Results 11  20
of
57
Analysis and Synthesis of PseudoPeriodic Job Arrivals in Grids: A Matching Pursuit Approach
 In Proceedings of the Seventh IEEE International Symposium on Cluster Computing and the Grid, Rio De Janeiro
, 2007
"... Pseudoperiodicity is one of the basic job arrival patterns on dataintensive clusters and Grids. In this paper, a signal decomposition methodology called matching pursuit is applied for analysis and synthesis of pseudoperiodic job arrival processes. The matching pursuit decomposition is well lo ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
Pseudoperiodicity is one of the basic job arrival patterns on dataintensive clusters and Grids. In this paper, a signal decomposition methodology called matching pursuit is applied for analysis and synthesis of pseudoperiodic job arrival processes. The matching pursuit decomposition is well localized both in time and frequency, and it is naturally suited for analyzing nonstationary as well as stationary signals. The stationarity of the processes can be quantitatively measured by permutation entropy, with which the relationship between stationarity and modeling complexity is excellently explained. Quantitative methods based on the power spectrum are also provided to measure the degree of periodicity present in the data. Matching pursuit is further shown to be able to extract patterns from signals, which is an attractive feature from a modeling perspective. Real world workload data from production clusters and Grids are used to empirically evaluate the proposed measures and methodologies. 1
Sparsifying Subband Decompositions
 Proc. of IEEE Workshop on Appl. of Sig. Proc. to Audio and Acoustics
, 2003
"... We present a solution for constructing overcomplete sparse subband decompositions. This is a generalization of the perturbed basis pursuit problem [2] specifically applied to an overcomplete subband representation. Our formulation is based upon the iterative reweighted least squares algorithm and c ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
We present a solution for constructing overcomplete sparse subband decompositions. This is a generalization of the perturbed basis pursuit problem [2] specifically applied to an overcomplete subband representation. Our formulation is based upon the iterative reweighted least squares algorithm and can be given a probabilistic interpretation. Although the convergence properties of this algorithm are known to be slow, we observe experimentally that only a few iterates are sufficient to generate a reasonably sparse approximation. Furthermore using subband bases provides us with an algorithm whose complexity grows linearly in time.
Convergence of a Sparse Representations Algorithm Applicable to Real or Complex Data
 IEEE Journ. of STSP
, 2007
"... Abstract—Sparse representations has become an important topic in recent years. It consists in representing, say, a signal (vector) as a linear combination of as few as possible components (vectors) from a redundant basis (of the vector space). This is usually performed, either iteratively (adding a ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
Abstract—Sparse representations has become an important topic in recent years. It consists in representing, say, a signal (vector) as a linear combination of as few as possible components (vectors) from a redundant basis (of the vector space). This is usually performed, either iteratively (adding a component at a time), or globally (selecting simultaneously all the needed components). We consider a specific algorithm, that we obtain as a fixed point algorithm, but that can also be seen as an iteratively reweighted leastsquares algorithm. We analyze it thoroughly and show that it converges to the global optimum. We detail the proof in the real case and indicate how to extend it to the complex case. We illustrate the result with some easily reproducible toy simulations, that further illustrate the potential tracking properties of the proposed algorithm. Index Terms—Convergence of numerical methods, fixedpoint algorithms, iterative methods, minimization methods, spectral analysis. I.
A prototype system for object coding of musical audio
 in Proc. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA
"... This article deals with low bitrate object coding of musical audio, and more precisely with the extraction of pitched sound objects in polyphonic music. After a brief review of existing methods, we discuss the potential benefits of recasting this problem in a Bayesian framework. We define pitched ob ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
This article deals with low bitrate object coding of musical audio, and more precisely with the extraction of pitched sound objects in polyphonic music. After a brief review of existing methods, we discuss the potential benefits of recasting this problem in a Bayesian framework. We define pitched objects by a set of probabilistic priors and derive efficient algorithms to infer active objects and their parameters. Preliminary experiments suggest that the proposed method results in a better sound quality than simple sinusoidal coding while achieving a lower bitrate. 1.
A Geometrical Study of Matching Pursuit parametrization
"... This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) g ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be applied. The main contribution of this paper is twofold. First, we prove that if a discrete dictionary reaches a minimal density criterion, then the corresponding discrete MP (dMP) is equivalent in terms of convergence to a weakened hypothetical continuous MP. Interestingly, the corresponding weakness factor depends on a density measure of the discrete dictionary. Second, we show that the insertion of a simple geometric gradient ascent optimization on the atom dMP selection maintains the previous comparison but with a weakness factor at least two times closer to unity than without optimization. Finally, we present numerical experiments confirming our theoretical predictions for decomposition of signals and images on regular discretizations of dictionary parametrizations.
