Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
Learning Overcomplete Representations
Neural Computation
A Bayesian Approach for Blind Separation of Sparse Sources
IEEE Transactions on Audio, Speech, and Language Processing
IEEE Transactions on Information Theory
Compressed Sensing and Redundant Dictionaries
IEEE Transactions on Information Theory
Sparse component analysis and blind source separation of underdetermined mixtures
IEEE Transactions on Neural Networks
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Missing data imputation using compressive sensing techniques for connected digit recognition
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
An iterative Bayesian algorithm for sparse component analysis in presence of noise
IEEE Transactions on Signal Processing
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Separation of underdetermined mixtures is an important problem in signal processing that has attracted a great deal of attention over the years. Prior knowledge is required to solve such problems and one of the most common forms of structure exploited is sparsity. Another central problem in signal processing is sampling. Recently, it has been shown that it is possible to sample well below the Nyquist limit whenever the signal has additional structure. This theory is known as compressed sensing or compressive sampling and a wealth of theoretical insight has been gained for signals that permit a sparse representation. In this paper we point out several similarities between compressed sensing and source separation. We here mainly assume that the mixing system is known, i.e. we do not study blind source separation. With a particular view towards source separation, we extend some of the results in compressed sensing to more general overcomplete sparse representations and study the sensitivity of the solution to errors in the mixing system.