Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Dictionary learning algorithms for sparse representation
Neural Computation
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
A Variational Method for Learning Sparse and Overcomplete Representations
Neural Computation
Learning Overcomplete Representations
Neural Computation
Proceedings of the 5th ACM workshop on Digital rights management
Underdetermined blind source separation in echoic environments using DESPRIT
EURASIP Journal on Applied Signal Processing
Unsupervised learning of individuals and categories from images
Neural Computation
Computational Intelligence and Security
An Efficient K-Hyperplane Clustering Algorithm and Its Application to Sparse Component Analysis
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Part II--Advances in Neural Networks
Underdetermined Blind Source Separation Using SVM
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks, Part III
CG-M-FOCUSS and Its Application to Distributed Compressed Sensing
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
A Two-Step Blind Extraction Algorithm of Underdetermined Speech Mixtures
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks, Part II
A fixed-point algorithm for blind source separation with nonlinear autocorrelation
Journal of Computational and Applied Mathematics
K-hyperline clustering learning for sparse component analysis
Signal Processing
Fast nonlinear autocorrelation algorithm for source separation
Pattern Recognition
A fast approach for overcomplete sparse decomposition based on smoothed l0 norm
IEEE Transactions on Signal Processing
Improved FOCUSS method with conjugate gradient iterations
IEEE Transactions on Signal Processing
Underdetermined blind source separation based on subspace representation
IEEE Transactions on Signal Processing
Underdetermined blind separation of non-sparse sources using spatial time-frequency distributions
Digital Signal Processing
Fast sparse representation based on smoothed lo norm
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Blind matrix decomposition via genetic optimization of sparseness and nonnegativity constraints
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Two conditions for equivalence of 0-norm solution and 1-norm solution in sparse representation
IEEE Transactions on Neural Networks
Classifying motor imagery EEG signals by iterative channel elimination according to compound weight
AICI'10 Proceedings of the 2010 international conference on Artificial intelligence and computational intelligence: Part II
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
A novel approach for underdetermined blind sources separation in frequency domain
ISNN'05 Proceedings of the Second international conference on Advances in neural networks - Volume Part II
FIR convolutive BSS based on sparse representation
ISNN'05 Proceedings of the Second international conference on Advances in neural networks - Volume Part II
Anechoic Blind Source Separation Using Wigner Marginals
The Journal of Machine Learning Research
IEA/AIE'11 Proceedings of the 24th international conference on Industrial engineering and other applications of applied intelligent systems conference on Modern approaches in applied intelligence - Volume Part I
K-EVD clustering and its applications to sparse component analysis
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
On a sparse component analysis approach to blind source separation
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Sparse deflations in blind signal separation
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Analysis of source sparsity and recoverability for SCA based blind source separation
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Identification of mixing matrix in blind source separation
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Estimation of delays and attenuations for underdetermined BSS in frequency domain
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
K-hyperplanes clustering and its application to sparse component analysis
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
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In this letter, we analyze a two-stage cluster-then-l1-optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l1 norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l1 -norm solution and the l0-norm solution is also analyzed according to a probabilistic framework. If the obtained l1 -norm solution is sufficiently sparse, then it is equal to the l0 -norm solution with a high probability. Furthermore, the l1 -norm solution is robust to noise, but the l0 -norm solution is not, showing that the l1 -norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown. It is also robust to additive noise and estimation error in the mixing matrix. Finally, four simulation examples and an EEG data analysis example are presented to illustrate the algorithm's utility and demonstrate its performance.