Blind Separation of Sources in Functional MRI Sequences

Abstract
Functional Magnetic Resonance Imaging (fMRI) is an important and popular tool for studying the human brain activity. In most fMRI scans, the BOLD technique is used, producing an image of the blood oxygenation level throughout the brain. High oxygenation levels represent high activity of brain regions responsible for performance of a specific task.
The process can be modeled as a linear mixture of independent localized sources of oxygenation, where no apriori information is known about their properties.
A problem of separating such sources is referred to as “Blind Source Separation” (BSS) and there exist powerful tools to solve it.
The project focuses on separating brain activity sources from a sequence of fMRI images using BSS methods and the approach of sparse representations.

The problem
The images produced by fMRI scans contain mixtures of localized sources of oxygenation, where no apriori information is known about their properties.
In addition, the images are affected by noise and other artifacts, resulting from head motion, brain background activity, the scanners themselves etc.
The mixing process can be modeled as a linear mixture of independent sources, and thus restoring the separate sources from the fMRI scan can be considered as a “Blind Source Separation” (BSS) problem.

Our goal is to separate the different oxygenation sources from the fMRI scan images, using BSS methods.

Figure 1 – Block diagram of the main algorithm used in the project

The solution
The solution consists of 2 stages –
1) Image preprocessing and sparse representation.
2) Implementing blind source separation methods.

The preprocessing stage included spatial smoothing of the images, identifying and removing the image “background” (static brain image, not including the task related activity), and sparse representation of the image using the Wavelet Packet transform.
Principal Component Analysis (PCA) was later introduced for the dimension reduction of the problem.

For solving BSS problems, there exist several methods, out of which we have implemented two:

1. Geometric mixing matrix estimation, using:
   • Angular histogram: Finding the most likely angle of the sources (represented as vectors), and reconstructing the mixing matrix from this angle
   • Projection to hyper-sphere and clustering: Projecting and clustering the sources on half a sphere, identifying the clusters’ centers of mass and reconstructing the mixing matrix according to the angles of these centers
2. ICA – Infomax:
   Independent Component Analysis (ICA) is a statistical technique for decomposing a dataset into independent subsets. Infomax is one of the ICA methods, which is based on maximizing the output entropy of a neural network with non-linear outputs.

Tools
The Project was programmed in Matlab 6, on a PC platform.
The main Matlab tools used were the Wavelet toolbox, image processing, clustering and PCA tools.

The ICA toolbox, developed by Scott Makeig of the Salk Institute, was used to implement Infomax separation.

Conclusions

• The sparse representation of mixtures prior to the application of geometric separation methods provided good separation results, by observation and SNR criteria. However, the geometric method proved to be unstable, sensitive to parameters, and limited by the complexity of increasing the number of mixtures and sources that could be handled
• Using the ICA Infomax algorithm for the separation gave better SNR results, increased robustness and enabled the separation of a larger number of sources
• Sparse representation of mixtures by means of wavelet packets prior to the application of ICA improved SNR and robustness
• Applying Principle Component Analysis before separation by ICA not only enabled automatic dimension reduction, but also provided added value in the form of background extraction and ability to freely “guess” the number of expected sources
• An expert opinion of the fMRI sequence separations expressed high potential for future development and implementation of the algorithm, and that it possessed real added value for the neuro-physiologic researcher community

Acknowledgments
We would like to thank our project supervisors, Michael & Alex Bronstein, and Dr. Michael Zibulevsky, for their guidance.
We would also like to thank Johanan Erez and the rest of the staff of the PSPL lab, for their support, and Anat Grinfeld from the Department of Biomedical Engineering, for providing data and insight.
We are also grateful to the Ollendorff Research Center Fund for supporting this project.