A novel underdetermined source recovery algorithm based on k-sparse component analysis

Sparse component analysis (SCA) is a popular method for addressing underdetermined blind source separation in array signal processing applications. We are motivated by problems that arise in the applications where the sources are densely sparse (i.e. the number of active sources is high and very close to the number of sensors). The separation performance of current underdetermined source recovery (USR) solutions, including the relaxation and greedy families, reduces with decreasing the mixing system dimension and increasing the sparsity level (k). In this paper, we present a k-SCA-based algorithm that is suitable for USR in low-dimensional mixing systems. Assuming the sources is at most (m−1) sparse where m is the number of mixtures; the proposed method is capable of recovering the sources from the mixtures given the mixing matrix using a subspace detection framework. Simulation results show that the proposed algorithm achieves better separation performance in k-SCA conditions compared to state-of-the-art USR algorithms such as basis pursuit, minimizing norm-L1, smoothed L0, focal underdetermined system solver and orthogonal matching pursuit

Comparison of success rate of multi-channel methods of speech signal separation

Separace nezávislých zdrojů signálů ze směsí zaznamenaných dat je základní problém v mnoha praktických situacích. Typický příklad je záznam řeči v prostředí za přítomnosti šumu či jiného mluvčího na pozadí. Touto problematikou se zabývá skupina metod nazvaných Separace zdrojů naslepo. Slepá separace je založena na odhadu N neznámých zdrojů z P měření, které jsou směsmi těchto neznámých zdrojů a neznámého prostředí. Představeny a v Matlabu implementovány jsou některé známé řešení okamžitých směsí, tj. Analýza nezávislých komponent a Časově kmitočtová analýza. V reálném prostředí však akustické signály nejsou okamžité směsi, ale směsi konvoluční. Pro tento případje představen a v Matlabu implementován algoritmus pro separaci konvolučních směsí v kmitočtové oblasti.Tato diplomová práce zkoumá porovnání a použitelnost těchto separačních algoritmů.The separation of independent sources from mixed observed data is a fundamental problem in many practical situations. A typical example is speech recordings made in an acoustic environment in the presence of background noise or other speakers. Problems of signal separation are explored by a group of methods called Blind Source Separation. Blind Source Separation (BSS) consists on estimating a set of N unknown sources from P observations resulting from the mixture of these sources and unknown background. Some existing solutions for instantaneous mixtures are reviewed and in Matlab implemented , i.e Independent Componnent Analysis (ICA) and Time-Frequency Analysis (TF). The acoustic signals recorded in real environment are not instantaneous, but convolutive mixtures. In this case, an ICA algorithm for separation of convolutive mixtures in frequency domain is introduced and in Matlab implemented. This diploma thesis examines the useability and comparisn of proposed separation algorithms.

Contributions to the problem of blind source separation, with emphasis on the study of sparse signals

Orientadores: Romis Ribeiro de Faissol Attux, Ricardo SuyamaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Neste trabalho, foi estudado o problema de Separação Cega de Fontes (BSS), com ênfase nos casos chamados de subparametrizados, isto é, em que o número de fontes é maior do que o de misturas. A primeira contribuição proposta foi a de um limitante relacionado ao erro de inversão intrínseco ao problema quando é utilizada uma estrutura linear de separação. As outras contribuições estão relacionadas à hipótese de que as fontes são esparsas: i) uma proposta de metodologia híbrida, que se utiliza de conceitos baseados em independência e esparsidade dos sinais de forma simultânea para estimar tanto o sistema misturador quanto o número de fontes existentes em misturas com dois sensores; ii) a utilização de ferramentas de otimização baseadas na operação do sistema imunológico para a estimação do sistema misturador em problemas intrinsecamente multimodais; por fim, iii) uma proposta de utilização de um critério baseado em esparsidade para separação de fontes, sendo derivado um processo de otimização baseado na norma ?1 para este fimAbstract: In this work, we studied the problem of Blind Source Separation (BSS), with emphasis on cases referred to as underdetermined, which occur when the number of sources is greater than the number of mixtures. The first contribution was a proposal of a bound to the inversion error that is intrinsic to the problem when a linear structure is used to perform separation. The other contributions are related to the hypothesis that the signals of the sources are sparse: i) the proposal of a hybrid methodology that employs concepts based on signal independence and sparsity to simultaneously estimate both the mixing system and the number of existing sources in mixtures with two sensors; ii) the use of optimization tools based on the modus operandi of the immune system to estimate the mixing system in problems that are inherently multimodal; finally, iii) the use of a criterion based on sparsity for source separation, which is derived from an optimization process based on the ?1 normDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

An Ica-based Method For Blind Source Separation In Sparse Domains

In this work, we propose and analyze a method to solve the problem of underdetermined blind source separation (and identification) that employs the ideas of sparse component analysis (SCA) and independent component analysis (ICA). The main rationale of the approach is to allow the possibility of reaching a method that is more robust with respect to the degree of sparseness of the involved signals and more effective in the use of information brought by multiple sensors. The ICA-based solution is tested with the aid of three representative scenarios and its performance is compared with that of one of the soundest SCA techniques available, the DEMIXN algorithm. © Springer-Verlag Berlin Heidelberg 2009.5441597604Hyvarinen, A., Karhunen, J., Oja, E., (2001) Independent Component Analysis, , John Wiley &Sons, New-YorkGribonval, R., Lesage, S., A survey of Sparse Component Analysis for Blind Source Separation: Principles, perspectives, and new challenges (2006) ESANN 2006 proceedings - European Symposium on Artificial Neural Networks, , Bruges, BelgiumBofill, P., Zibulevsky, M., Underdetermined blind source separation using sparse representations (2001) Signal Processing, 81, pp. 2353-2363Yilmaz, O., Rickard, S., Blind Separation of Speech Mixtures via Time-Frequency Masking (2004) IEEE Transactions on Signal Processing, 52, pp. 1830-1847Van Hulle, M.M., Clustering Approach to Square and Non-Square Blind Source Separation (1999) Proc. IEEE Neural Networks for Signal Processing, 9, pp. 315-323Abrard, F., Deville, Y., Blind separation of dependent sources using the time-frequency ratio of mixtures approach (2003) Proc. ISSPA, , FranceArberet, S., Gribonval, R., Bimbot, F.: A Robust Method to Count and Locate Audio Sources in a Stereophonic Linear Instantaneous Mixture. In: Rosca, J.P., Erdogmus, D., Principe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, 3889, pp. 536-543. Springer, Heidelberg (2006)Noorshams, N., Babaie-Zadeh, M., Jutten, C.: Estimating the Mixing Matrix in Sparse Component Analysis Based on Converting a Multiple Dominant to a Single Dominant Problem. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, 4666, pp. 397-405. Springer, Heidelberg (2007)Rioul, O., Vetterli, M., Wavelets and Signal Processing (1991) IEEE Signal Processing Magazine, 8, pp. 14-38Duda, R.O., Hart, P.E., Stork, D.G., (2001) Pattern Classification, , John Wiley &Sons, New-YorkComon, P., Independent component analysis, A new concept? (1994) Signal Processing, 36, pp. 287-314Comon, P., Moreu, E., Improved contrast dedicated to blind separation in communications (1997) Proc. ICASSP, pp. 3453-3456. , Munich, pp, April 20-2