12,138 research outputs found
Blind source separation using temporal predictability
A measure of temporal predictability is defined and used to separate linear mixtures of signals. Given any set of statistically independent source signals, it is conjectured here that a linear mixture of those signals has the following property: the temporal predictability of any signal mixture is less than (or equal to) that of any of its component source signals.
It is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un-mixing matrix that maximizes a measure of temporal predictability for each recovered signal. This matrix is obtained as the solution to a generalized eigenvalue problem; such problems have scaling characteristics of O (N3), where N is the number of signal mixtures. In contrast to independent component analysis, the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals. It is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian, sub-gaussian, and gaussian probability density functions and on mixtures of voices and music
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
Multiscale blind source separation.
We provide a new methodology for statistical recovery of single linear mixtures of piecewise constant signals (sources) with unknown mixing weights and change points in a multiscale fashion. We show exact recovery within an epsilon-neighborhood of the mixture when the sources take only values in a known finite alphabet. Based on this we provide the SLAM (Separates Linear Alphabet Mixtures) estimators for the mixing weights and sources. For Gaussian error, we obtain uniform confidence sets and optimal rates (up to log-factors) for all quantities. SLAM is efficiently computed as a nonconvex optimization problem by a dynamic program tailored to the finite alphabet assumption. Its performance is investigated in a simulation study. Finally, it is applied to assign copy-number aberrations from genetic sequencing data to different clones and to estimate their proportions
Blind Source Separation with Compressively Sensed Linear Mixtures
This work studies the problem of simultaneously separating and reconstructing
signals from compressively sensed linear mixtures. We assume that all source
signals share a common sparse representation basis. The approach combines
classical Compressive Sensing (CS) theory with a linear mixing model. It allows
the mixtures to be sampled independently of each other. If samples are acquired
in the time domain, this means that the sensors need not be synchronized. Since
Blind Source Separation (BSS) from a linear mixture is only possible up to
permutation and scaling, factoring out these ambiguities leads to a
minimization problem on the so-called oblique manifold. We develop a geometric
conjugate subgradient method that scales to large systems for solving the
problem. Numerical results demonstrate the promising performance of the
proposed algorithm compared to several state of the art methods.Comment: 9 pages, 2 figure
Performing Nonlinear Blind Source Separation with Signal Invariants
Given a time series of multicomponent measurements x(t), the usual objective
of nonlinear blind source separation (BSS) is to find a "source" time series
s(t), comprised of statistically independent combinations of the measured
components. In this paper, the source time series is required to have a density
function in (s,ds/dt)-space that is equal to the product of density functions
of individual components. This formulation of the BSS problem has a solution
that is unique, up to permutations and component-wise transformations.
Separability is shown to impose constraints on certain locally invariant
(scalar) functions of x, which are derived from local higher-order correlations
of the data's velocity dx/dt. The data are separable if and only if they
satisfy these constraints, and, if the constraints are satisfied, the sources
can be explicitly constructed from the data. The method is illustrated by using
it to separate two speech-like sounds recorded with a single microphone.Comment: 8 pages, 3 figure
Convolutive Blind Source Separation Methods
In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks
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