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# Dissertation

I defended my Doctor title at the 13th of July of 2006 in Granada, Spain. The subject of the thesis is the development of a new method for the blind source separation, applied to fMRI data:

Ingo R. Keck,

*ICA Incompleto Paralelo: Una nueva herramienta para el análisis de datos fMRI / Parallel Incomplete ICA – A New Tool to Analyse fMRI Data Sets,*Dissertation, Departamento de Arquitectura y Tecnología de Computadores, Universidad de Granada, Juli 2006.

### Summary

Nowadays communication gains more and more importance every day. In many real world situations one needs to send and receive information. Generally, on the way to the receiver the signal suffers of different distortions that corrupt the signal, so that in the end one receives a mixture of information that has to be processed to find the correct results. There exists a huge number of fields where the processing of signals has fundamental importance; these are: data communication, speech and image processing, seismology, medicine, acoustics, sonar, instrumentation, robotic, etc.

The problem of blind source separation consist of the recovery of the original signals based on the mixtures detected by the sensors when only these mixtures are known. The main characteristic of this method is that no information about the original sources or how they were mixed together has to be known.

One widely known example of this concept that gives a general idea of this problem is the so called „Cocktail Party“ effect. It shows that humans are able to hear and separate different voices from a background of noise and other voices that are speaking at the same time. After the separation has taken place these recovered voices or individual sources are called „independent components.“

In this dissertation the main theme is to utilise the tool independent component analysis (ICA) on brain activity data-sets gained from functional magnetic resonance imaging (fMRI). To understand how the brain works one has to mention that the human brain is separated in two hemispheres (right and left) and each of them divides itself into small parts that are related to different types of activities like sensing, smelling, seeing, etc. Every action, thought and sensation is produced by activation of the neural cells in the brain. When a group of neurones start firing, the current in the neural dendrites increases and transmission of information happens. This leads to an increase in blood flow as the cells need more energy. So, every increase of activation in the brain leads also to an increase of blood flow in the same region of the brain.

Magnetic resonance imaging allows us to see the anatomy of the internal organs of the human body. In contrast to this functional MRI allows us to see the change in blood flow in the brain and thus the activity in the brain.

This dissertation has the following structure:

*Chapter 1:*Introduction in Blind Source Separation. In this chapter the definitions and the mathematical formulation of the independent component analysis are presented. First the fundaments of mathematical statistics are presented and the importance of signal separation. Then the basics of information theory are given so that all the necessary steps to introduce independent component analysis are complete. After this principal component analysis (PCA) and independent component analysis (ICA) are described together with their definitions, restrictions and algorithms. Finally, a comparison of PCA and ICA is given.

*Chapter 2:*ICA Reliability. In this chapter the fundamental theories and methods are presented that allow the simply and straightforward application of the methods given in this dissertation. The reliability and the stability testing methods for ICA are presented with the emphasis on fMRI.

*Chapter 3:*Application of ICA: fMRI. This chapter gives an introduction to the fundamentals of fMRI, together with the advantages and disadvantages of ICA applied to fMRI. The general linear model method and ICA are applied to experimental data and thus the positive and negative sides of ICA are demonstrated.

*Chapter 4:*Incomplete ICA. In this chapter first an introduction to the theory and the idea of incomplete ICA is given. Then the method of clustering with incomplete ICA is presented. Various examples are presented that show the efficiency of this method in clustering. Then the application of this method to fMRI data sets is presented.

*Chapter 5:*Parallel incomplete ICA. In this chapter a description how to apply the incomplete ICA clustering algorithm is given. An example shows the gains resulting from the parallel version of the method.

In the section „Conclusions and Perspectives“ a summary of the work done in this dissertation is give. At the same time future work and the fields of research are given that should be taken in account for future research.