Underdetermined blind audio source separation using modal decomposition
EURASIP Journal on Audio, Speech, and Music Processing
EURASIP Journal on Applied Signal Processing
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
K-hyperline clustering learning for sparse component analysis
Signal Processing
Improved FOCUSS method with conjugate gradient iterations
IEEE Transactions on Signal Processing
Glimpsing IVA: a framework for overcomplete/complete/undercomplete convolutive source separation
IEEE Transactions on Audio, Speech, and Language Processing - Special issue on processing reverberant speech: methodologies and applications
FIR convolutive BSS based on sparse representation
ISNN'05 Proceedings of the Second international conference on Advances in neural networks - Volume Part II
Maximum contrast analysis for nonnegative blind source separation
Computers & Mathematics with Applications
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
Post-nonlinear underdetermined ICA by bayesian statistics
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
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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Results of the analysis of the performance of minimum ℓ1-norm solutions in underdetermined blind source separation, that is, separation of n sources from m(1-norm solutions are known to be justified as maximum a posteriori probability (MAP) solutions under a Laplacian prior. Previous works have not given much attention to the performance of minimum ℓ1-norm solutions, despite the need to know about its properties in order to investigate its practical effectiveness. We first derive a probability density of minimum ℓ1-norm solutions and some properties. We then show that the minimum ℓ1-norm solutions work best in a case in which the number of simultaneous nonzero source time samples is less than the number of sensors at each time point or in a case in which the source signals have a highly peaked distribution. We also show that when neither of these conditions is satisfied, the performance of minimum ℓ1-norm solutions is almost the same as that of linear solutions obtained by the Moore-Penrose inverse. Our results show when the minimum ℓ1-norm solutions are reliable.