228 research outputs found

    Underdetermined blind separation by combining sparsity and independence of sources

    Full text link
    In this paper, we address underdetermined blind separation of N sources from their M instantaneous mixtures, where N>M , by combining the sparsity and independence of sources. First, we propose an effective scheme to search some sample segments with the local sparsity, which means that in these sample segments, only Q(Q < M) sources are active. By grouping these sample segments into different sets such that each set has the same Q active sources, the original underdetermined BSS problem can be transformed into a series of locally overdetermined BSS problems. Thus, the blind channel identification task can be achieved by solving these overdetermined problems in each set by exploiting the independence of sources. In the second stage, we will achieve source recovery by exploiting a mild sparsity constraint, which is proven to be a sufficient and necessary condition to guarantee recovery of source signals. Compared with some sparsity-based UBSS approaches, this paper relaxes the sparsity restriction about sources to some extent by assuming that different source signals are mutually independent. At the same time, the proposed UBSS approach does not impose any richness constraint on sources. Theoretical analysis and simulation results illustrate the effectiveness of our approach

    Extracting individual contributions from their mixture: a blind source separation approach, with examples from space and laboratory plasmas

    Full text link
    Multipoint or multichannel observations in plasmas can frequently be modelled as an instantaneous mixture of contributions (waves, emissions, ...) of different origins. Recovering the individual sources from their mixture then becomes one of the key objectives. However, unless the underlying mixing processes are well known, these situations lead to heavily underdetermined problems. Blind source separation aims at disentangling such mixtures with the least possible prior information on the sources and their mixing processes. Several powerful approaches have recently been developed, which can often provide new or deeper insight into the underlying physics. This tutorial paper briefly discusses some possible applications of blind source separation to the field of plasma physics, in which this concept is still barely known. Two examples are given. The first one shows how concurrent processes in the dynamical response of the electron temperature in a tokamak can be separated. The second example deals with solar spectral imaging in the Extreme UV and shows how empirical temperature maps can be built.Comment: expanded version of an article to appear in Contributions to Plasma Physics (2010

    A fast approach for overcomplete sparse decomposition based on smoothed L0 norm

    Full text link
    In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined Sparse Component Analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Contrary to previous methods, which usually solve this problem by minimizing the L1 norm using Linear Programming (LP) techniques, our algorithm tries to directly minimize the L0 norm. It is experimentally shown that the proposed algorithm is about two to three orders of magnitude faster than the state-of-the-art interior-point LP solvers, while providing the same (or better) accuracy.Comment: Accepted in IEEE Transactions on Signal Processing. For MATLAB codes, see (http://ee.sharif.ir/~SLzero). File replaced, because Fig. 5 was missing erroneousl

    A Novel Method based on Gaussianity and Sparsity for Signal Separation Algorithms

    Get PDF
    Blind source separation is a very known problem which refers to finding the original sources without the aid of information about the nature of the sources and the mixing process, to solve this kind of problem having only the mixtures, it is almost impossible , that why using some assumptions is needed in somehow according to the differents situations existing in the real world, for exemple, in laboratory condition, most of tested algorithms works very fine and having good performence because the  nature and the number of the input signals are almost known apriori and then the mixing process is well determined for the separation operation.  But in fact, the real-life scenario is much more different and of course the problem is becoming much more complicated due to the the fact of having the most of the parameters of the linear equation are unknown. In this paper, we present a novel method based on Gaussianity and Sparsity for signal separation algorithms where independent component analysis will be used. The Sparsity as a preprocessing step, then, as a final step, the Gaussianity based source separation block has been used to estimate the original sources. To validate our proposed method, the FPICA algorithm based on BSS technique has been used

    Post-nonlinear speech mixture identification using single-source temporal zones & curve clustering

    Get PDF
    International audienceIn this paper, we propose a method for estimating the nonlinearities which hold in post-nonlinear source separation. In particular and contrary to the state-of-art methods, our proposed approach uses a weak joint-sparsity sources assumption: we look for tiny temporal zones where only one source is active. This method is well suited to non-stationary signals such as speech. The main novelty of our work consists of using nonlinear single-source confidence measures and curve clustering. Such an approach may be seen as an extension of linear instantaneous sparse component analysis to post-nonlinear mixtures. The performance of the approach is illustrated with some tests showing that the nonlinear functions are estimated accurately, with mean square errors around 4e-5 when the sources are " strongly" mixed

    Dictionary Learning for Sparse Representations With Applications to Blind Source Separation.

    Get PDF
    During the past decade, sparse representation has attracted much attention in the signal processing community. It aims to represent a signal as a linear combination of a small number of elementary signals called atoms. These atoms constitute a dictionary so that a signal can be expressed by the multiplication of the dictionary and a sparse coefficients vector. This leads to two main challenges that are studied in the literature, i.e. sparse coding (find the coding coefficients based on a given dictionary) and dictionary design (find an appropriate dictionary to fit the data). Dictionary design is the focus of this thesis. Traditionally, the signals can be decomposed by the predefined mathematical transform, such as discrete cosine transform (DCT), which forms the so-called analytical approach. In recent years, learning-based methods have been introduced to adapt the dictionary from a set of training data, leading to the technique of dictionary learning. Although this may involve a higher computational complexity, learned dictionaries have the potential to offer improved performance as compared with predefined dictionaries. Dictionary learning algorithm is often achieved by iteratively executing two operations: sparse approximation and dictionary update. We focus on the dictionary update step, where the dictionary is optimized with a given sparsity pattern. A novel framework is proposed to generalize benchmark mechanisms such as the method of optimal directions (MOD) and K-SVD where an arbitrary set of codewords and the corresponding sparse coefficients are simultaneously updated, hence the term simultaneous codeword optimization (SimCO). Moreover, its extended formulation ‘regularized SimCO’ mitigates the major bottleneck of dictionary update caused by the singular points. First and second order optimization procedures are designed to solve the primitive and regularized SimCO. In addition, a tree-structured multi-level representation of dictionary based on clustering is used to speed up the optimization process in the sparse coding stage. This novel dictionary learning algorithm is also applied for solving the underdetermined blind speech separation problem, leading to a multi-stage method, where the separation problem is reformulated as a sparse coding problem, with the dictionary being learned by an adaptive algorithm. Using mutual coherence and sparsity index, the performance of a variety of dictionaries for underdetermined speech separation is compared and analyzed, such as the dictionaries learned from speech mixtures and ground truth speech sources, as well as those predefined by mathematical transforms. Finally, we propose a new method for joint dictionary learning and source separation. Different from the multistage method, the proposed method can simultaneously estimate the mixing matrix, the dictionary and the sources in an alternating and blind manner. The advantages of all the proposed methods are demonstrated over the state-of-the-art methods using extensive numerical tests
    corecore