| The blind source separation problem is to extract the underlying source signals/images from a set of their linear mixtures, where the mixing matrix is unknown. This situation is common, eg in acoustics, radio, electro/magneto encephalography, functional MRI, hyperspectral imaging, etc.
In order to obtain high quality separation, we exploit the property of the sources to have a sparse representation in a corresponding (possibly overcomplete) signal dictionary. Such a dictionary may consist of wavelets, wavelet packets, etc., or be obtained by learning from a given family of signals/images. Starting from the maximum posteriori framework, which is applicable to the case of more sources than mixtures, we derive a few other categories of objective functions, which provide faster and more robust computations, when there are an equal number of sources and mixtures.
This work can be considered a natural generalization of the Bell- Sejnowski Infomax algorithm and maximum posteriori approach of Lewicki-Sejnowski to the blind source separation. In our method independence and sparsity are not required from the sources themselves, but rather from their decomposition coefficients, which is more natural in many practical cases. On the other hand presented approach may be considered an extension of basis pursuit of Chen-Donoho-Sanders to the case of signal mixtures.
Our experiments with artificial signals, musical sounds and with natural images demonstrate significantly better separation than other known techniques. |
