Functional Magnetic Resonance Imaging is an important and useful tool for exploring the human brain activity.
Functional Magnetic Resonance Imaging is an important and useful tool for exploring the human brain activity. Usually an image of the blood oxygenation levels throughout the brain is produced. High levels represent activity of brain regions responsible for performance of specific tasks.
The process can be modeled as a linear superposition of independent localized sources of oxygenation, with no a priory information available.
A problem of separating such sources is known as Blind Source Separation problem (BSS). This project focuses on separating brain activity sources from a sequence of genuine fMRI images using one of the BSS methods – sparse Independent Component Analysis (sparse ICA), based on the approach of sparse representation.
The mixtures consist of spatially independent source patterns. Our mathematical goal is to recover such spatially independent sources that are responsible for the tasks performed by the subject of the experiment.
The problem is stated as an optimization problem, where certain cost function, that describes statistical dependency between restored sources, is ought to be minimized.
The basic approach
The solution of the current BSS problem consists of four basic stages:
1) Image preprocessing
2) Data decorrelation and compression by Principal Component Analysis
3) Its sparse representation
4) Implementing blind source separation methods for ICA- Natural Gradient and Relative Newton
Simulations with Natural Pictures
Natural pictures were taken and their mixtures were created. The mixing matrix is then discarded and the mixtures are fed to the BSS algorithm. The obtained results are proving that the algorithm is adequate.
Simulations with fMRI
It was concluded that the Relative Newton method is better than Natural Gradient method, both in terms of stability and speed.
The Relative Newton algorithm implementation for the real fMRI data produced comfortable framework for source separation analysis.
The separation of real fMRI data sequences resulted in frames of the expected activation in Visual Cortex of the brain as well as in the region responsible for face recognition.
It is clear that fMRI sequence analysis has a high potential for future scientific development.
We would like to thank our supervisor Michael Bronstein and our lab engineer Johanan Erez for their support and guidance.
We are also grateful to the Ollendorff Minerva Center Fund for supporting this project.