1,516 research outputs found
Blind separation of underdetermined mixtures with additive white and pink noises
This paper presents an approach for underdetermined
blind source separation in the case of additive Gaussian
white noise and pink noise. Likewise, the proposed approach is applicable in the case of separating I + 3 sources from I mixtures with additive two kinds of noises. This situation is more challenging and suitable to practical real world problems. Moreover, unlike to some conventional approaches, the sparsity conditions are not imposed. Firstly, the mixing matrix is estimated based on an algorithm that combines short time Fourier transform and rough-fuzzy clustering. Then, the mixed
signals are normalized and the source signals are recovered using modified Gradient descent Local Hierarchical Alternating Least Squares Algorithm exploiting the mixing matrix obtained from the previous step as an input and initialized by multiplicative algorithm for matrix factorization based on alpha divergence. The experiments and simulation results
show that the proposed approach can separate I + 3 source
signals from I mixed signals, and it has superior evaluation performance compared to some conventional approaches
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
Underdetermined blind source separation based on Fuzzy C-Means and Semi-Nonnegative Matrix Factorization
Conventional blind source separation is based on over-determined with more sensors than sources but the underdetermined is a challenging case and more convenient to actual situation. Non-negative Matrix Factorization (NMF) has been widely applied to Blind Source Separation (BSS) problems. However, the separation results are sensitive to the initialization of parameters of NMF. Avoiding the subjectivity of choosing parameters, we used the Fuzzy C-Means (FCM) clustering technique to estimate the mixing matrix and to reduce the requirement for sparsity. Also, decreasing the constraints is regarded in this paper by using Semi-NMF. In this paper we propose a new two-step algorithm in order to solve the underdetermined blind source separation. We show how to combine the FCM clustering technique with the gradient-based NMF with the multi-layer technique. The simulation results show that our proposed algorithm can separate the source signals with high signal-to-noise ratio and quite low cost time compared with some algorithms
Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples
This paper presents a novel power spectral density estimation technique for
band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The
technique employs multi-coset sampling and incorporates the advantages of
compressed sensing (CS) when the power spectrum is sparse, but applies to
sparse and nonsparse power spectra alike. The estimates are consistent
piecewise constant approximations whose resolutions (width of the piecewise
constant segments) are controlled by the periodicity of the multi-coset
sampling. We show that compressive estimates exhibit better tradeoffs among the
estimator's resolution, system complexity, and average sampling rate compared
to their noncompressive counterparts. For suitable sampling patterns,
noncompressive estimates are obtained as least squares solutions. Because of
the non-negativity of power spectra, compressive estimates can be computed by
seeking non-negative least squares solutions (provided appropriate sampling
patterns exist) instead of using standard CS recovery algorithms. This
flexibility suggests a reduction in computational overhead for systems
estimating both sparse and nonsparse power spectra because one algorithm can be
used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure
Approximate Message Passing for Underdetermined Audio Source Separation
Approximate message passing (AMP) algorithms have shown great promise in
sparse signal reconstruction due to their low computational requirements and
fast convergence to an exact solution. Moreover, they provide a probabilistic
framework that is often more intuitive than alternatives such as convex
optimisation. In this paper, AMP is used for audio source separation from
underdetermined instantaneous mixtures. In the time-frequency domain, it is
typical to assume a priori that the sources are sparse, so we solve the
corresponding sparse linear inverse problem using AMP. We present a block-based
approach that uses AMP to process multiple time-frequency points
simultaneously. Two algorithms known as AMP and vector AMP (VAMP) are evaluated
in particular. Results show that they are promising in terms of artefact
suppression.Comment: Paper accepted for 3rd International Conference on Intelligent Signal
Processing (ISP 2017
Audio Source Separation Using Sparse Representations
This is the author's final version of the article, first published as A. Nesbit, M. G. Jafari, E. Vincent and M. D. Plumbley. Audio Source Separation Using Sparse Representations. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 10, pp. 246-264. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch010file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04The authors address the problem of audio source separation, namely, the recovery of audio signals from recordings of mixtures of those signals. The sparse component analysis framework is a powerful method for achieving this. Sparse orthogonal transforms, in which only few transform coefficients differ significantly from zero, are developed; once the signal has been transformed, energy is apportioned from each transform coefficient to each estimated source, and, finally, the signal is reconstructed using the inverse transform. The overriding aim of this chapter is to demonstrate how this framework, as exemplified here by two different decomposition methods which adapt to the signal to represent it sparsely, can be used to solve different problems in different mixing scenarios. To address the instantaneous (neither delays nor echoes) and underdetermined (more sources than mixtures) mixing model, a lapped orthogonal transform is adapted to the signal by selecting a basis from a library of predetermined bases. This method is highly related to the windowing methods used in the MPEG audio coding framework. In considering the anechoic (delays but no echoes) and determined (equal number of sources and mixtures) mixing case, a greedy adaptive transform is used based on orthogonal basis functions that are learned from the observed data, instead of being selected from a predetermined library of bases. This is found to encode the signal characteristics, by introducing a feedback system between the bases and the observed data. Experiments on mixtures of speech and music signals demonstrate that these methods give good signal approximations and separation performance, and indicate promising directions for future research
On the stable recovery of the sparsest overcomplete representations in presence of noise
Let x be a signal to be sparsely decomposed over a redundant dictionary A,
i.e., a sparse coefficient vector s has to be found such that x=As. It is known
that this problem is inherently unstable against noise, and to overcome this
instability, the authors of [Stable Recovery; Donoho et.al., 2006] have
proposed to use an "approximate" decomposition, that is, a decomposition
satisfying ||x - A s|| < \delta, rather than satisfying the exact equality x =
As. Then, they have shown that if there is a decomposition with ||s||_0 <
(1+M^{-1})/2, where M denotes the coherence of the dictionary, this
decomposition would be stable against noise. On the other hand, it is known
that a sparse decomposition with ||s||_0 < spark(A)/2 is unique. In other
words, although a decomposition with ||s||_0 < spark(A)/2 is unique, its
stability against noise has been proved only for highly more restrictive
decompositions satisfying ||s||_0 < (1+M^{-1})/2, because usually (1+M^{-1})/2
<< spark(A)/2.
This limitation maybe had not been very important before, because ||s||_0 <
(1+M^{-1})/2 is also the bound which guaranties that the sparse decomposition
can be found via minimizing the L1 norm, a classic approach for sparse
decomposition. However, with the availability of new algorithms for sparse
decomposition, namely SL0 and Robust-SL0, it would be important to know whether
or not unique sparse decompositions with (1+M^{-1})/2 < ||s||_0 < spark(A)/2
are stable. In this paper, we show that such decompositions are indeed stable.
In other words, we extend the stability bound from ||s||_0 < (1+M^{-1})/2 to
the whole uniqueness range ||s||_0 < spark(A)/2. In summary, we show that "all
unique sparse decompositions are stably recoverable". Moreover, we see that
sparser decompositions are "more stable".Comment: Accepted in IEEE Trans on SP on 4 May 2010. (c) 2010 IEEE. Personal
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