667 research outputs found
Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation
This paper concerns underdetermined linear instantaneous and convolutive
blind source separation (BSS), i.e., the case when the number of observed mixed
signals is lower than the number of sources.We propose partial BSS methods,
which separate supposedly nonstationary sources of interest (while keeping
residual components for the other, supposedly stationary, "noise" sources).
These methods are based on the general differential BSS concept that we
introduced before. In the instantaneous case, the approach proposed in this
paper consists of a differential extension of the FastICA method (which does
not apply to underdetermined mixtures). In the convolutive case, we extend our
recent time-domain fast fixed-point C-FICA algorithm to underdetermined
mixtures. Both proposed approaches thus keep the attractive features of the
FastICA and C-FICA methods. Our approaches are based on differential sphering
processes, followed by the optimization of the differential nonnormalized
kurtosis that we introduce in this paper. Experimental tests show that these
differential algorithms are much more robust to noise sources than the standard
FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for
linear instantaneous and convolutive underdetermined mixture
Identifiability for Blind Source Separation of Multiple Finite Alphabet Linear Mixtures
We give under weak assumptions a complete combinatorial characterization of
identifiability for linear mixtures of finite alphabet sources, with unknown
mixing weights and unknown source signals, but known alphabet. This is based on
a detailed treatment of the case of a single linear mixture. Notably, our
identifiability analysis applies also to the case of unknown number of sources.
We provide sufficient and necessary conditions for identifiability and give a
simple sufficient criterion together with an explicit construction to determine
the weights and the source signals for deterministic data by taking advantage
of the hierarchical structure within the possible mixture values. We show that
the probability of identifiability is related to the distribution of a hitting
time and converges exponentially fast to one when the underlying sources come
from a discrete Markov process. Finally, we explore our theoretical results in
a simulation study. Our work extends and clarifies the scope of scenarios for
which blind source separation becomes meaningful
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
Fourier PCA and Robust Tensor Decomposition
Fourier PCA is Principal Component Analysis of a matrix obtained from higher
order derivatives of the logarithm of the Fourier transform of a
distribution.We make this method algorithmic by developing a tensor
decomposition method for a pair of tensors sharing the same vectors in rank-
decompositions. Our main application is the first provably polynomial-time
algorithm for underdetermined ICA, i.e., learning an matrix
from observations where is drawn from an unknown product
distribution with arbitrary non-Gaussian components. The number of component
distributions can be arbitrarily higher than the dimension and the
columns of only need to satisfy a natural and efficiently verifiable
nondegeneracy condition. As a second application, we give an alternative
algorithm for learning mixtures of spherical Gaussians with linearly
independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected;
exposition improve
Blind identification of underdetermined mixtures of complex sources based on the characteristic function
International audienceIn this work we consider the problem of blind identification of underdetermined mixtures using the generating function of the observations. This approach had been successfully applied on real sources but had not been extended to the more attractive case of complex mixtures of complex sources. This is the main goal of the present study. By developing the core equation in the complex case, we arrive at a particular tensor stowage which involves an original tensor decomposition. Exploiting this decomposition, an algorithm is proposed to blindly estimate the mixing matrix. Three versions of this algorithm based on 2nd, 3rd and 4th-order derivatives of the generating function are evaluated on complex mixtures of 4-QAM and 8-PSK sources and compared to the 6-BIOME algorithm by means of simulation results
Joint Analysis of Multiple Datasets by Cross-Cumulant Tensor (Block) Diagonalization
International audienceIn this paper, we propose approximate diagonalization of a cross-cumulant tensor as a means to achieve independent component analysis (ICA) in several linked datasets. This approach generalizes existing cumulant-based independent vector analysis (IVA). It leads to uniqueness, identifiability and resilience to noise that exceed those in the literature, in certain scenarios. The proposed method can achieve blind identification of underdetermined mixtures when single-dataset cumulant-based methods that use the same order of statistics fall short. In addition, it is possible to analyse more than two datasets in a single tensor factorization. The proposed approach readily extends to independent subspace analysis (ISA), by tensor block-diagonalization. The proposed approach can be used as-is or as an ingredient in various data fusion frameworks, using coupled decompositions. The core idea can be used to generalize existing ICA methods from one dataset to an ensemble
- …