This work presents a brief introduction to the blind source separation using independent component analysis (ICA) techniques. The main objective of the blind source separation (BSS) is to obtain, from observations composed by different mixed signals, those different signals that compose them. This objective can be reached using two different techniques, the spatial and the statistical one. The first one is based on a microphone array and depends on the position and separation of them. It also uses the directions of arrival (DOA) from the different audio signals. On the other hand, the statistical separation supposes that the signals are statistically independent, that they are mixed in a linear way and that it is possible to get the mixtures with the right sensors (Hyvärinen, Karhunen & Oja, 2001) (Parra, 2002). The last technique is the one that is going to be studied in this work. It is due to this technique is the newest and is in a continuous development. It is used in different fields such as natural language processing (Murata, Ikeda & Ziehe, 2001) (Saruwatari, Kawamura & Shikano, 2001), bioinformatics, image processing (Cichocki & Amari, 2002) and in different real life applications such as mobile communications (Saruwatari, Sawai, Lee, Kawamura, Sakata & Shikano, 2003). Specifically, the technique that is going to be used is the Independent Component Analysis (ICA). ICA comes from an old technique called PCA (Principal Component Analysis) (Hyvärinen, Karhunen & Oja, 2001) (Smith, 2006). PCA is used in a wide range of scopes such as face recognition or image compression, being a very common technique to find patterns in high dimension data. The BSS problem can be of two different ways; the first one is when the mixtures are linear. It means that the data are mixed without echoes or reverberations, while the second one, due to these conditions, the mixtures are convolutive and they are not totally independent because of the signal propagation through dynamic environments. It is the “Cocktail party problem”. Depending on the mixtures, there are several methods to solve the BSS problem. The first case can be seen as a simplification of the second one. The blind source separation based on ICA is also divided into three groups; the first one are those methods that works in the time domain, the second are those who works in the frequency domain and the last group are those methods that combine frequency and time domain methods. A revision of the technique state of these methods is proposed in this work.
The problem consists in several sources that are mixed in a system, these mixtures are recorded and then they have to be separated to obtain the estimations of the original sources. As was mentioned above, BSS problems can be of two different types; the first one, when the mixtures are linear, see equation 3, and the second one, when the mixtures are convolutive, see equation 5.
In the first case each source signal is multiplied by a constant which depends on the environment, and then they are added. Convolutive mixtures are not totally independent due to the signal propagation through dynamic environments. This makes that the signals are not simply added. The first case is the ideal one, and the second is the most common case, because in real room recordings the mixing systems are of this type. Figure 1 shows the mixing system in the case of two sources two mixtures:
2 sources – 2 mixtures system.