
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Abstract — The Adress algorithm has been demonstrated to be capable of separating sound sources from instantaneous linear mixtures, provided that the sources have a unique pan position in the stereo field. However, a shortcoming of the Adress algorithm is that all timefrequency bins outside of the chosen azimuth range are set to zero, resulting in audible artifacts in the resynthesised sound. Here we show that an inpainting algorithm based on NMF is capable of estimating these missing values and improves on the results obtained using Adress only.
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.
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"... pp W on a ogy stitu Tec ed line nel factorization) have been demonstrated effective to mitisample size is 8 bits, and Fig. 2 shows two realworld clipped speech signals with and without automatic gain adjustment, respectively. Although often ignored in speaker recognition, the clipping phenomenon ..."
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pp W on a ogy stitu Tec ed line nel factorization) have been demonstrated effective to mitisample size is 8 bits, and Fig. 2 shows two realworld clipped speech signals with and without automatic gain adjustment, respectively. Although often ignored in speaker recognition, the clipping phenomenon has gained much attention in other fields
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.
Electrotechnics, Signals and Systems Advances in Telecommunications International Journal of
"... Systems (IJATES2) is an allelectronic international scientific journal with the aim to bring the most recent and unpublished research and development results in the area of electronics to the scientific and technical societies, and is supported by the ISES (International Science and Engineering Soc ..."
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Systems (IJATES2) is an allelectronic international scientific journal with the aim to bring the most recent and unpublished research and development results in the area of electronics to the scientific and technical societies, and is supported by the ISES (International Science and Engineering Society, o.s.). The journal’s scope covers all the aspects of telecommunication, signal processing, theory and design of circuits and systems for electronics. The IJATES2 is ready to publish experimental and theoretical full papers and letters submitted by prospective authors. Paper submitted for publication must be written in English and must follow a prescribed format. All papers are subjected to a critical peerreview prior to publication. The IJATES2 is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. This journal provides immediate