Global Testing under Sparse Alternatives: ANOVA, Multiple Comparisons and the Higher Criticism
"... Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a commo ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern highdimensional settings. Suppose we have p covariates and that under the alternative, the response only depends upon on the order of p 1−α of those, 0 ≤ α ≤ 1. Under moderate sparsity levels, i.e. 0 ≤ α ≤ 1/2, we show that ANOVA is essentially optimal under some conditions on the design. This is no longer the case under strong sparsity constraints, i.e. α> 1/2. In such settings, a multiple comparison procedure is often preferred and we establish its optimality when α ≥ 3/4. However, these two very popular methods are suboptimal, and sometimes powerless, under moderately strong sparsity where 1/2 < α < 3/4. We suggest a method based on the Higher Criticism that is powerful in the whole range α> 1/2. This optimality property is true for a variety of designs, including the classical (balanced) multiway designs and more modern ‘p> n ’ designs arising in genetics and signal processing. In addition to the standard fixed effects model, we establish similar results for a random effects model where the nonzero coefficients of the regression vector are normally distributed.
Sparse Decomposition over MultiComponent Redundant Dictionaries
"... In many applications  such as compression, denoising and source separation  a good and efficient signal representation is characterized by sparsity. This means that many coefficients are close to zero, while only few ones have a nonnegligible amplitude. On the other hand, realworld signals  su ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
In many applications  such as compression, denoising and source separation  a good and efficient signal representation is characterized by sparsity. This means that many coefficients are close to zero, while only few ones have a nonnegligible amplitude. On the other hand, realworld signals  such as audio or natural images  clearly present peculiar structures. In this paper we introduce a global optimization framework that aims at respecting the sparsity criterion while decomposing a signal over an overcomplete, multicomponent dictionary. We adopt a probabilistic analysis which can lead to consider the signal internal structure. As an example that fits this framework, we propose the Weighted Basis Pursuit algorithm, based on the solution of a convex, nonquadratic problem. Results show that this method can provide sparse signal representations and sparse mterms approximations. Moreover, Weighted Basis Pursuit provides a faster convergence compared to Basis Pursuit.
BAYESIAN COMPUTATIONAL MODELS FOR INHARMONICITY IN MUSICAL INSTRUMENTS
"... In this paper we describe recent advances in harmonic models for musical signal analysis. In particular we consider cases where inharmonic musical instruments are present. A particular model corresponding to a plucked string instrument is adopted and its parameters are automatically estimated from t ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
In this paper we describe recent advances in harmonic models for musical signal analysis. In particular we consider cases where inharmonic musical instruments are present. A particular model corresponding to a plucked string instrument is adopted and its parameters are automatically estimated from the data. In addition we describe new Bayesian prior distributions for musical pitch, which allow automatic adjustment to the pitch of the instruments, adaptive modelling of harmonic decay across frequency and automatic selection of the basis function window length. The methods are implemented using sophisticated MCMC algorithms and results demonstrated on a small set of examples, including harpsichord and guitar. The methods are readily adapted to polyphonic settings for pitch transcription and can be expected to lead to improvements in that setting. 1.
Singlechannel mixture decomposition using Bayesian harmonic models
 in Proc. ICA, 2006
, 2006
"... Abstract. We consider the source separation problem for singlechannel music signals. After a brief review of existing methods, we focus on decomposing a mixture into components made of harmonic sinusoidal partials. We address this problem in the Bayesian framework by building a probabilistic model ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. We consider the source separation problem for singlechannel music signals. After a brief review of existing methods, we focus on decomposing a mixture into components made of harmonic sinusoidal partials. We address this problem in the Bayesian framework by building a probabilistic model of the mixture combining generic priors for harmonicity, spectral envelope, note duration and continuity. Experiments suggest that the derived blind decomposition method leads to better separation results than nonnegative matrix factorization for certain mixtures. 1
Sparse Representation in Structured Dictionaries With Application to Synthetic Aperture Radar
"... Abstract—Sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently. In this paper, we develop a new, heuristic, graphstructured, sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictiona ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract—Sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently. In this paper, we develop a new, heuristic, graphstructured, sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries and whose dictionary elements can be arranged in a hierarchy. Around this algorithm, we construct a methodology for advanced image formation in wideangle synthetic aperture radar (SAR), defining an approach for joint anisotropy characterization and image formation. Additionally, we develop a coordinate descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation using that dictionary. The motivation is to characterize a phenomenon in wideangle SAR that has not been given much attention before: migratory scattering centers, i.e., scatterers whose apparent spatial location depends on aspect angle. Finally, we address the topic of recovering solutions that are sparse in more than one objective domain by introducing a suitable sparsifying cost function. We encode geometric objectives into SAR image formation through sparsity in two domains, including the normal parameter space of the Hough transform. Index Terms—Hough transforms, inverse problems, optimization methods, overcomplete dictionaries, sparse signal representations, synthetic aperture radar, tree searching. I.