Wavelet Analysis for Brain-Function Imaging

The purpose of this paper is to present a new algorithmic procedure for the analysis of brain images. This procedure is specifically designed to image the activity and functional organization of the brain. Our results are tested on data collected and previously analyzed with the technique known as in vivo optical imaging of intrinsic signals. Our procedure enhances the applicability of this technique and facilitates the extension of the underlying ideas to other imaging problems (e.g., functional MRI). The thrust of the paper is two fold. First, we give a systematic method to control the blood vessel artifacts which typically reduce the dynamic range of the image. We propose a mathematical model for the vibrations in time of the veins and arteries and we design a new method for cleaning the images of the vessels with the highest time variations. This procedure is based on the analysis of the singularities of the images. The use of wavelet transform is of crucial importance in characterizing the singularities and reconstructing appropriate versions of the original images. The second important component of our work is the analysis of the time evolution of the fine structure of the images. We show that, once the images have been cleaned of the blood vessel vibrations/variations, the principal component of the time evolutions of the signals is due to the functional activity following the stimuli. The part of the brain where this function takes place can be localized and delineated with precision.