Piecewise linear source separation
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEPublished 14 November 2003Open access
Rémi Gribonval
Citations46
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
A new framework, called piecewise linear separation, for blind source separation of possibly degenerate mixtures, including the extreme case of a single mixture of several sources is proposed.
Abstract
International audience
Keywords
Computer Science
Elsevier eBooksA Wavelet Tour of Signal Processing
16,401 Citations1999Stéphane Mallat
An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
IEEE Transactions on Information TheoryDe-noising by soft-thresholding
9,411 Citations1995David L. Donoho
The authors prove two results about this type of estimator that are unprecedented in several ways: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures.
IEEE Transactions on Signal ProcessingMatching pursuits with time-frequency dictionaries
9,115 Citations1993Stéphane Mallat, Zhifeng Zhang
The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
SIAM Journal on Scientific ComputingAtomic Decomposition by Basis Pursuit
6,899 Citations1998Scott Shaobing Chen, David L. Donoho +1 more
Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
NatureEmergence of simple-cell receptive field properties by learning a sparse code for natural images
5,840 Citations1996Bruno A. Olshausen, David J. Field
It is shown that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex.
SIAM ReviewAtomic Decomposition by Basis Pursuit
5,145 Citations2001Scott Shaobing Chen, David L. Donoho +1 more
IEEE Transactions on Information TheoryGreed is Good: Algorithmic Results for Sparse Approximation
3,648 Citations2004Joel A. Tropp
This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries and develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal.
IEEE Transactions on Information TheoryEntropy-based algorithms for best basis selection
3,173 Citations1992Ronald R. Coifman, Mladen Victor Wickerhauser
Adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals, and relies heavily on the remarkable orthogonality properties of the new libraries.
Proceedings of the National Academy of SciencesOptimally sparse representation in general (nonorthogonal) dictionaries via ℓ <sup>1</sup> minimization
2,941 Citations2003David L. Donoho, Michael Elad
This article obtains parallel results in a more general setting, where the dictionary D can arise from two or several bases, frames, or even less structured systems, and sketches three applications: separating linear features from planar ones in 3D data, noncooperative multiuser encoding, and identification of over-complete independent component models.
Vision ResearchThe “independent components” of natural scenes are edge filters
2,269 Citations1997Anthony J. Bell, T. J. Sejnowski
It is shown that a new unsupervised learning algorithm based on information maximization, a nonlinear "infomax" network, when applied to an ensemble of natural scenes produces sets of visual filters that are localized and oriented.
IEEE Transactions on Information TheoryUncertainty principles and ideal atomic decomposition
1,967 Citations2001David L. Donoho, Xiaoming Huo
It is proved that if S is representable as a highly sparse superposition of atoms from this time-frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the l/sup 1/ norm of the coefficients among all decompositions.
Proceedings of the IEEEBlind signal separation: statistical principles
1,852 Citations1998J.-F. Cardoso
The objectives of this paper are to review some of the approaches that have been developed to address blind signal separation and independent component analysis, to illustrate how they stem from basic principles, and to show how they relate to each other.
Neural ComputationBlind Source Separation by Sparse Decomposition in a Signal Dictionary
754 Citations2001Michael Zibulevsky, Barak A. Pearlmutter
Nature NeuroscienceEfficient coding of natural sounds
692 Citations2002Michael S. Lewicki
It is reported that several basic auditory nerve fiber tuning properties can be accounted for by adapting a population of filter shapes to encode natural sounds efficiently.
IEEE Transactions on Information TheoryOn Sparse Representations in Arbitrary Redundant Bases
569 Citations2004J.-J. Fuchs
The purpose of this contribution is to generalize some recent results on sparse representations of signals in redundant bases and give a sufficient condition for the unique sparsest solution to be the unique solution to both a linear program or a parametrized quadratic program.
Blind separation of disjoint orthogonal signals: demixing N sources from 2 mixtures
402 Citations2002Alexander Jourjine, Scott Rickard +1 more
A novel method for blind separation of any number of sources using only two mixtures when sources are (W-)disjoint orthogonal, that is, when the supports of the (windowed) Fourier transform of any two signals in the mixture are disjoint sets.
One Microphone Source Separation
390 Citations2000Sam T. Roweis
A technique called refiltering is presented which recovers sources by a nonstationary reweighting of frequency sub-bands from a single recording, and it is argued for the application of statistical algorithms to learning this masking function.
Ideal Denoising in an orthonormal basis chosen from a library of bases
245 Citations1994David L. Donoho, Iain M. Johnstone +1 more
IEEE Transactions on Signal ProcessingHarmonic decomposition of audio signals with matching pursuit
239 Citations2003Rémi Gribonval, Emmanuel Bacry
A simple note detection algorithm is described that shows how one could use a harmonic matching pursuit to detect notes even in difficult situations, e.g., very different note durations, lots of reverberation, and overlapping notes.
Approximation of functions over redundant dictionaries using coherence
190 Citations2003Anna C. Gilbert, S. Muthukrishnan +1 more
The technical crux of the result is the proof that two commonly used local search techniques, when combined appropriately, gives a provably near-optimal signal representation over redundant dictionaries with small coherence.
