## Abstract

We formulate conditions (k-SCA-conditions) under which we can represent a given (m × N) -matrix X (data set) uniquely (up to scaling and permutation) as a multiplication of m ×n and n × N matrices A and S (often called mixing matrix or dictionary and source matrix, respectively), such that S is sparse of level n-m+k in sense that each column of S has at least n - m + k zero elements. We call this the k-Sparse Component Analysis problem (k-SCA). Conditions on a matrix S are presented such that the k-SCA-conditions are satisfied for the matrix X = AS, where A is an arbitrary matrix from some class. This is the Blind Source Separation problem and the above conditions are called identifiability conditions. We present new algorithms: for matrix identification (under k-SCA-conditions), and for source recovery (under identifiability conditions). The methods are illustrated with examples, showing good separation of the high-frequency part of mixtures of images after appropriate sparsification.

Original language | English |
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Pages (from-to) | V-493-V-496 |

Journal | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |

Volume | 5 |

Publication status | Published - 2004 |

Externally published | Yes |

Event | Proceedings - IEEE International Conference on Acoustics, Speech, and Signal Processing - Montreal, Que, Canada Duration: 17 May 2004 → 21 May 2004 |