PROPOSALS FOR PERFORMANCE MEASUREMENT IN SOURCE SEPARATION
100 Citations2003Rémi Gribonval, Emmanuel Vincent +3 more
When the sources are estimated from a degenerate set of mixtures by applying a demixing matrix, it is proved that there are upper bounds on the achievable Source to Interference Ratio.
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).Non negative sparse representation for Wiener based source separation with a single sensor
93 Citations2004Laurent Benaroya, Lorcan Mc Donagh +2 more
This method generalizes Wiener filtering with locally stationary, non-Gaussian, parametric source models and uses a sparse non negative decomposition algorithm of its own to perform the separation of two sound sources from a single sensor.
Cambridge University Press eBooksBlind source separation by sparse decomposition in a signal dictionary
85 Citations2001Michael Zibulevsky, Barak A. Pearlmutter +2 more
This work suggests a two-stage separation process: a priori selection of a possibly overcomplete signal dictionary in which the sources are assumed to be sparsely representable, followed by unmixing the sources by exploiting the their sparse representability.
IEEE International Conference on Acoustics Speech and Signal ProcessingSparse decomposition of stereo signals with Matching Pursuit and application to blind separation of more than two sources from a stereo mixture
63 Citations2002Rémi Gribonval
A method of sparse decomposition of stereo audio signals is developed, and its application to blind separation of more than two sources from only two linear mixtures is tested.
Network Computation in Neural SystemsLearning the higher-order structure of a natural sound
55 Citations1996Anthony J. Bell, Terrence J. Sejnowski
Analysis of sound signals with high resolution matching pursuit
52 Citations2002Rémi Gribonval, Emmanuel Bacry +3 more
A high resolution matching pursuit is developed: it is a fast, high time-resolution, time-frequency analysis algorithm, that makes it likely to be used far musical applications.
WIENER BASED SOURCE SEPARATION WITH HMM/GMM USING A SINGLE SENSOR
42 Citations2003Laurent Benaroya
This method generalizes the Wiener filtering with Gaussian Mixture distributions and with Hidden Markov Models and derives a new algorithm for the re-estimation of the sources with these mixture models, during the separation phase.
Statistical properties of STFT ratios for two channel systems and applications to blind source separation
39 Citations2000Radu Bălan
This paper analyzes and extends a source separation method based on the use of STFT ratios of two sensor inputs, called DUET, and proves that considerably weaker assumptions about the classes of input signals are required to apply the derived techniques.
Clustering approach to square and non-square blind source separation
38 Citations2003Marc M. Van Hulle
A new heuristic is introduced that relies on the tendency of the mixture samples to cluster around the source directions in mixture space to solve BSS problems with not only square but also non-square mixing matrices.
On underdetermined source separation
37 Citations1999Anas Abu Taleb, Christian Jutten
It is shown that the sources can be restored up to an arbitrary additive random vector in the particular case of discrete sources, very relevant for digital communications, and this vector is certain.
ALGEBRAIC OVERCOMPLETE INDEPENDENT COMPONENT ANALYSIS
36 Citations2003Khurram Waheed, Fathi M. Salem
Overcomplete ICA is solved in two stages, AICA is used to estimate the rectangular mixing matrix, which is followed by optimal source inferencing using L1 norm based interior point LP technique, and some practical techniques are discussed to enhance the algebraic resolution of the AICA solution for cases where some of the columns of the mixing matrix are algebraically “close” to each other.
IEEE International Conference on Acoustics Speech and Signal ProcessingSparse decomposition of stereo signals with matching pursuit and application to blind separation of more than two sources from a stereo mixture
25 Citations2002Gribonval
BLIND SEPARATION OF POSITIVE SOURCES USING NON-NEGATIVE PC A
21 Citations2003Erkki Oja, Mark D. Plumbley +1 more
This paper proposes the use of a ‘Non-Negative PCA’ algorithm which is a special case of the nonlinear PCA algorithm, but with a rectification nonlinearity, and shows that this algorithm will find such non-negative well-grounded independent sources.
University of Regensburg Publication Server (University of Regensburg)A HISTOGRAM-BASED OVERCOMPLETE ICA ALGORITHM
18 Citations2003Fabian J. Theis, Carlos G. Puntonet +1 more
A new approach based on an estimated histogram of the sensor data is presented, which searches for the points fulfilling the overcomplete Geometric Convergence Condition, which has been shown to be a limit condition of overcomplete geometric BSS.
Independent component analysis of largely underdetermined mixtures
17 Citations2003Lieven De Lathauwer, Bart De Moor +2 more
Algebraic means for Independent Component Analysis (ICA) with more sources than sensors with bounds on the number of sources that generically guarantee uniqueness of the decomposition is derived.
Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEApproximation with highly redundant dictionaries
16 Citations2003Rmi Gribonval, Morten Nielsen
It is proved that any decomposition has this nice property if the number of its nonzero coefficients does not exceed a quantity which is called the spread of the dictionary, and how much approximation power can be gained by replacing a single basis with such redundant dictionaries is discussed.
